MATHEMATICS WITHIN A-LEVEL SCIENCE 2010 EXAMINATIONS

Transcription

1 Background ensure parity across system. way mamatics is assessed within sciences to at a-level that a framework is developed to regulate of mamatical requirements for each of sciences organisations. score recommends that re is a review mamatics is assessed across different awarding in addition, findings show a disparity in way effectively to stem higher education employment. students ability to have necessary skills to progress way that subjects are taught refore on re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. se will diff between phy work did not was being ap a-level speci mamatics gar eviden score s ove aims findings inform de difficulty assessments physics. how exam MATHEMATICS WITHIN A-LEVEL SCIENCE 21 EXAMINATIONS FULL REPORT FROM SCORE level than required. this is likely to have an impact on are assessed are covered repeatedly often at a lower physics specifications are not assessed. those that mamatical requirements listed in biology, chemistry science a-levels. findings show that a large number of type, extent difficulty of mamatical questions within any evidence for this concern, score investigated subject s analytical nature. to explore wher re was that science assessments at a-level are not reflecting describe many scientific phenomena yet re is concern mamatics enables students to underst ExEcutivE summary

2 CONTENTS ExEcutivE CHAPTER 1: summary INTRODUCTION 4 mamatics 1.1 Background enables students to underst 4 describe many scientific phenomena yet re is concern 1.2 Research aims 4 that science assessments at a-level are not reflecting subject s 1.3 Overview analytical of findings nature. to explore wher re was 4 any 1.4 evidence Related for literature this concern, research score investigated 4 type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical CHAPTER 2: requirements listed in biology, chemistry 7 physics specifications are not assessed. those that 2.1 Research design overview 7 are assessed are covered repeatedly often at a lower level 2.2 Research than required. design this is likely Phase to 1 have an impact on 7 way that subjects are taught refore on 2.3 Research design Phase 2 1 students ability to have necessary skills to progress effectively 2.4 Research to stem design higher Phase education 3 employment. 11 in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. CHAPTER 3: score recommends that re is a review gar evidence on type, extent difficulty of 13 of 3.1 Physics mamatical requirements for each of sciences mamatics required to access sciences in current 13 at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics Phase is 1: assessed A-level papers within sciences to 13 was being appropriately met by assessments. ensure parity across Extent system. work did not compare mamatical requirements 13 between physics, chemistry biology as it is accepted Background Type 15 se will differ between disciplines. re has been growing Difficulty concern across science 16 findings aim to provide score with evidence to community about mamatical Appropriateness dem of science 23 inform development of policy on type, extent qualifications, specifically that Gcse a-level science Phase 2 Physics A-level in comparison with GCSE difficulty of mamatics in criteria qualifications are not meeting needs of students in mamatics National Curriculum assessments Level Descriptors for a-levels in biology, chemistry 25 way y assess analytical nature of science. physics. project also supports score s work on Phase 3 Survey findings 31 in 29 score published evidence on Gcse science how examinations system should operate to ensure examination papers which reported a wide variation in science qualifications are fit for purpose also its amount of mamatics assessed across awarding work on improving coherence between sciences 3.2 Chemistry 33 organisations confirmed that use of mamatics mamatics Phase 1: A-level papers 33 within context of science was examined in a very in project, we looked across all assessments at limited way. score organisations Extent felt that this was 33 a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching Type practical examination papers. 36 learning of sciences, offers a valuable aid in understing describing Difficulty scientific phenomena; 37 as such it should be appropriately represented in Appropriateness 43 biology, chemistry physics curricula ir assessments Phase 2 Chemistry A-level in comparison with GCSE mamatics National Curriculum Level Descriptors 45 to provide furr evidence to support se Phase 3 Survey findings 49 concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 2 SCORE Maths in science report

3 3.3 methodology Biology groups comprised practising a-level teachers, 52 project was designed in three phases. teachers with experience in curriculum research Phase 1: A-level papers 52 first was to establish nature of mamatics development individuals working for awarding Extent assessed within biology, chemistry physics organisations as markers, question writers or examiners. 52 a-level examinations in Type 21. full suite of stardisation exercises were employed throughout 54 examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within Difficulty ocr WJec were analysed using four across subject expert groups. 55 measures that follow: Appropriateness second phase aimed to measure coherence type Phase of mamatics. 2 Biology A-level mamatical in comparison areas with between GCSE teaching learning of mamatics assessed were categorised mamatics against stated National Curriculum Level sciences. Descriptors re is an assumption that 63 mamatical requirements for biology, chemistry mamatical concepts used to access sciences Phase 3 Survey findings 67 physics respectively 1. are first taught within a mamatical context, i.e. within mamatics curriculum. project compared 2. extent of mamatics. proportion mamatical requirements for sciences at a-level 3.4 Views of from question industry parts within a paper that 7 with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions APPENDICES a 212 mamatics Gcse specification 3. this work that required mamatics. 72 was carried out by a researcher by a mamatics 3. Appendix difficulty 1: of mamatics. Summer 21 this A-level was measured papers analysed teacher. 72 against Appendix 3 criteria: 2: Mamatical number of requirements steps in a for physics A-level aim of third phase was to determine nature 71 calculation, familiarity of context Appendix 3: Mamatical requirements for chemistry of mamatics A-level that community would like to see 72 complexity of question. each category in a-level science assessments. this was achieved had Appendix varying levels 4: Mamatical of difficulty requirements each was for biology A-level 75 through an online survey for stakeholders in science measured as a proportion of total number of Appendix 5a: Examples of mamatical questions community. within Depending on ir expertise, participants question parts containing mamatics. it was not a science A-level of a single step calculation, a multiple answered survey for biology, chemistry or physics measured against number of marks. step calculation an extended step calculation a-level assessment. participants were chosen in appropriateness of mamatics. We three groups; teaching profession; higher education; Appendix 5b: Examples of mamatical questions within a science looked at wher answer required scientific professional bodies. an online survey was completed by A-level of a Level 1, Level 2, Level 3 Level 4 complexity 81 comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; this Appendix was measured 5c: Examples as a proportion of mamatical of total questions 38 within for chemistry; a science 32 for physics). participants from number A-level of of question a Level parts 1, Level containing 2 mamatics. Level 3 context industry were also consulted more generally but as most 83 science-related industries employ at a graduate level a subject Appendix expert group 5d: Examples was established of mamatical for each questions within a science ir comments tended to focus more on outcomes of three A-level sciences. where each all marks, group some analysed of full marks, none of marks require at graduate level rar than directly referring to a-level. suite of scientific 21 examinations comprehension papers in of addition aqa, ccea, to mamatical skill 85 edexcel, Appendix ocr 6: WJec Framework for ir for respective analysing subjects A-level ory practical papers 88 at a two-day workshop. examination papers included all ory Appendix papers 7: Acknowledgements (Units 1, 2, 4 5) 9 experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. 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4 CHAPTER 1: INTRODUCTION ExEcutivE 1.1 BACKGROUND summary mamatics There has been enables growing students concern to underst across describe science many community scientific about phenomena use yet of re mamatical is concern that assessments science assessments in science at qualifications. a-level are not reflecting subject s analytical nature. to explore wher re was any In 29 evidence SCORE for this published concern, score research investigated on GCSE type, science extent examination difficulty papers. of mamatical The report questions showed within science a wide a-levels. variation in findings amount show of that mamatics a large number of mamatical assessed across requirements awarding listed organisations in biology, chemistry confirmed physics that specifications use of are mamatics not assessed. within those that are assessed context of are science covered was repeatedly examined often in a at very a lower level limited than way. required. SCORE this organisations likely to have felt an impact that this on was way unacceptable. that subjects Mamatics are taught is integral refore to on students teaching ability learning to have of necessary sciences, skills to progress offers effectively a valuable to aid stem in understing higher education describing employment. in scientific addition, phenomena; findings show as such a disparity it should in be way mamatics appropriately is represented assessed across in biology, different awarding chemistry organisations. physics curricula score recommends ir assessments. that re is a review of mamatical requirements for each of sciences at To a-level provide furr that a evidence framework to is support developed se to regulate concerns, way mamatics SCORE set is assessed up this project within to sciences investigate to ensure mamatics parity across found system. in summer 21 science assessments for biology, chemistry physics Background A-levels across unitary awarding organisations in Engl, Wales Norrn Irel. re has been growing concern across science community 1.2 RESEARCH about AIMS mamatical dem of science qualifications, specifically that Gcse a-level science qualifications SCORE s overall are not objective meeting for this needs project of students was to in gar way evidence y assess on analytical type, extent nature of difficulty science. of mamatics assessed in science A-levels to in establish 29 score wher published current evidence assessments on Gcse reflected science examination mamatical papers requirements which reported of a wide sciences. variation The in work amount did not of compare mamatics assessed mamatical across requirements awarding organisations between biology, confirmed chemistry that physics use of as mamatics it is within accepted context se will of science differ between was examined disciplines. in a very limited way. score organisations felt that this was unacceptable. The findings aim mamatics to provide is SCORE integral with to evidence teaching to inform learning of development sciences, of policy offers on a valuable type, aid in extent understing difficulty of describing mamatics scientific phenomena; in as specifications such it should be assessments appropriately represented for A-levels in biology, biology, chemistry chemistry physics. physics The project curricula also supports ir assessments. SCORE s work on how examinations system should operate to ensure science qualifications are to fit for provide purpose furr evidence also its to work support on improving se concerns, coherence score between set up this sciences project to investigate mamatics. mamatics found in 21 science assessments at In a-level project, across we looked unitary awarding across all organisations assessments in engl, at A-level Wales for 21, norrn including irel. ory practical examination papers. 1.3 OVERVIEW OF FINDINGS The main findings of research were as follows: A large number of mamatical requirements listed in 21 biology, chemistry physics AS A2 specifications were assessed in a limited way or not at all within examination papers. There is a measurable variation between awarding organisations in terms of amount difficulty of mamatics that is assessed in biology, chemistry physics AS A2 examination papers. Participants in our survey felt that in some cases amount of mamatics assessed in A-level science examinations was too low. aims The examination questions that did require score s overall objective for this project was to mamatics were felt to be of insufficient difficulty; gar evidence on type, extent difficulty of too many involved only single step questions, mamatics required to access sciences in current require only simple recall, a-level specifications to establish wher this were set only in familiar contexts. was being appropriately met by assessments. work did not compare mamatical requirements There were many mamatical requirements between physics, chemistry biology as it is accepted identified in biology, chemistry physics A-levels se will differ between disciplines. that go beyond current GCSE mamatics. findings aim to provide score with evidence to 1.4 RELATED LITERATURE AND RESEARCH inform development of policy on type, extent Relevant difficulty literature of mamatics previous in research criteria findings are assessments presented below. for a-levels in biology, chemistry physics. project also supports score s work on how SCORE: examinations GCSE science system 28 should examinations operate to ensure science This project qualifications explored are fit fitness for purpose for purpose also of its GCSE work science on improving examination coherence papers, focusing between on how sciences examination mamatics. papers assessed particular aspects of GCSE science. One aspect was extent in type of project, mamatics we looked required across all by assessments questions at a-level wher for this a given was year, including same across both experimental awarding practical organisations. examination Findings papers. showed that dem type of mamatics within GCSE science papers was limited. The assessed mamatical content, in some cases, did not correspond with mamatics found in science specifications. This was particularly true for more advanced mamatics. The mamatics found was judged to be limited in terms of both type extent of mamatics required by students. The project considered only examinations mselves not internal assessment/coursework; it was accepted that this may account for discrepancies across awarding organisations. 4 SCORE Maths in science report

5 SCORE: methodology GCSE science examinations 28, 29 project 21 was designed in three phases. The first was SCORE to establish research above nature was of extended mamatics to include assessed similar within analyses biology, of chemistry 29 physics 21 science a-level examinations GCSEs. While in 21. re had full been suite modest of increases examinations papers amount from aqa, of mamatics ccea, edexcel, required in ocr GCSEs WJec over were three analysed cycles using of assessments, four much measures of that mamatics follow: was found to be at Key Stage 2 level of difficulty with dem type of 1. mamatics type of mamatics. still found to mamatical be limited when areas compared assessed to were lists categorised of mamatical against requirements stated provided mamatical by some requirements awarding organisations for biology, chemistry in ir specifications. physics respectively extent of mamatics. proportion IOP: of Mind question Gap, parts July within 211 a paper that The Institute included of mamatics Physics had was concerns, measured borne as was out of anecdotal proportion evidence, of that marks within current se physics questions mamatics that required A-levels mamatics. were not preparing students sufficiently for studying physics or engineering as an 3. undergraduate. difficulty of This mamatics. concern this was was two-fold: measured that first-year against undergraduates 3 criteria: number were not of steps proficient in a in mamatical calculation, skills familiarity needed, of context that lack of mamatical complexity content of question. in physics each category A-levels was not had motivating varying levels students of difficulty who enjoyed each was solving mamatical measured problems as a proportion from of to take total furr number related of study. question 55% of parts academics containing mamatics. surveyed in it was not project measured felt that against students number were of not marks. very, or not at 4. all well appropriateness prepared to cope of mamatics. with mamatical We content looked of undergraduate at wher answer study. required 92% felt scientific that a lack of comprehension fluency in mamatics in addition to was mamatical a barrier to skill. students this achieving was measured ir as potential. a proportion of total number of question parts containing mamatics. In IOP research, integration, identifying particular equations a subject expert techniques group was to established deal with for problems, each vectors of three sciences. scalars were each group identified analysed by academics full suite students of 21 examinations as being more papers difficult of aqa, content ccea, areas. The edexcel, IOP research ocr also WJec showed for ir how respective academics subjects were concerned at a two-day that workshop. in physics examination A-level papers re included was not enough all ory promotion papers of (Units contextual 1, 2, 4 understing 5) of experimental topic. practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. Royal groups Statistical comprised Society: practising The a-level Future teachers, of Statistics teachers with in experience our Schools in curriculum Colleges, research January development 212 individuals working for awarding This organisations report analysed as markers, question current writers provision or examiners. statistics stardisation in schools exercises were colleges. employed There throughout are three recommendations analysis to verify from reliability of report judgements that are within relevant to across current subject discussion: expert groups. 1. Recommendation 3: national education policy second phase aimed to measure coherence should ensure that all students are equipped between teaching learning of mamatics with a working knowledge of basic statistics, sciences. re is an assumption that including necessary associated mamatical mamatical concepts used to access sciences competence are first taught within a mamatical context, i.e. within mamatics curriculum. project compared 2. Recommendation 8: curriculum should be mamatical requirements for sciences at a-level designed so that, wherever possible, students with mamatics curriculum prior to Key stage 5 have met statistical techniques in mamatics using current national curriculum level descriptions before y need to use m in or subjects a 212 mamatics Gcse specification 3. this work 3. was Recommendation carried out by a researcher 15: statistics by a mamatics content teacher. within mamatics, up to GCSE, should include some aim of topics third that phase are eir was to not determine currently covered nature of mamatics or are only treated that lightly community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. 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6 ExEcutivE Dr. Jenny Koenig summary for UK Centre for Bioscience HEA: A survey of mamatics enables students to underst mamatics lscape within bioscience describe many scientific phenomena yet re is concern undergraduate postgraduate UK higher that science assessments at a-level are not reflecting education, June 211 subject s analytical nature. to explore wher re was This report was prompted in part by any evidence for this concern, score investigated understing that biology was becoming a type, extent difficulty of mamatical questions within more quantitative science with greater of levels science a-levels. findings show that a large number of of mamatics so mamatics skills of mamatical requirements listed in biology, chemistry biologists needed to increase to meet this dem. physics specifications are not assessed. those that The report explained how amongst bioscience are assessed are covered repeatedly often at a lower undergraduates, re was a wide variety in ir level than required. this is likely to have an impact on mamatics qualifications. There were specific way that subjects are taught refore on concerns about undergraduate students abilities students ability to have necessary skills to progress to rearrange simple equations reliably use ratio effectively to stem higher education employment. proportion. in addition, findings show a disparity in way mamatics is assessed across different awarding Advisory Committee on Mamatics organisations. score recommends that re is a review Education (ACME): Mamatical Needs, of mamatical requirements for each of sciences Mamatics in workplace in Higher at a-level that a framework is developed to regulate Education, June 211 way mamatics is assessed within sciences to The report outlines mamatical needs from ensure parity across system. perspective of higher education employers. ACME s first recommendation in report is that a Background large majority of young people should continue with re some has form been of mamatics growing concern post-16. across ACME s science third community recommendation about refers mamatical to how, in dem a revised of National science qualifications, Curriculum, re specifically should that be Gcse greater emphasis a-level science on qualifications essential mamatics are not meeting techniques needs of students application in of mamatics. way y assess ACME s analytical recommendation nature of science. 1 refers to using mamatics in a range of familiar in 29 score published evidence on Gcse science unfamiliar contexts. ACME s recommendation 14 examination papers which reported a wide variation in is that universities should make clear level amount of mamatics assessed across awarding extent of mamatics within ir degrees. organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. The Nuffield Foundation: Mamatics in or subjects at A-level, 212 The Nuffield Foundation has completed a project which analysed mamatical content of or A-levels: business studies, computer science, economics, geography, psychology sociology. The same methodology was used as in first phase of SCORE research, that is, A-level assessments were analysed against a framework of measures of type, extent difficulty of mamatical content. The same method of analysis of data was also utilised. The results from Nuffield research (due April 212) should determine wher re are common areas among a wider spread of subjects at A-level that would aims benefit from changes to mamatics GCSE or future mamatics for post-16. score s overall objective for this project was to gar evidence on type, extent difficulty of mamatics required to access sciences in current a-level specifications to establish wher this was being appropriately met by assessments. work did not compare mamatical requirements between physics, chemistry biology as it is accepted se will differ between disciplines. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 6 SCORE Maths in science report

7 CHAPTER 2: METHODOLOGY 2.1 methodology RESEARCH DESIGN OVERVIEW The project was designed in three in three phases. stages. The first was first was to establish to establish nature nature of of mamatics currently assessed assessed within biology, within science chemistry A-level physics papers. The a-level second examinations compared in 21. current full suite mamatical of requirements examinations papers for biology, from aqa, chemistry ccea, edexcel, physics A-level ocr with WJec GCSE were mamatics analysed using order four to identify overlap measures or that gaps follow: in mamatical content. The third 1. reviewed type of mamatics. findings with members mamatical from areas science assessed community were categorised focused against on nature stated of mamatics mamatical that requirements community for biology, would chemistry like to see in A-level physics science respectively assessments. 1. Views were gared from teachers, professional bodies, higher education 2. extent industry. of mamatics. proportion of question parts within a paper that A working included group mamatics was established was measured to oversee as was research proportion project of marks to inform within se methodology questions policy that required implications. mamatics. The group comprised representatives 3. difficulty from: of mamatics. this was measured The against Institute 3 criteria: of Physics number of steps in a Society calculation, of Biology familiarity of context Royal Society complexity of Chemistry of question. each category The had Royal varying Society levels of difficulty each was AQA measured as a proportion of total number of ACME question parts containing mamatics. it was not Institute measured of Education against number of marks. Institute of Mamatics its Applications Sixth 4. Form appropriateness College of mamatics. We Industry looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% RESEARCH groups comprised DESIGN practising PHASE a-level teachers, 1 teachers with experience in curriculum research Phase 1 aimed to establish nature of development individuals working for awarding mamatics assessed within biology, chemistry organisations as markers, question writers or examiners. physics A-level summer 21 examinations 1. stardisation exercises were employed throughout Papers from five awarding organisations that analysis to verify reliability of judgements within offered single science A-levels in Engl, Wales across subject expert groups. Norrn Irel were analysed: AQA, CCEA, Edexcel, second OCR phase aimed WJEC to 2 measure. coherence between teaching learning of mamatics The analysis sciences. did not re compare is an assumption mamatical that content mamatical across concepts sciences used to as access it is accepted sciences re are first different taught mamatical within a mamatical requirements context, for i.e. biology, within chemistry mamatics physics. curriculum. project compared mamatical requirements for sciences at a-level A with framework mamatics was developed curriculum in prior order to Key to make stage 5 judgements using current about national type, curriculum extent, level difficulty descriptions a appropriateness 212 mamatics of Gcse mamatics specification within 3. this work each was carried of out examination by a researcher papers for by biology, a mamatics chemistry teacher. physics A-level. The framework incorporated measures used in previous research aim suggestions of third from phase was working to determine group. A nature pilot exercise of mamatics was carried that out community to test would validity like to of see framework in a-level science assessments. effectiveness this of was achieved analysis process through an 3. Figure online survey 1 outlines for stakeholders measures in of science framework community. Depending used on analysis ir expertise, of science participants A-level examination answered papers. survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 Summer 21 papers were analysed to represent an A-level rar than AS 29 A2 21 papers. This was because awarding organisations usually commission a group of examiners who are responsible for all assessments for a single examining session; it is unlikely that any comparison would be made with papers for or sessions during course of that process. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, 2 chemistry Where awarding physics. organisations mamatical offered requirements more than are one available specification in full report. for a science A-level, one with highest uptake was 2 a complete chosen. science Where a-level re were is made options up of 6 questions, units. marks or sections from within ory an papers A-level, (Unit 1, 2, awarding 4 5) make organisations up 8% of were complete contacted asked a-level which assessment option had highest marks from uptake practical that option experimental was used papers in (Unit final 3 analysis, 6) make for up example, remaining for 2%. AQA in Physics analysis, A, paper 5, question parts rar than marks were used in calculation but we maintained 8:2 weighting. option C was used in analysis. Appendix 1 details summer 21 A-level papers analysed in research. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 3 The revised report mamatics from Gcses. pilot exercise testing validity of framework is available from SCORE Secretariat. SCORE Maths in science report 7

8 ExEcutivE Figure 1: Measures summary used to analyse mamatics assessed within science A-level examinations mamatics enables students to underst describe many scientific phenomena yet re is concern EXTENT that science assessments at a-level are not reflecting 1. Question number part: This allowed for subject s analytical nature. to explore wher re was number of questions question parts any evidence for this concern, score investigated with mamatical content to be worked type, extent difficulty of mamatical questions within out as a proportion of total number of science a-levels. findings show that a large number of questions parts, giving a measure of mamatical requirements listed in biology, chemistry extent of mamatical content. A physics specifications are not assessed. those that question part was smallest division that are assessed are covered repeatedly often at a lower a question was divided into which may be a level than required. this is likely to have an impact on whole question, as in most multiple choice way that subjects are taught refore on question or it may be, for example, Q3aii. students ability to have necessary skills to progress effectively to stem higher education employment. 2. The number of marks that required in addition, findings show a disparity in way mamatics: The percentage of marks mamatics is assessed across different awarding awarded for mamatical comprehension organisations. score recommends that re is a review was calculated as a proportion of overall of mamatical requirements for each of sciences marks available in paper. This provided at a-level that a framework is developed to regulate a second measure of extent of way mamatics is assessed within sciences to mamatical content. Whole marks were ensure parity across system. counted rar than parts of marks. Background TYPE re 3. The has type been of growing mamatics: concern across The mamatical science community requirements about for mamatical biology, chemistry dem of science qualifications, physics, specifically as set by that Ofqual Gcse 4, were a-level used science qualifications to identify are not type meeting of mamatics needs of students in way assessed y assess how analytical frequently nature y of science. occur in assessments. The mamatical in 29 score published evidence on Gcse science requirements for physics are stated in examination papers which reported a wide variation in Appendix 2, for chemistry in Appendix 3 amount of mamatics assessed across awarding for biology in Appendix 4. All of organisations confirmed that use of mamatics requirements needed for each question within context of science was examined in a very part were recorded. The mamatical limited way. score organisations felt that this was requirements for three subjects are unacceptable. mamatics is integral to teaching different so comparisons across subjects learning of sciences, offers a valuable aid are not straightforward, for example, ratios, in understing describing scientific phenomena; fractions percentages is listed under 1c) as such it should be appropriately represented in in physics requirements under 1b) biology, chemistry physics curricula ir in chemistry requirements. assessments. DIFFICULTY 4. The number of steps in a calculation: This aspect of difficulty discriminated between mamatical questions where only one step was needed to gain solution to a problem (single step), where more than one step was needed in one calculation to gain solution to a problem (multiple step) where a value, for example x, had to be found that value, x, used in a subsequent calculation in order to find solution to problem, y (extended calculation). Appendix aims 5a gives an example at A-level of single, multiple extended type questions. score s overall objective for this project was to gar evidence on type, extent difficulty of 5. The complexity of task: This aspect mamatics required to access sciences in current of difficulty established complexity a-level specifications to establish wher this of mamatical question as defined was being appropriately met by assessments. by Geoff Wake s 5 four descriptions of work did not compare mamatical requirements increasing difficulty. Level 1 complexity between physics, chemistry biology as it is accepted is defined as straightforward or routine, se will differ between disciplines. which requires recall of procedures relatively findings aim straightforward to provide score application. with evidence Level to inform 2 requires development application of policy on understing type, extent of mamatics difficulty of in mamatics one domain. in Level criteria 3 requires assessments understing for a-levels in use biology, of mamatics chemistry physics. across domains project also supports necessitates score s a decision work on how about examinations direction system in which should to operate proceed. to ensure Level science 4 involves qualifications complex are fit activity for purpose requiring also synsis its work on improving application across coherence a number between of domains sciences with mamatics. structuring or decision making being necessary. Appendix 5b gives an example at in A-level project, of we looked four categories. across all assessments at a-level for a given year, including both experimental practical 6. Familiarity examination of context: papers. It is generally accepted that if a context is more familiar it is easier to apply mamatics than if context is unfamiliar. Three categories were used to judge familiarity of mamatical question, in relation to recognising which to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 4 Mamatical requirements form part of Criteria set by Ofqual for biology, chemistry physics A-level. continues 5 Drake, P., Wake, G. Noyes, A. Assessing functionality in school mamatics examinations: what does being human have to do with it? Research in Mamatics Education, SCORE Maths in science report

9 Figure methodology 1: continued project was designed in three phases. first was to establish nature of mamatics assessed mamatics within to apply, biology, as chemistry defined by Geoff physics a-level Wake s examinations work referenced in 21. above. full These suite of levels examinations were: Level papers 1 typically from aqa, met ccea, through edexcel, learning ocr programme; WJec Level were 2 analysed some using novel aspects; four measures Level 3 that situation follow: unlikely to have been met before. Appendix 5c gives an example at A-level 1. type of mamatics. mamatical areas of three levels of familiarity. assessed were categorised against stated APPROPRIATENESS mamatical requirements for biology, chemistry 7. Application: physics respectively A judgement 1. was made on 2. wher extent of content mamatics. of question proportion part reflected of question how mamatics parts within a paper is used that in real included world mamatics in a scientific was context. measured This as was identified proportion in of SCORE marks within GCSE se review questions as a that particular required issue mamatics. for biology one that merited investigation at A-level. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not A subject measured expert against group of number 6-8 participants of marks. was established for each of three sciences. The 4. appropriateness of mamatics. We groups comprised practising A-level teachers, looked at wher answer required scientific teachers with experience in curriculum research comprehension in addition to mamatical skill. development individuals working for this was measured as a proportion of total awarding organisations as markers, question number of question parts containing mamatics. writers or examiners. Each group took part in a dedicated a subject expert workshop, group was established analysed for full each suite of 21 three examinations sciences. each papers group for analysed ir respective full subjects, suite of 21 using examinations framework papers above. of aqa, A ccea, different framework edexcel, ocr was used WJec for for A-level ir respective ory papers subjects A-level at a two-day practical workshop. papers examination (see Appendix papers 6 for included framework all ory templates). papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. groups comprised practising a-level teachers, teachers with experience in curriculum research development individuals working for awarding organisations 8. Relationship as markers, to question: question A judgement writers or examiners. was stardisation made as to exercises wher were mamatics employed throughout was a analysis structural to verify part of reliability question of judgements or wher within it across was just subject tagged expert on. groups. This was identified in SCORE GCSE review as an issue across second phase aimed to measure coherence sciences at GCSE. between teaching learning of mamatics sciences. re is an assumption that 9. Mamatics skill or scientific comprehension: mamatical concepts used to access sciences This measure differentiates between marks are first taught within a mamatical context, i.e. within within a mamatical question part that mamatics curriculum. project compared require scientific comprehension marks mamatical requirements for sciences at a-level which are given purely based on mamatics with mamatics curriculum prior to Key stage 5 skills. Analysts made a judgement between using current national curriculum level descriptions three categories: wher all marks in a 212 mamatics Gcse specification 3. this work a question part required mamatics skill was carried out by a researcher by mamatics only, wher marks included a mixture of teacher. scientific comprehension mamatical skill or aim wher of third all of phase marks was to required determine scientific nature of mamatics comprehension. that Appendix community 5d would provides like to an see in a-level example science at A-level assessments. of this measure. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics In analysis of science A-levels, all six units a-level assessment. participants were chosen in which make up a complete A-level were analysed. three groups; teaching profession; higher education; Units 1, 2, 4 5 are ory papers. Units professional bodies. an online survey was completed by 3 6 are referred to in this research as 97 participants across three groups (27 for biology; practical papers 6. Subject expert groups were given 38 for chemistry; 32 for physics). participants from A-level papers associated mark schemes, industry were also consulted more generally but as most A-level specifications, data sheets any science-related industries employ at a graduate level or necessary materials from awarding ir comments tended to focus more on outcomes organisations needed to fully comprehend at graduate level rar than directly referring to a-level. dem scope of complete A-level. The data was analysed for single papers an average was calculated for ory papers (Units 1, 2, 4 5) practical papers (Units 3 6). These averages were n recalibrated to provide an average for complete A-level where ory papers make 8% contribution of complete A-level practical papers make up 2% contribution The five nature awarding of organisations units 3 use 6 varied mamatical across requirements awarding organisations defined by ofqual in across developing subjects. ir specifications They are for referred biology, to in chemistry physics. mamatical requirements are available in full report. specifications as experimental practical papers, experimental tasks, laboratory tasks, practical skills, practical tasks 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete investigations, project work, controlled assessments or coursework. Following a pilot exercise, it was accepted that in se units a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question we were parts not rar comparing than marks like were with used like, in but that calculation judgements but we maintained about mamatics 8:2 weighting. expected to be met used by an average 3 student edexcel could 212 a be specification made. The was analysts used for considered purpose of most analysis challenging as it was judgement considered representative in se cases of typical to be content identifying found in number of marks revised that mamatics would require Gcses. mamatics, however, in ir groups y did feel that reliable judgements could be made. SCORE Maths in science report 9

10 ExEcutivE Stardisation summary exercises were employed throughout analysis to verify reliability of mamatics enables students to underst judgements within across subject expert describe many scientific phenomena yet re is concern groups. These included: that science assessments at a-level are not reflecting subject s analytical nature. to explore wher re was An individual sample analysis prior to two-day any evidence for this concern, score investigated group workshop. Each analyst on subject type, extent difficulty of mamatical questions within expert groups was sent a sample of A-level science a-levels. findings show that a large number of questions, along with instructions for analysing mamatical requirements listed in biology, chemistry questions. The results from exercise were physics specifications are not assessed. those that compared at workshop in order to reach are assessed are covered repeatedly often at a lower agreement on meaning of measures. level than required. this is likely to have an impact on Changing way that subjects make-up are of taught subject refore expert on students groups ability throughout to have necessary analysis to skills verify to progress effectively reliability to of stem judgements higher education across employment. groups. in addition, findings show a disparity in way mamatics Whole group is assessed discussions across to clarify different issues awarding as y organisations. arose to ensure score all groups recommends were that in agreement re is a review with of existing mamatical measures. requirements for each of sciences at a-level that a framework is developed to regulate Groups way mamatics checking is ir assessed final judgements within sciences against to ensure those parity made across at start system. of analysis session to check that y had not slipped throughout Background process. re has been growing concern across science Students scripts were not analysed in this community about mamatical dem of science research; if y had been re may have qualifications, specifically that Gcse a-level science been instances of students using higher level qualifications are not meeting needs of students in mamatics in ir responses to Units 3 6. way y assess analytical nature of science. For purpose of this project, however, analysts in considered 29 score more published typical evidence responses expected Gcse science by examination teachers papers markers, which both reported those a wide given variation in mark in schemes amount of mamatics what y would assessed expect across from awarding ir organisations own professional confirmed experience. that It was use accepted of mamatics that within mamatics context of higher of science complexities was examined in a a greater very limited number way. of score extended organisations calculations felt may that be this present was in unacceptable. such scripts, mamatics although y is integral may not to be rewarded teaching with learning a greater of number sciences, of marks offers than a were valuable possible aid in to understing be given mark describing scheme. scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. 2.3 RESEARCH DESIGN PHASE 2 In Phase 2 we measured extent to which mamatical requirements of biology, chemistry physics A-level had been previously taught in mamatics curriculum. This provided an indication of coherence between sciences mamatics. Two comparisons were used to compare coherence of science A-levels mamatics accessed up to Key Stage 4: comparison with National Curriculum level descriptors comparison with 212 mamatics GCSE specification. The National Curriculum level descriptors go from Level 1, easiest level, up to Level 8. aims Mamatics beyond Level 8 is classified as EP, score s exceptional overall performance. objective for The this content project was areas to from gar mamatical evidence on requirements type, extent were difficulty levelled of mamatics against National required to Curriculum access level sciences descriptors in current a-level by two specifications mamaticians to with establish experience wher in this teaching was being research. appropriately Their responses met by were assessments. collated work considered. did not compare As mamatical mamatical requirements requirements between were not physics, set in a chemistry context of expectations, biology as it is some accepted se of will areas differ were between open to disciplines. interpretation. In se cases mamatics experts gave a range of levels findings that aim mamatics to provide score could with correspond evidence to inform to depending development on actual of policy expectations type, of extent an assessment difficulty of item. mamatics in criteria assessments for a-levels in biology, chemistry physics. The collated project levels also were supports n furr score s analysed work on by how lead examinations researcher system subject should specialists operate to who ensure science had been qualifications involved with are fit for Phase purpose 1 analysis also its of work papers. on improving This allowed coherence levels between to considered sciences in terms mamatics. of contexts that items were set in levels could be refined. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 7 The 8:2 ratio of ory practical papers refers to weighting of marks in a complete A-level. In analysis averages were taken as a proportion of question parts containing mamatics rar than as a proportion of marks awarded for mamatics but we maintained 8:2 weighting. The results are not dissimilar but a more accurate measure would have been obtained with averages based on proportion of marks awarded for mamatics. 1 SCORE Maths in science report

11 Secondly, methodology mamatical requirements found in project A-level was specifications designed in three were phases. analysed against first GCSE was to mamatics establish nature specification of mamatics to see wher assessed or within not biology, mamatical chemistry requirements physics that featured a-level examinations in science in 21. A-level specifications full suite of were covered examinations in papers GCSE from mamatics aqa, ccea, specification. edexcel, This ocr comparison WJec were indicates analysed using mamatics four that students measures who that follow: are not studying mamatics beyond GCSE will need to be taught within science 1. curriculum type of mamatics. in order to access mamatical all content areas areas assessed of science were categorised A-level. The against results are stated shown for students mamatical studying requirements GCSE mamatics for biology, chemistry at both Foundation physics Higher respectively level. 1. The Edexcel 212 A 2. specification extent of was mamatics. used for purpose proportion of analysis of as question it was considered parts within representative a paper that of typical included content mamatics found in was revised measured mamatics as was GCSEs. proportion of marks within se questions that required mamatics. The analysis was carried out by lead researcher 3. a mamatics difficulty of mamatics. teacher who this had was taught measured GCSE against A-level 3 criteria: mamatics number of steps had in taught a mamatics calculation, sessions familiarity for students of context taking all three of A-level complexity sciences. of His question. experience each category over time meant had that varying furr levels comments of difficulty could each be added, was for example, measured wher as a proportion content of area total had number been of removed question from parts GCSE containing specifications. mamatics. it was not measured against number of marks. 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% RESEARCH groups comprised DESIGN practising PHASE a-level teachers, 3 teachers with experience in curriculum research The aim of third phase of research was development individuals working for awarding to gar opinions of science community organisations as markers, question writers or examiners. on findings from Phase 1 2. In order stardisation exercises were employed throughout to do so, a survey was sent to members of analysis to verify reliability of judgements within science community focused on nature across subject expert groups. of mamatics that y would like to see in A-level second science phase aimed assessments. to measure Four coherence participant groups between were teaching identified: learning of mamatics A-level sciences. re teachers is an assumption that mamatical Higher education concepts representatives used to access sciences are Representatives first taught within from a mamatical professional context, bodies i.e. within Industry mamatics representatives. curriculum. project compared mamatical requirements for sciences at a-level The with first mamatics three of se curriculum groups prior responded to Key stage to an 5 online using survey current in national order to curriculum give ir opinions level descriptions 8. The industry a 212 representatives mamatics Gcse responded specification to a short 3. this work questionnaire was carried out eir by a researcher over telephone by a mamatics or in writing. teacher. The online survey was taken in two parts to avoid prejudicing aim of third results. phase Part was A to asked determine respondents nature for of mamatics general comments that community about would mamatics like to see in in a-level current science science assessments. A-levels. These this was comments achieved were based through on an previous online survey experience for stakeholders of science in A-levels, science on community. viewing Depending a complete on A-level ir expertise, 9 on participants reviewing a selection answered of questions survey for biology, with mamatical chemistry or content physics 1. In a-level Part assessment. B respondents were participants asked were for ir chosen views in on three groups; way mamatics teaching profession; is assessed higher within education; A-level Sciences professional having bodies. been an online given survey findings was completed from by first 97 participants phase of across research. three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 8 The online survey responses are available from SCORE Secretariat. 91 A five complete awarding A-level organisations ory use paper mamatical for ir subject. requirements The papers defined that by were ofqual chosen in developing sat in ir specifications middle of for data biology, range from first chemistry phase of physics. research, mamatical i.e. y sat requirements in mid-range are for available extent in of full report. paper involving mamatics, mid-range in terms of 2 a complete difficulty science included a-level is a made typical up range of 6 units. of mamatical marks from content. ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, 1 question A set parts of questions rar than with marks mamatical were used in content. calculation The questions but we maintained were chosen 8:2 to weighting. cover range of mamatical requirements 3 that edexcel were 212 assessed a specification in A-level was used papers for purpose were of chosen analysis so that as it re was considered was an even representative spread from of typical across content all of found awarding organisations revised mamatics from Gcses. AS A2 papers. SCORE Maths in science report 11

12 ExEcutivE The online survey summary was completed by nearly 1 online survey data, basic statistics were generated. participants, with breakdown for each subject Where questions were open-ended, responses mamatics enables students to underst in Table 1. This represents a very small proportion were coded categorised. Similar codes were describe many scientific phenomena yet re is concern of science community, in some participant used to report responses from industry that science assessments at a-level are not reflecting groups, numbers were so small that findings can questionnaire. subject s analytical nature. to explore wher re was only offer guidance on how mamatics should be any evidence for this concern, score investigated assessed within sciences at A-level should For industry, most effective means of garing type, extent difficulty of mamatical questions within not be regarded as strong evidence. opinions on mamatical element of science a-levels. findings show that a large number of science A-levels was through written or telephone mamatical requirements listed in biology, chemistry Data was analysed separately for different questionnaire. Six representatives in total took part physics specifications are not assessed. those that participant groups so that similarities in questionnaire. are assessed are covered repeatedly often at a lower differences of opinion could be identified. The level than required. this is likely to have an impact on results were reported for whole group apart way that subjects are taught refore on from where re were significant differences students ability to have necessary skills to progress of opinion between groups. A variety of effectively to stem higher education employment. question types were used in survey to elicit in addition, findings show a disparity in way aims data relevant to research questions. From mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review of mamatical requirements for each of sciences gar evidence on type, extent difficulty of mamatics required to access sciences in current at Table a-level 1: Number that a framework of participants is developed completing to regulate online a-level survey specifications for Phase 3to establish wher this way mamatics is assessed within sciences to ensure SUBJECT parity across NUMBER system. OF PARTICIPANTS was being appropriately met by assessments. work did not compare mamatical requirements Background Teachers between physics, chemistry biology as it is accepted Higher education Professional Bodies Total se will differ between disciplines. re Biology has been growing 21 concern across science findings aim to provide score with evidence to community about mamatical dem of science Chemistry 2 11 inform development 7 of policy on 38 type, extent qualifications, specifically that Gcse a-level science difficulty of mamatics in criteria qualifications Physics are not 21 meeting needs of students 7 in 4 32 way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 12 SCORE Maths in science report

13 CHAPTER 3: DETAILED FINDINGS The methodology detailed findings from Phases 1, 2 3 are separated project into was biology, designed chemistry in three phases. physics. The awarding first was to organisations establish nature are not of named mamatics are represented assessed within by A-E. biology, These chemistry representations physics are a-level same examinations throughout. in 21. full suite of average groups percentage comprised of practising question a-level parts teachers, containing mamatics teachers with experience in a complete in curriculum A-level. research Figure 2 illustrates development percentage individuals of working question for awarding parts a organisations complete A-level as markers, containing question mamatics writers or examiners. for stardisation five awarding exercises organisations. were employed throughout examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within 3.1 PHYSICS ocr WJec were analysed using four across subject expert groups. Figure 2: Percentage of question parts measures PHASE that follow: 1: A-LEVEL PAPERS second phase aimed to measure coherence containing mamatics in a complete physics EXTENT type of mamatics. mamatical areas between teaching learning of mamatics A-level for five awarding organisations assessed were categorised against stated sciences. re is an assumption that This measure seeks to capture how much of mamatical requirements for biology, chemistry mamatical concepts used to access sciences A-level physics assessment is mamatical physics respectively 1. are first taught within a mamatical context, i.e. within Theory Practical (independent of type, appropriateness or mamatics Contribution curriculum. (8%) project Contribution compared (2%) difficulty). 2. extent It is quantified of mamatics. by proportion proportion of mamatical 7 requirements for sciences at a-level questions of or question parts parts within within a paper a complete that with mamatics 6 curriculum prior to Key stage 5 A-level included that require mamatics mamatics was measured as proportion was using current 5 national curriculum level descriptions of marks proportion requiring of mamatics. marks within se Table questions 2a shows 4 a 212 mamatics Gcse specification 3. this work percentage that required of mamatics. question parts containing 3 was carried out by a researcher by a mamatics mamatics within each unit percentage 2 3. difficulty of mamatics. this was measured teacher. of question parts containing mamatics for 1 against 3 criteria: number of steps in a ory only practical only papers. Table 2b aim of third phase was to determine nature calculation, familiarity of context A B C D E takes into account weighting of ory papers of mamatics that community would like to see complexity of question. each category Awarding Organisations (8%) practical papers (2%) to calculate in a-level science assessments. this was achieved had varying levels of difficulty each was through an online survey for stakeholders in science measured as a proportion of total number of community. Depending on ir expertise, participants question parts containing mamatics. it was not answered survey for biology, chemistry or physics Table measured 2a: Percentage against of number question of marks. parts containing mamatics within each unit within a-level assessment. participants were chosen in set of ory practical papers across five awarding organisations 4. appropriateness of mamatics. We three groups; teaching profession; higher education; looked at wher answer required scientific comprehension in addition to mamatical A skill. AS units this was 1 measured 2 as a proportion of 49 total B 57 professional bodies. an online survey was completed by 97 participants C across Dthree groups (27 Efor biology; 38 for chemistry; for 42physics). participants 51 from number of question parts containing mamatics. industry were also consulted more generally but as most AS unit science-related industries employ at a graduate level a A2 subject units expert 4 group 5 was established for 62 each 48 ir comments 63 tended to 46 focus more on 63 outcomes of three sciences. each group analysed full at graduate level rar than directly referring to a-level. suite A2 unit of 21 6 examinations papers of aqa, 58ccea, edexcel, Theory ocr papers only WJec for ir respective 56 subjects at a two-day workshop. examination papers included Practical papers only 57 all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory Table papers 2b: make Percentage up 8% of of complete question a-level parts weighted to take account of ory component (8%) experimental practical component practical papers (2%) remaining of A-level 2% 2. assessments Percentage of question parts in a complete A level A B C D E Theory contribution (8%) five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, Practical chemistry contribution physics. mamatical (2%) requirements 11 are available in 5 full report a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete Total a-level A-level assessment marks from practical 56 experimental papers 47 (Unit 3 6) 6 make up remaining 47 2%. in analysis, 59 question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 13

14 ExEcutivE Table 3a shows summary percentage of marks requiring Figure 3: Percentage of marks requiring mamatics for each unit for ory only mamatics in a complete physics A-level for mamatics enables students to underst practical only papers. Table 3b takes into account five awarding organisations describe many scientific phenomena yet re is concern weighting of ory papers (8%) practical that science assessments at a-level are not reflecting papers (2%) to calculate average percentage subject s analytical nature. to explore wher re was of marks requiring mamatics in a complete Theory Practical any evidence for this concern, score investigated Contribution (8%) Contribution (2%) A-level. Figure 3 illustrates this as a graph. type, extent difficulty of mamatical questions within 6 science a-levels. findings show that a large number of 5 mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress A B C D E effectively to stem higher education employment. Awarding Organisations in addition, findings show a disparity in way aims mamatics is assessed across different awarding organisations. score recommends that re is a review score s overall objective for this project was to gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current Table 3a: Percentage of marks 11 that require mamatics within each unit within set of at a-level that a framework is developed to regulate a-level specifications to establish wher this ory practical papers across five awarding organisations way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements A B between physics, C chemistry D biology as E it is accepted Background AS units se will differ 66 between 4disciplines. 49 re AS unit has 3been growing concern across 44science 15 findings 33aim to provide 55 score with evidence 74 to community about mamatical dem of science A2 units inform development 62 of 45 policy on type, 66 extent qualifications, specifically that Gcse a-level science difficulty of mamatics in criteria qualifications A2 unit 6 are not meeting needs of 5 students in assessments for a-levels in biology, chemistry Theory way y papers assess only analytical nature of 49science. 55 physics. 64project also supports 43 score s 58work on in Practical 29 score papers published only evidence on Gcse 47 science examination papers which reported a wide variation in amount of mamatics assessed across awarding 23 how examinations 3 system 63 should operate 5 to ensure science qualifications are fit for purpose also its work on improving coherence between sciences organisations confirmed that use of mamatics mamatics. within Table 3b: context Percentage of science of marks was examined requiring in a mamatics very within a total A-level, weighted to take account in project, we looked across all assessments at limited of way. ory score component organisations (8%) felt that practical this was component (2%) of A-level assessments a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching practical examination papers. learning of sciences, offers a Avaluable aid B C D E in understing describing scientific phenomena; Theory contribution (8%) 39 as such it should be appropriately represented in biology, Practical chemistry contribution physics (2%) curricula 9 ir assessments. Total A-level to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. Percentage of question parts in a complete A level 11 A mark was judged to require mamatics if part or all of mark could not be achieved without mamatics. 14 SCORE Maths in science report

15 methodology TYPE groups comprised practising a-level teachers, project was designed in three phases. teachers with experience in curriculum research The number of occurrences of each mamatical requirement listed in Physics A-level was measured to first was to establish nature of mamatics development individuals working for awarding identify type of mamatics assessed frequency of each type of mamatics assessed. The assessed within biology, chemistry physics organisations as markers, question writers or examiners. results are displayed in Figure 4. a-level examinations in 21. full suite of stardisation exercises were employed throughout examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within ocr WJec were analysed using four across subject expert groups. Mamatical requirements listed x-axis on Figure 4 measures that follow: second phase aimed to measure coherence 1. Arithmetic Computation 4. Geometry Trigonometry (a) 1. use a type calculator of mamatics. for addition, subtraction, mamatical multiplication areas (a) between calculate areas teaching of triangles, learning circumferences of mamatics areas of assessed division; were categorised against stated circles, sciences. surface areas re is an volumes assumption of rectangular that blocks, (b) recognise use expressions in decimal form; mamatical requirements for biology, chemistry mamatical cylinders concepts spheres; used to access sciences ( stard from deleted from this requirement (b) physics respectively 1. are use first Pythagoras taught within orem, a mamatical similarity of context, triangles i.e. within recorded separately as 1(h) to illustrate how commonly angle sum of a triangle; mamatics curriculum. project compared 2. each extent occurred.) of mamatics. proportion (c) use sines, cosines tangents in physical problems; (c) use ratios, fractions percentages; (d) mamatical use sinѳ tanѳ requirements Ѳ cos for Ѳ 1 sciences for small Ѳ; at a-level of question parts within a paper that (d) use calculators to find use x n, 1/x, x 2, x, log l x, e x, (e) with underst mamatics relationship curriculum between prior degrees to Key stage radians 5 included log mamatics was measured as was e x; using translate current from national one to curriculum or. level descriptions (e) proportion use calculators of to hle marks sinѳ, within cosѳ, se tanѳ, questions sin -1 Ѳ, cos - a 212 mamatics Gcse specification 3. this work that 1 5. Graphs Ѳ, tan required -1 Ѳ when mamatics. Ѳ is expressed in degrees or radians. (a) was translate carried information out by a researcher between graphical, by a numerical mamatics (f) recognise use SI prefixes 1-12, 1-9, 1-6, 1-3, 1 3, 3. difficulty of mamatics. this was measured teacher. algebraic forms; (b) plot two variables from experimental or or data using (g) against hle calculations 3 criteria: so that number significant of steps figures in are a neir appropriate aim of scales third phase for graph was plotting; to determine nature calculation, lost or carried beyond familiarity what is of justified; context (c) of mamatics plot data on a that log-linear community graph determine would like wher to see (h) stard complexity form. of question. each category in a-level y change science exponentially assessments. determine this was achieved exponent; 2. Hling had varying datalevels of difficulty each was (d) through plot data an online a log-log survey graph for stakeholders decide wher in data science (a) measured show an awareness as a proportion of order of of magnitude total number of physical of obey a power law determine exponent; community. Depending on ir expertise, participants question quantities parts make containing order of mamatics. magnitude calculations; it was not (e) select appropriate variables for graph plotting; (b) use an appropriate number of significant figures; (f) answered underst survey that y = for mx biology, + c represents chemistry a linear or physics measured against number of marks. (c) find arithmetic means medians; a-level relationship assessment. rearrange participants relationships were into this chosen form in (d) 4. express appropriateness changes as percentages of mamatics. vice We versa; three where groups; appropriate; teaching profession; higher education; (e) underst use logarithmic scales in relation to (g) looked at wher answer required scientific professional determine bodies. slope an / gradient online survey intercept was completed of a linear by quantities which range over several orders of magnitude. graph in appropriate physical units; comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; (h) determine gradient of a tangent to a non-linear 3. Algebra this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from graph by drawing use slope of tangent as a (a) change subject of an equation by manipulation of number of question parts containing mamatics. industry measure were of also rate of consulted change; more generally but as most terms, including positive negative, integer (i) science-related choose by inspection industries a straight employ line at or a curved graduate line which level a subject fractional expert indices group was square established roots for each ir will comments serve as tended best straight to focus line more through on a set outcomes of data of (b) substitute three sciences. numerical each values group into algebraic analysed equations full using appropriate units for physical quantities at graduate points presented level rar graphically; than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, (j) underst possible physical significance of area (c) check dimensional consistency of physical equations edexcel, ocr substitute numerical WJec for values ir into respective such equations subjects between a curve x axis be able to calculate it using at a two-day appropriate workshop. units for physical examination quantities; papers included or measure it by counting squares as appropriate; (k) underst use slope of a tangent to a curve as all (d) solve ory simple papers algebraic (Units equations 1, 2, 4 including 5) y=k/x, y=k/x 2 a means to obtain gradient. Underst use experimental (e) formulate practical use simple papers algebraic (Units equations 3 as 6). notation d/dt for a rate of change; mamatical models of physical situations, identify calculations were based on assumption that ory (l) underst use multiplicative scales (1, 1, 1...); inadequacy of such models papers make up 8% of complete a-level (m) use logarithmic plots to test exponential power law (f) underst use symbols: <, <<, >>, >, ~,,, experimental x, x, dx/dt practical papers remaining 2% 2. variations; (n) sketch simple functions including y = k/x, y = kx 2 y = k/x 2, y = sinѳ, y = cosѳ, y = e -kx. (o) underst or recognise physical significance of a straight line passing or not passing through origin. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 15

16 ExEcutivE Figure 4: The summary number of occurrences for each mamatical requirement in a full suite of examination papers for a complete physics A-level in each of awarding organisations. mamatics enables students to underst It has no relation to number of marks awarded for each mamatical requirement. describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical nature. to explore wher re was Awarding Organisations any evidence for this concern, score investigated A B C D E type, extent 12 difficulty of mamatical questions within science a-levels. findings show that a large number of 1 mamatical requirements listed in biology, chemistry physics 8specifications are not assessed. those that are assessed are covered repeatedly often at a lower 6 level than required. this is likely to have an impact on way that subjects are taught refore on 4 students ability to have necessary skills to progress effectively to 2stem higher education employment. in addition, findings show a disparity in way aims mamatics is 1aassessed 1b 1c 1d 1eacross 1f 1g 1h 2adifferent 2b 2c 2d awarding 2e 3a 3b 3c 3d 3e 3f 4a 4b 4c 4d 4e 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n score s overall objective for this project was to Arithmetic Hling Data Algebra Geometry Graphs organisations. score Computation recommends that re is a review gar Trigonometry evidence on type, extent difficulty of of mamatical requirements for each Mamatical of sciences Requirements mamatics for Physics required A-Level to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements DIFFICULTY between Table 4a physics, shows chemistry percentage biology of mamatical as it is accepted Background se question will differ parts between classified as disciplines. containing single For each of following measures, percentages step (S), multiple step (M) or extended step (E) re are stated has been as a growing proportion concern of across number science of calculations findings aim within to provide each A-level score unit with evidence as an to community question parts. about The mamatical percentages dem do not relate of science inform average for development ory only of policy practical on type, only extent papers. qualifications, in any way to specifically number that of Gcse marks awarded a-level science for These difficulty figures of are mamatics calculated as in a percentage criteria qualifications mamatical are understing. not meeting needs of students in assessments of question for a-levels parts identified in biology, as chemistry containing way y assess analytical nature of science. physics. project also supports score s work on NUMBER OF STEPS mamatics. Table 4b shows se percentages in 29 score published evidence on Gcse science how examinations system should operate to ensure The number of steps involved in a calculation was of total number of question parts Table 4c examination papers which reported a wide variation in science qualifications are fit for purpose also its used as one measure of difficulty, based takes into account weighting of ory papers amount of mamatics assessed across awarding work on improving coherence between sciences assumption that questions containing mamatics (8%) practical papers (2%) to calculate organisations confirmed that use of mamatics mamatics. that required multiple step or extended calculation average percentage of single step, multiple step within (e.g. value context x had of to science be found was examined used in a very extended step calculations in a complete in project, we looked across all assessments at limited subsequent way. score calculation organisations in order felt to that find this was solution A-level. Figure 5a illustrates percentage of a-level for a given year, including both experimental unacceptable. to problem, mamatics y) were more is integral difficult to than teaching single single, multiple extended step calculations in practical examination papers. step learning calculations, of sciences, as y require offers students a valuable to aid a complete A-level for each of five awarding in use understing higher order skills describing extended scientific reasoning. phenomena; organisations. Figures 5b 5c illustrate se as Appendix such it should 5a shows be appropriately an example represented of each type in of percentages for ory only practical only biology, calculation. chemistry physics curricula ir papers respectively. assessments. Number of Occurrences to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 16 SCORE Maths in science report

17 Table methodology 4a: Percentage of single, multiple extended step groups calculations comprised practising in physics a-level A-level, teachers, calculated project was a designed percentage in three of phases. question parts identified teachers as containing with experience mamatics in curriculum research first was to establish nature of mamatics development individuals working for awarding assessed within biology, chemistry physics organisations as markers, question writers or examiners. A B C D E a-level examinations in 21. full suite of stardisation exercises were employed throughout Number of steps E M S E M S examinations papers from aqa, ccea, edexcel, analysis E to Mverify S reliability E Mof judgements S E within M S ocr AS units WJec 1 were 2 analysed 16 using four across 19 55subject 27 expert 9 groups measures AS unit 3that follow: second 31 phase 69 aimed to 5 measure 5 2 coherence type of mamatics. mamatical areas between teaching learning of mamatics A2 units assessed were categorised against stated sciences. re is an assumption that A2 unit mamatical requirements for biology, chemistry mamatical 2 concepts 8 used 39to access 61 sciences 5 5 Theory papers physics respectively only are 1 first taught 58 within 34 7a mamatical context, i.e. within 9 mamatics curriculum. project compared Practical 2. extent papers of only mamatics proportion mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work Table that 4b: required Percentage mamatics. of single, multiple extended step calculations in physics A-level, was carried out by a researcher by a mamatics calculated as a percentage of total number of question parts in a complete A-level 3. difficulty of mamatics. this was measured teacher. against 3 criteria: number of steps in a A B Caim of third phase D was to determine E nature calculation, familiarity of context of mamatics that community would like to see Number complexity of stepsof question. E Meach Scategory E M S E M S E M S E M S in a-level science assessments. this was achieved had varying levels of difficulty each was AS units through 13 an 37online 18survey 4 for 2 stakeholders 18 7 in 38science 7 measured as a proportion of total number of community. Depending on ir expertise, participants AS unit question 3 parts containing mamatics it was not answered survey for biology, chemistry or physics A2 units measured 4 against 5 number of marks a-level assessment participants were 18chosen 43 in 3 A2 4. unit appropriateness 6 of mamatics We 16 16three groups; 7 teaching 26 profession; 32 5 higher education; looked at wher answer required scientific professional bodies. an online survey was completed by Theory papers only comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Practical this was papers measured onlyas a proportion of total for chemistry; for 26 physics). 35 participants 1 2 from 47 number of question parts containing mamatics. industry were also consulted more generally but as most science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full Table 4c: Percentage of single, multiple extended at graduate step calculations level rar than in directly physics referring A-level, to a-level. suite of 21 examinations papers of aqa, ccea, weighted to take account of ory component (8%) practical component (2%) edexcel, ocr WJec for ir respective subjects of A-level assessments at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) A B experimental practical papers (Units 3 6). calculations Number of were steps based on E assumption M S that E ory M papers Theory make papers up 8% only of 11 complete 22 a-level experimental (8%) practical papers remaining 2% 2. S 14 C E 6 M 3 S 18 D E 2 M 15 S 18 E E 1 M 33 S 4 Practical papers only (2%) A-level total five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, (weighted) chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 17

18 ExEcutivE Figure 5a: Percentage summary of mamatical question parts identified as containing single, mamatics enables students to underst multiple extended step calculations in a describe many scientific phenomena yet re is concern complete physics A-level for each of five that science assessments at a-level are not reflecting awarding organisations subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty TOTAL of mamatical questions within science a-levels. findings show that a large number of Extended Multiple Single mamatical requirements listed in biology, chemistry 7 physics specifications are not assessed. those that 6 are assessed 5 are covered repeatedly often at a lower level than required. 4 this is likely to have an impact on way that 3 subjects are taught refore on students ability 2 to have necessary skills to progress effectively to 1 stem higher education employment. in addition, findings show a disparity in way A B C D E mamatics is assessed across different awarding Awarding Organisations organisations. score recommends that re is a review of mamatical requirements for each of sciences Percentage of question parts in a complete A level at a-level that a framework is developed to regulate Figure way mamatics 5b: Percentage is assessed of mamatical within sciences to ensure question parity parts across identified system. as containing single, multiple extended step calculations in Background ory examination papers for physics A-level re has been growing concern across science community about mamatical THEORY dem of science qualifications, specifically Extended that Multiple Gcse Single a-level science qualifications 7 are not meeting needs of students in way y 6 assess analytical nature of science. Percentage of question parts in a complete A level 5 in 29 score 4 published evidence on Gcse science examination 3 papers which reported a wide variation in amount 2of mamatics assessed across awarding organisations 1 confirmed that use of mamatics within context of science was examined in a very A B C D E limited way. score organisations Awarding Organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. Figure 5c: Percentage of mamatical question parts identified as containing single, multiple extended step calculations in practical examination papers for physics A-level Percentage of question parts in a complete A level aims Extended PRACTICAL Multiple Single A B C D E score s overall objective for this project was to Awarding Organisations gar evidence on type, extent difficulty of mamatics required to access sciences in current a-level specifications to establish wher this was being appropriately met by assessments. work did not compare mamatical requirements between physics, chemistry biology as it is accepted se will differ between disciplines. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 18 SCORE Maths in science report

19 COMPLEXITY methodologyof TASK Question project parts was that designed contained three mamatics phases. within a first full was suite to of establish A-level examinations nature of were mamatics measured against assessed four within levels of biology, complexity, chemistry with Level physics 4 being considered a-level examinations most in difficult. 21. These full suite levels of included Level examinations 1 (straight papers forward/routine), from aqa, ccea, Level edexcel, 2 (requires understing ocr WJec were application analysed using of mamatics four complexity groups comprised within each practising A-level a-level unit teachers, as an average teachers with for ory experience only in curriculum practical research only papers. These development figures are individuals calculated working as a percentage for awarding of organisations question as markers, parts identified question as writers containing or examiners. mamatics. stardisation Table exercises 5b shows were employed se percentages throughout of analysis total verify number reliability of question of judgements parts within Table 5c takes across into subject account expert weighting groups. of ory papers within measures one that domain), follow: Level 3 (requires understing (8%) practical papers (2%) to calculate second phase aimed to measure coherence application of mamatics across domains) average percentage of Level 1, 2 3 complexity 1. type of mamatics. mamatical areas between teaching learning of mamatics Level 4 (requires synsis application in a complete A-level. Figure 6a illustrates assessed were categorised against stated sciences. re is an assumption that of mamatics across a number of domains). percentage of Level 1, 2 3 complexity type mamatical requirements for biology, chemistry mamatical concepts used to access sciences Appendix 5b shows an example of each level of calculations in a complete A-level for each of physics respectively 1. are first taught within a mamatical context, i.e. within complexity. five awarding organisations. Figures 6b 6c mamatics curriculum. project compared 2. extent of mamatics. proportion illustrate se percentages for ory only mamatical requirements for sciences at a-level Table of 5a shows question parts percentage within a paper of mamatical that practical only papers respectively. with mamatics curriculum prior to Key stage 5 question included parts mamatics classified as was Level measured 1, 2 or as 3 was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics Table 5a: Percentage of Level 1, 2 3 complexity 3. difficulty of mamatics. this was measured teacher. type calculations in physics A-level, calculated as a percentage of question parts identified as containing mamatics against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see complexity of question. A each category B C D E in a-level science assessments. this was achieved Complexity had varying levels of difficulty 3 2 each 1 was through 3 an 2online 1 survey 3 for 2stakeholders 1 3 in 2 science 1 measured as a proportion of total number of AS units community Depending 14 on ir 14 expertise, 87 4 participants question parts containing mamatics. it was not answered survey for biology, chemistry or physics AS unit measured 3 against number 2 16 of marks a-level assessment. participants were chosen in A2 4. units appropriateness 4 5 of 17 mamatics We three 5 groups; 45 teaching 5 9profession; higher 11education; 86 4 A2 unit looked 6 at wher answer 2 required 8 scientific professional 25bodies. 75 an online 22survey 78 was completed 5 5by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Theory papers only this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from Practical number papers of question only parts 1 containing 18 81mamatics industry were 5 also 5consulted 21 more 79 generally but 28as most 73 science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full at graduate level rar than directly referring to a-level. Table suite of 5b: 21 Percentage examinations of papers Level of 1, aqa, 2 ccea, 3 complexity type calculations in physics A-level, calculated edexcel, ocr as a percentage WJec for ir of respective total subjects number of question parts in a complete A-level at a two-day workshop. examination papers included all ory papers (Units 1, A2, 4 5) B experimental practical papers (Units 3 6). Complexity calculations were based on assumption that ory papers AS units make 1 up 8% 2 of 6complete 3 a-level experimental AS unit 3 practical papers 1 9 remaining 46 2% C D E A2 units A2 unit Theory papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 12 Level revised 4 mamatics was omitted Gcses. from findings as very few examination papers included questions of this complexity. Practical papers only SCORE Maths in science report 19

20 ExEcutivE Table 5c: Percentage summary of Level 1, 2 3 complexity type calculations in physics A-level, weighted mamatics to take account enables of students ory to underst component (8%) practical component (2%) of A-level describe assessments many scientific phenomena yet re is concern that science assessments at a-level A are not reflecting B subject s analytical nature. to explore wher re was Complexity any evidence for this concern, score investigated type, Theory extent papers difficulty only of mamatical 7 28 questions 11 2 within 27 science (8%) a-levels. findings show that a large number of 1 14 C D E mamatical Practical papers requirements only listed in 2 biology, 9 chemistry (2%) physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level A-level than required. total this is likely 7 to have 3 an 2 impact 2 on (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively Figure 6a: to stem Percentage higher education of mamatical employment. Figure 6c: Percentage of mamatical in addition, findings show a disparity way aims question parts identified as containing question parts identified as contanining mamatics Level 1, Level is assessed 2 Level across 3 complexity-type different awarding organisations. calculations score in a complete recommends A-level that re for each is a review of of five mamatical awarding requirements organisations for each of sciences at a-level that a framework is developed to regulate way mamatics is TOTAL assessed within sciences to score s Level 1, overall Level objective 2 Level for this 3 project complexity-type was to gar calculations evidence in on practical type, extent examination difficulty papers of mamatics for physics required A-level to access sciences in current a-level specifications to establish wher this was being appropriately PRACTICAL met by assessments. ensure parity across system. Level 3 Level 2 Level 1 work did not compare Level 3 Level mamatical 2 Level 1 requirements between physics, chemistry biology as it is accepted 7 7 Background 6 se will differ 6 between disciplines. re has 5 been growing concern across science 5 findings aim to provide score with evidence to community 4about mamatical dem of science 4 inform development of policy on type, extent qualifications, 3 specifically that Gcse a-level science 3 difficulty of mamatics in criteria 2 2 qualifications are not meeting needs of students in assessments for a-levels in biology, chemistry 1 1 way y assess analytical nature of science. physics. project also supports score s work on A B C D E A B C D E in 29 score published evidence on Gcse science how examinations system should operate to ensure Awarding Organisations Awarding Organisations examination papers which reported a wide variation in science qualifications are fit for purpose also its amount of mamatics assessed across awarding organisations Figure 6b: Percentage confirmed of that mamatical use of mamatics work on improving coherence between sciences mamatics. within question context parts of identified science was examined contanining a very in project, we looked across all assessments at limited Level way. 1, Level score 2 organisations Level 3 complexity-type felt that this was a-level for a given year, including both experimental unacceptable. calculations mamatics in ory examination is integral to papers teaching for practical examination papers. physics learning A-level of sciences, offers a valuable aid in understing describing scientific phenomena; Percentage of question parts in a complete A level as such it should be appropriately THEORY represented in biology, chemistry Level 3 physics Level 2 curricula Level 1 ir assessments. Percentage of question parts in a complete A level 7 6 to provide furr evidence to support se 5 concerns, score set up this project to investigate 4 mamatics 3 found in 21 science assessments at a-level across 2 unitary awarding organisations in engl, Wales norrn irel. 1 A B C D E Awarding Organisations Percentage of question parts in a complete A level 2 SCORE Maths in science report

21 CONTEXT methodology The question project was parts designed that contained three phases. mamatics within first was a full to establish suite of A-level nature examinations of mamatics were classified assessed within as Level 1, biology, Level chemistry 2 or Level 3, physics with Level 1 a-level most examinations familiar context. in 21. Level full 1 suite is a of context typically examinations met papers through from aqa, learning ccea, programme, edexcel, Level ocr 2 is WJec a context were that analysed contains using some four novel ory groups only comprised practical practising only papers. a-level teachers, These figures are teachers calculated with experience as a percentage in curriculum of research question parts development identified as individuals containing working mamatics. for awarding Table 6b organisations shows se as markers, percentages question of writers total or number examiners. of stardisation question parts exercises Table were 6c employed takes into throughout account analysis weighting to verify of ory reliability papers of judgements (8%) within practical papers across (2%) subject to calculate expert groups. average percentage aspects measures that Level follow: 3 is an unfamiliar context unlikely of Level 1, 2 3 context in a complete A-level. second phase aimed to measure coherence to have been met before. Appendix 5c shows an Figure 7a illustrates percentage of Level 1, 2 1. type of mamatics. mamatical areas between teaching learning of mamatics example of levels of familiarity. 3 context calculations in a complete A-level for assessed were categorised against stated sciences. re is an assumption that each of five awarding organisations. Figures 7b mamatical requirements for biology, chemistry mamatical concepts used to access sciences Table 6a shows percentage of mamatical 7c illustrate se percentages for ory only physics respectively 1. are first taught within a mamatical context, i.e. within question parts classified as Level 1, 2 or 3 context practical only papers respectively. mamatics curriculum. project compared within 2. each extent A-level of unit mamatics. as an average proportion for mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work Table that 6a: required Percentage mamatics. of Level 1, 2 3 context-type was calculations carried out by in a researcher physics A-level, by a mamatics calculated as a percentage of question parts identified as containing 3. difficulty of mamatics. this was measured teacher. mamatics against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity A of context B C D E of mamatics that community would like to see Context complexity of question. 3 2 each 1 category in a-level 3 2science 1 assessments this was 3 achieved 2 1 had varying levels of difficulty each was AS units through 14 an 26online 61 survey for 12stakeholders 89 in science 1 measured as a proportion of total number of community. Depending on ir expertise, participants AS unit question 3 parts containing mamatics it was not answered survey for biology, chemistry or physics A2 units measured 4 against 5 number 7 4of marks a-level 4 assessment participants were chosen in 1 A2 4. unit appropriateness 6 of 6mamatics We 75 25three 33groups; 13 teaching 53 profession; 1 higher education; looked at wher answer required scientific professional bodies. an online survey was completed by Theory papers only comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Practical this was papers measured only as a 3proportion of total 88 number of question parts containing mamatics for chemistry; for 3physics). 7 participants 22 from 78 industry were also consulted more generally but as most science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full Table 6b: Percentage of Level 1, 2 3 context-type at graduate calculations level rar in physics than directly A-level, referring calculated to a-level. suite of 21 examinations papers of aqa, ccea, as a percentage of total number of question parts in a complete A-level edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, A2, 4 5) B experimental Context practical papers 3 2(Units 13 36). 2 1 C D E calculations were based on assumption that ory AS units papers make up 8% of complete a-level experimental AS unit 3 practical papers 12 remaining 44 2% A2 units A2 unit Theory papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. Practical papers only SCORE Maths in science report 21

22 ExEcutivE Table 6c: Percentage summary of Level 1, 2 3 context-type calculations in physics A-level, weighted mamatics to take account enables of students ory to underst component (8%) practical component (2%) of A-level describe assessments many scientific phenomena yet re is concern that science assessments at a-level A are not reflecting B subject s analytical nature. to explore wher re was Context any evidence for this concern, score investigated type, Theory extent papers difficulty only of mamatical 2 15 questions 27 within 23 science (8%) a-levels. findings show that a large number of 1 2 C D E mamatical Practical papers requirements only listed in 2 biology, 9 chemistry (2%) physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level A-level than required. total this is likely 2 to have 17 an 36 impact on (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively Figure 7a: to Percentage stem higher education of mamatical employment. question Figure 7c: Percentage of mamatical question in addition, findings show a disparity in way aims parts identified as containing calculations set parts identified as containing calculations set mamatics in a Familiar, is assessed with Some across Novel different Aspects, awarding organisations. Unfamiliar context score in recommends a complete that A-level re is for a review of each mamatical of five awarding requirements organisations for each of sciences at a-level that a framework is developed to regulate way mamatics is TOTAL assessed within sciences to score s in a Familiar, overall with objective Some for Novel this project Aspects, was to gar Unfamiliar evidence context in type, practical extent examination difficulty of mamatics papers for physics required to A-level access sciences in current a-level specifications to establish wher this was being appropriately PRACTICAL met by assessments. ensure parity across system. Unfamiliar Some Novel Familiar work did not compare Unfamiliar mamatical Some Novel Familiar requirements between physics, chemistry biology as it is accepted 7 7 Background 6 se will differ 6 between disciplines. re has 5 been growing concern across science 5 findings aim to provide score with evidence to community 4about mamatical dem of science 4 inform development of policy on type, extent qualifications, 3 specifically that Gcse a-level science 3 difficulty of mamatics in criteria 2 2 qualifications are not meeting needs of students in assessments for a-levels in biology, chemistry 1 1 way y assess analytical nature of science. physics. project also supports score s work on A B C D E A B C D E in 29 score published evidence on Gcse science how examinations system should operate to ensure Awarding Organisations Awarding Organisations examination papers which reported a wide variation in science qualifications are fit for purpose also its amount of mamatics assessed across awarding organisations Figure 7b: Percentage confirmed of that mamatical use of mamatics question work on improving coherence between sciences mamatics. within parts identified context of as science containing was examined calculations in a very set in project, we looked across all assessments at limited in a Familiar, way. score with organisations Some Novel felt Aspects, that this was a-level for a given year, including both experimental unacceptable. Unfamiliar context mamatics in ory is integral examination to teaching papers practical examination papers. for physics learning of A-level sciences, offers a valuable aid in understing describing scientific phenomena; Percentage of question parts in a complete A level as such it should be appropriately THEORY represented in biology, chemistry Unfamiliar physics Some curricula Novel Familiar ir assessments. Percentage of question parts in a complete A level 7 6 to provide furr evidence to support se 5 concerns, score set up this project to investigate 4 mamatics 3 found in 21 science assessments at a-level across 2 unitary awarding organisations in engl, Wales norrn irel. 1 A B C D E Awarding Organisations Percentage of question parts in a complete A level 22 SCORE Maths in science report

23 methodology APPROPRIATENESS addition groups to comprised mamatical practising skill it a-level was classified teachers, as project was designed in three phases. some teachers scientific with experience comprehension in curriculum research question parts APPLICATION first was to establish nature of mamatics where development all marks required individuals scientific working for comprehension awarding Judgements were made as to wher content assessed within biology, chemistry physics were organisations classified as markers, scientific question comprehension. writers or examiners. of question part reflected how mamatics is a-level examinations in 21. full suite of Appendix stardisation 5d shows exercises an example were employed of each throughout category. used in real world in scientific context. All of examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within question parts with mamatics were judged to Table ocr WJec were analysed using four across 7a shows subject expert percentage groups. of mamatical reflect appropriate way in which mamatics question parts classified as all marks (S), some could measures be used that follow: in a real scientific context. second phase aimed to measure coherence marks (B) or no marks (M) requiring scientific 1. type of mamatics. mamatical areas between teaching learning of mamatics comprehension within each A-level unit as an STRUCTURAL OR TAGGED ON assessed were categorised against stated sciences. re is an assumption that average for ory only practical only papers. One of measures was to ascertain wher mamatical requirements for biology, chemistry mamatical concepts used to access sciences These figures are calculated as a percentage mamatics was a structural part of physics respectively 1. are first taught within a mamatical context, i.e. within of question parts identified as containing question or wher mamatics was tagged mamatics curriculum. project compared 2. extent of mamatics. proportion mamatics. Table 7b shows se percentages on to question. In all of question parts with mamatical requirements for sciences at a-level of question parts within a paper that of total number of question parts Table 7c mamatical content mamatics was judged with mamatics curriculum prior to Key stage 5 included mamatics was measured as was takes into account weighting of ory papers to be a structural part of question. using current national curriculum level descriptions proportion of marks within se questions (8%) practical papers (2%) to calculate a 212 mamatics Gcse specification 3. this work MATHEMATICS that required mamatics. SKILLS OR SCIENTIFIC average percentage of mamatical question parts was carried out by a researcher by a mamatics COMPREHENSION where all marks, some marks or no marks require 3. difficulty of mamatics. this was measured teacher. Mamatical question parts within a full suite of scientific comprehension in a complete A-level. against 3 criteria: number of steps in a A-level examinations were measured against Figure aim 8a of illustrates third phase percentage was to determine of mamatical nature calculation, familiarity of context extent to which scientific comprehension was question of mamatics parts that where all, community some would no like marks to see complexity of question. each category required to achieve full marks. If a question part require in a-level scientific science assessments. comprehension this in was a complete achieved had varying levels of difficulty each was required no scientific comprehension to acquire A-level through for an online each of survey five for stakeholders awarding organisations. in science measured as a proportion of total number of full marks it was classified as no scientific Figures community. 8b Depending 8c illustrate on ir se expertise, percentages participants for question parts containing mamatics. it was not comprehension (mamatical skill only), if part ory answered only survey practical for biology, only chemistry papers respectively. or physics measured against number of marks. of marks required scientific comprehension in a-level assessment. participants were chosen in 4. appropriateness of mamatics. We looked at wher answer required scientific three groups; teaching profession; higher education; professional bodies. an online survey was completed by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Table 7a: Percentage of mamatical question parts this was measured as a proportion of total 38 classified for chemistry; as all 32 mark for physics). (S), some participants marks from (B) no marks (M) requiring scientific comprehension number of question parts containing mamatics. industry in were physics also consulted A-level, more calculated generally as but a as most percentage of question parts identified as containing science-related mamatics industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full A B at Cgraduate level rar D than directly referring E to a-level. suite of 21 examinations papers of aqa, ccea, edexcel, Scientific ocr WJec for Sir Brespective M subjects S B M S B M S B M S B M at comprehension a two-day workshop. examination papers included all AS units ory 1 papers 2 (Units 1, 832, ) experimental practical papers (Units 3 6). AS unit calculations were based on assumption that ory papers A2 units make 4 up 8% 5 of 99 complete a-level 2 97 experimental A2 unit 6 practical papers 3 remaining 7 832% Theory papers only Practical papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 23

24 ExEcutivE Table 7b: Percentage summary of mamatical type question parts where all marks (S), some marks (B) or no marks (M) require scientific comprehension in physics A-level, calculated as a percentage of mamatics enables students to underst total number of question parts in a complete A-level describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical nature. to explore A wher re B was any Scientific evidence for this concern, Sscore B investigated M S B type, comprehension extent difficulty of mamatical questions within science a-levels. findings show that a large number of AS units mamatical requirements listed in biology, chemistry AS physics unit 3 specifications are 9not assessed. 47those 15 that are A2 assessed units 4 are covered 5 repeatedly 61 often 1 at 47a lower level than required. this is likely to have an impact on A2 way unit that 6 subjects are taught 17 refore on students Theory ability papers to have only necessary 51 3 skills 2 to progress 51 M C S B M D S B 1 M E S B 2 M effectively to stem higher education employment. Practical papers only in addition, findings show a disparity in way 3 aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of Table 7c: Percentage of mamatical type question parts where all marks (S), some marks (B) of mamatical requirements for each of sciences mamatics required to access sciences in current no marks (M) require scientific comprehension in physics A-level, weighted to take account at a-level that a framework is developed to regulate a-level specifications to establish wher this of ory component (8%) practical component (2%) of A-level assessments way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements A B between C physics, chemistry D biology Eas it is accepted Background Scientific S B M S B M se S will Bdiffer between M S Bdisciplines. M S B M re comprehension has been growing concern across science findings aim to provide score with evidence to community about mamatical dem of science Theory papers only inform 46 2development 6 3of policy on 5 45 type, extent 1 qualifications, specifically that Gcse a-level science (8%) difficulty of mamatics in criteria qualifications are not meeting needs of students in assessments for a-levels in biology, chemistry Practical way y papers assess only analytical 3 nature 9of science (2%) physics. project also supports score s work on in 29 score published evidence on Gcse science how examinations system should operate to ensure A-level total examination papers which reported a wide variation in science qualifications are fit for purpose also its (weighted) amount of mamatics assessed across awarding work on improving coherence between sciences organisations confirmed that use of mamatics mamatics. within context of science was examined in a very in project, we looked across all assessments at limited way. score organisations felt that this was a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching practical examination papers. learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 24 SCORE Maths in science report

25 Figure methodology 8a: Percentage of mamatical question project parts was designed requiring in three scientific phases. comprehension first was to establish in addition nature of to mamatical mamatics skill assessed to achieve within all biology, marks, chemistry some of physics marks or a-level no marks examinations a complete in 21. physics full suite A-level of for each examinations of papers five awarding from aqa, organisations ccea, edexcel, ocr WJec were analysed using four measures that follow: TOTAL 1. type Comprehension of mamatics. Comprehension mamatical Comprehension areas 7 assessed were categorised against stated 6 mamatical requirements for biology, chemistry 5 physics respectively 1. Percentage of question parts in a complete A level 4 Scientific Some Scientific No Scientific 2. extent 3 of mamatics. proportion of 2question parts within a paper that included 1 mamatics was measured as was proportion of marks within se questions A B C D E that required mamatics. Awarding Organisations 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a Figure calculation, 8b: Percentage familiarity of mamatical of context question complexity parts requiring of question. scientific each category comprehension had varying levels in addition of difficulty to mamatical each was skill to measured achieve as all a proportion marks, some of total of number marks of or no question marks parts in ory containing examination mamatics. papers it was for not physics measured A-level against number of marks. 4. appropriateness of mamatics. We looked at wher THEORY answer required scientific comprehension Scientific in addition Some Scientific to mamatical No Scientific skill. Comprehension Comprehension Comprehension this 7 was measured as a proportion of total number 6 of question parts containing mamatics. Percentage of question parts in a complete A level 5 a subject expert group was established for each 4 of three sciences. each group analysed full 3 suite of 21 examinations papers of aqa, ccea, 2 edexcel, ocr WJec for ir respective subjects 1 at a two-day workshop. examination papers included A B C D E all ory papers (Units 1, 2, 4 5) Awarding Organisations experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. Figure groups 8c: comprised Percentage practising of mamatical a-level teachers, question teachers with parts experience requiring in curriculum scientific research comprehension development individuals addition working to mamatical for awarding skill organisations to achieve as markers, all marks, question some writers of or examiners. marks or stardisation no marks in exercises practical were examination employed throughout papers for analysis physics to verify A-level reliability of judgements within across subject expert groups. second phase aimed PRACTICAL to measure coherence between teaching Scientific learning Some Scientific of mamatics No Scientific Comprehension Comprehension Comprehension sciences. 7 re is an assumption that mamatical 6 concepts used to access sciences are first taught 5 within a mamatical context, i.e. within 4 mamatics curriculum. project compared 3 mamatical requirements for sciences at a-level 2 with mamatics curriculum prior to Key stage 5 1 using current national curriculum level descriptions a 212 mamatics A B Gcse C specification D 3 E. this work was carried out by a Awarding researcher Organisations by a mamatics teacher. Percentage of question parts in a complete A level aim of third phase was to determine nature of mamatics PHASE 2 that PHYSICS community A-LEVEL would like IN to see COMPARISON in a-level science assessments. WITH GCSE this MATHEMATICS was achieved AND through NATIONAL an online survey CURRICULUM for stakeholders LEVEL in science DESCRIPTORS community. Depending on ir expertise, participants Two answered comparisons survey were for biology, used to chemistry establish or physics coherence a-level assessment. of physics A-levels participants were mamatics chosen in accessed three groups; up teaching to Key Stage profession; 4: comparison higher education; with professional National bodies. Curriculum an online level survey descriptors was completed by comparison 97 participants with across 212 three mamatics groups (27 for GCSE biology; specification. 38 for chemistry; These 32 comparisons for physics). are participants displayed from in Table industry 8. were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 25

26 ü ExEcutivE Table 8: Comparison summary of mamatical requirements for physics A-level with mamatics found mamatics in National enables Curriculum students to Level underst Descriptors GCSE mamatics specification describe many scientific phenomena yet re is concern that Mamatical science assessments requirements at a-level are not reflecting Corresponding subject s as listed analytical in nature. physics to explore A-level wher re NC was level(s) for any specification evidence for this concern, score investigated mamatics type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry Found in Edexcel GCSE specification Foundation (F) Higher (H) Comment 1. Arithmetic physics specifications Computation are not assessed. those that are (a) assessed use a calculator are covered for repeatedly addition, often at L4 a lower to L5 (L4 + level subtraction, than required. multiplication this is likely to have division; an impact on decimals, way that subjects are taught refore to on L5 x ) F ü H ü students ability to have necessary skills to progress (b) recognise use expressions L5 ü ü effectively to stem higher education employment. in decimal; (stard form deleted in addition, findings show a disparity in way aims from this requirement recorded mamatics is assessed across different awarding score s overall objective for this project was to separately as 1(h)) organisations. score recommends that re is a review gar evidence on type, extent difficulty of of (c) use mamatical ratios, fractions requirements for each of L5 sciences to L8 (L5 for ü ü mamatics required to access Percentages: sciences reverse in current at percentages; a-level that a framework is developed to regulate calculations a-level specifications to establish percentages wher are this way mamatics is assessed within sciences fractions to to L8 was for being appropriately met by exclusive assessments. to higher level ensure parity across system. proportion) work did ünot compare ü mamatical Ratios requirements between physics, chemistry biology as it is accepted ü ü Background Fractions se will differ between disciplines. re (d) use has calculators been growing to concern find across use x n, science L6 to EP (L6 for ü ü x n, 1/x, x 2, x findings aim to provide score with evidence to community 1/x, x 2, x, about log l x, e mamatical, log e x; dem of x science, 1/x, x 2, x, inform development of policy on type, extent qualifications, specifically that Gcse a-level log science l x, e x, log e x) û û log difficulty of mamatics l x, e x, log in criteria e x qualifications are not meeting needs of students in assessments for a-levels in biology, chemistry (e) way use y calculators assess to analytical hle sinѳ, nature of science. EP û ü Degrees physics. project also supports score s work on cosѳ, tanѳ, sin -1 Ѳ, cos -1 Ѳ, tan -1 Ѳ in 29 score published evidence on Gcse science how ûexaminations û system Radians should operate appear to in ensure when Ѳ is expressed in degrees or examination papers which reported a wide variation in science qualifications are fit for AS purpose level mamatics also its radians. amount of mamatics assessed across awarding work on improving coherence specification between sciences organisations (f) recognise confirmed use SI prefixes that 1 use of, mamatics EP mamatics. û within 1-9, 1-6 context, 1-3, 1 of science, 1 6 was 1 examined in a very in project, we looked across all assessments at limited way. score organisations felt that this was (g) hle calculations so that L7 to EP a-level üfor a given üyear, including Round both to experimental nearest unacceptable. mamatics is integral to teaching significant figures are neir lost or practical examination papers. integer or to any learning of sciences, offers a valuable aid carried beyond what is justified; in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. (h) stard form. L8 û ü number of significant figures û ü Extended usage of significant figures to provide furr evidence to support se concerns, 2. Hling score data set up this project to investigate NC levels mamatics (a) show an found awareness in 21 of science order assessments of L5 to EP at magnitude a-level across of physical unitary quantities awarding organisations (depending on F H Comments engl, make order Wales of magnitude norrn calculations; irel. context e.g. mass of humans or mass of electrons) û û Not a concept taught in mamatics 26 SCORE Maths in science report

27 Table methodology 8: continued groups comprised practising a-level teachers, project was designed in three phases. teachers with experience in curriculum research (b) use an appropriate number of L7 ü ü first was to establish nature of mamatics development individuals working for awarding significant figures; assessed within biology, chemistry physics organisations as markers, question writers or examiners. a-level (c) find examinations arithmetic means in 21. medians; full suite of L5 to L7 stardisation ü exercises ü were employed throughout examinations papers from aqa, ccea, edexcel, (depending on analysis to verify reliability of judgements within ocr WJec were analysed using four wher across subject expert groups. measures that follow: data is discreet, second phase aimed to measure coherence continuous or 1. type of mamatics. mamatical areas between teaching learning of mamatics grouped) assessed were categorised against stated sciences. re is an assumption that (d) express mamatical changes requirements as percentages for biology, chemistry L7 to L8 mamatical ü concepts ü used Changes to access as a sciences vice physics versa; respectively 1. are first taught within a mamatical percentage context, i.e. within mamatics û curriculum. ü project compared 2. extent of mamatics. proportion Percentages as mamatical requirements for sciences at a-level of question parts within a paper that changes with mamatics curriculum prior to Key stage 5 (e) underst included mamatics use logarithmic was measured as was EP û û using current national curriculum This appears level descriptions in scales proportion in relation of to marks quantities within which se questions a 212 mamatics Gcse A-level specification mamatics 3. this work range that over required several mamatics. orders of magnitude. was carried out by a researcher specification by a mamatics Algebra difficulty of mamatics. this was measured NC levels teacher. F H Comments against 3 criteria: number of steps in a (a) change subject of an equation L8 to EP aim üof third üphase was In to Foundation determine Level nature calculation, familiarity of context by manipulation of terms, including of mamatics that community students would are like required to see to complexity of question. each category positive negative, integer in a-level science assessments. change this was achieved subject of a had varying levels of difficulty each was fractional indices square roots through an online survey for stakeholders formula. in science measured as a proportion of total number of community. Depending on ir expertise, participants question parts containing mamatics. it was not answered survey for biology, In Higher chemistry level or this physics measured against number of marks. a-level assessment. participants includes were cases chosen where in 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. three groups; teaching profession; subject higher education; is both professional bodies. an online sides survey of was completed original by 97 participants across three formula groups or (27 where for biology; 38 for chemistry; 32 for physics). power of participants a subject from industry were also consulted appears. more generally but as most science-related industries employ at a graduate level a (b) subject substitute expert numerical group was values established into for each L5 to L8 ü ü ir comments tended to focus more on outcomes of algebraic three equations sciences. each using group appropriate analysed full at graduate level rar than directly referring to a-level. suite units of for 21 physical examinations quantities papers of aqa, ccea, edexcel, (c) check ocr dimensional WJec for ir consistency respective subjects EP at of a physical two-day equations workshop. examination substitute papers included all numerical ory values papers into (Units such 1, 2, equations 4 5) experimental using appropriate practical units for papers physical (Units 3 6). calculations quantities; were based on assumption that ory û û Not a concept taught in mamatics papers make up 8% of complete a-level (d) solve simple algebraic equations L6 to EP û ü Inverse relationships are experimental practical papers remaining 2% 2. including y=k/x, y=k/x 2 not in specification at Foundation level 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 27

28 ExEcutivE Table 8: continued summary mamatics (e) formulate enables use students simple to underst algebraic L5 to EP describe equations many as scientific mamatical phenomena models yet re is concern that of physical science assessments situations, at a-level identify are not reflecting subject s inadequacy analytical of such nature. models to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry ü ü Formulate use simple algebraic equations as mamatical models of physical situations: only simple equations would appear at Foundation level mamatics physics specifications are not assessed. those that û û are assessed are covered repeatedly often at a lower Identifying level than required. this is likely to have an impact on adequacies of such way that subjects are taught refore on models: this is not students ability to have necessary skills to progress a concept taught in effectively to stem higher education employment. mamatics in addition, findings show a disparity in way aims (f) underst use symbols: <, L2 to EP ü ü =, <,>,~ mamatics <<, >>, >, is ~, assessed,, x, across x, dx/dt different awarding score s û overall objective û for <<, this >> project These was symbols to organisations. score recommends that re is a review gar evidence on type, are extent not used difficulty in of of mamatical requirements for each of sciences mamatics required to access mamatics sciences GCSE in current or at a-level that a framework is developed to regulate a-level specifications to establish A-level wher this way mamatics is assessed within sciences to was being appropriately met by assessments. û ü ensure parity across system. work did not compare mamatical requirements between û physics, chemistry û, x, biology x, dx/dt as it is appear accepted Background se will differ between disciplines. in AS mamatics re has been growing concern across science specification findings aim to provide score with evidence to community 4. Geometry about mamatical Trigonometry dem of NC science levels inform F development H of policy Comments on type, extent qualifications, specifically that Gcse a-level science (a) calculate areas of triangles, L6 to EP difficulty ü of ümamatics Areas in of triangles, criteria qualifications are not meeting needs of students in circumferences areas of circles, assessments for a-levels in biology, circumferences chemistry way y assess analytical nature of science. surface areas volumes of physics. project also supports areas score s of circles, work surface on in rectangular 29 score blocks, published cylinders evidence on Gcse science examination spheres; papers which reported a wide variation in how examinations system areas should operate volumes to ensure of science qualifications are fit for rectangular purpose blocks also its amount of mamatics assessed across awarding work on ûimproving ü coherence between sciences Cylinders spheres organisations confirmed that use of mamatics mamatics. (b) use Pythagoras orem, similarity L5 to L8 (L5 ü ü 3D Pythagoras is only within context of science was examined in a very of triangles angle sum of a angle sum of in project, we looked across found all assessments in Higher level at limited way. score organisations felt that this was triangle; triangle, L7 a-level for a given year, including specification both experimental unacceptable. mamatics is integral to teaching Pythagoras, L8 practical examination papers. learning of sciences, offers a valuable aid similarities of in understing describing scientific phenomena; triangles) as such it should be appropriately represented in biology, (c) use chemistry sines, cosines physics tangents curricula in ir L8 assessments. physical problems; û ü (d) use sinѳ tanѳ Ѳ cos Ѳ 1 EP û û This is only found in to provide furr evidence to support se for small Ѳ; A-level mamatics concerns, score set up this project to investigate specification as it mamatics found in 21 science assessments requires use of at a-level across unitary awarding organisations in radians engl, Wales norrn irel. (e) underst relationship between EP û û degrees radians translate from one to or. 28 SCORE Maths in science report

29 Table methodology 8: continued project was designed in three phases. first 5. Graphs was to establish nature of mamatics NC levels assessed (a) translate within information biology, between chemistry physics L4 to L7 a-level graphical, examinations numerical in 21. algebraic full suite of examinations forms; papers from aqa, ccea, edexcel, groups comprised practising a-level teachers, teachers with experience in curriculum research development F Hindividuals Comments working for awarding organisations ü as markers, ü question writers or examiners. stardisation exercises were employed throughout analysis to verify reliability of judgements within ocr WJec were analysed using four across subject expert groups. (b) plot two variables from experimental L6 ü ü measures that follow: or or data using appropriate scales second phase aimed to measure coherence for 1. graph type plotting; of mamatics. mamatical areas between teaching learning of mamatics assessed were categorised against stated sciences. re is an assumption that (c) plot data on a log-linear graph EP û û Not found in mamatical requirements for biology, chemistry mamatical concepts used to access sciences determine wher y change mamatics A-level physics respectively 1. are first taught within a mamatical context, i.e. within exponentially determine specification mamatics curriculum. project compared exponent; 2. extent of mamatics. proportion mamatical requirements for sciences at a-level (d) plot of data question a log-log parts within graph a paper that EP with ûmamatics û curriculum Not prior found to in Key stage 5 decide included wher mamatics data obey was a power measured law as was using current national curriculum mamatics level descriptions A-level proportion determine of exponent; marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. (e) select appropriate variables for EP was carried û out by ûa researcher In mamatics, by a mamatics graph 3. plotting; difficulty of mamatics. this was measured teacher. students would not be against 3 criteria: number of steps in a aim of third phase was expected to determine to identify nature an calculation, familiarity of context of mamatics that community independent would like variable to see or complexity of question. each category in a-level science assessments. select this two was variables achieved for had varying levels of difficulty each was through an online survey for stakeholders graph plotting from science a set measured as a proportion of total number of community. Depending on ir ofmore expertise, than participants 2 variables question parts containing mamatics. it was not (f) underst that y = mx + c L8 to EP answered ü survey ü for biology, Recognise chemistry that or physics measured against number of marks. represents a linear relationship a-level assessment. participants y = mx + were c represents chosen in rearrange 4. appropriateness relationships of into mamatics. this form We three groups; teaching profession; a straight higher line education; graph where looked appropriate; at wher answer required scientific professional bodies. an online survey was completed by û û Rearrange relationships comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; into this form: taken to this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from mean reducing a more number of question parts containing mamatics. industry were also consulted more generally but as most complex function to a science-related industries employ at a graduate level a subject expert group was established for each linear function ir comments tended to focus more on outcomes of three sciences. each group analysed full (g) determine slope / gradient EP at graduate ü level rar ü than directly Slope referring to a-level. suite of 21 examinations papers of aqa, ccea, intercept of a linear graph in edexcel, ocr WJec for ir respective subjects appropriate physical units; at a two-day workshop. examination papers included û ü all ory papers (Units 1, 2, 4 5) Intercept experimental (h) determine practical gradient papers of a (Units tangent 3 EP 6). calculations to a non-linear were graph based by on drawing assumption that ory papers use make slope up of 8% of tangent complete as a a-level experimental measure of rate practical of change; papers remaining 2% 2. û û Taken out of GCSE mamatics specification (i) choose by inspection a straight line which will serve as best straight line through a set of data points presented graphically; include curved lines L7 ü ü Curved lines are not considered in mamatics specification in relation 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% to best of complete fit a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 29

30 ExEcutivE Table 8: continued summary mamatics enables students to underst (j) underst possible physical EP û û Counting squares describe many scientific phenomena yet re is concern significance of area between a taken out of GCSE that science assessments at a-level are not reflecting curve x axis be able to mamatics subject s analytical nature. to explore wher re was calculate it or measure it by counting specification any evidence for this concern, score investigated squares as appropriate; type, extent difficulty of mamatical questions within science (k) underst a-levels. findings use show slope that of a large number EP of û û mamatical a tangent to requirements a curve as listed a means in to biology, chemistry obtain physics specifications gradient. Underst are not assessed. those that are use assessed notation are covered d/dt for repeatedly a rate of often at a lower level change; than required. this is likely to have an impact on (l) underst way that subjects use are multiplicative taught refore EPon students scales (1, ability 1, to 1 have...); necessary skills to progress û û effectively to stem higher education employment. (m) use logarithmic plots to test EP in addition, findings show a disparity in way aims û û exponential power law variations; mamatics is assessed across different awarding score s overall objective for this project was to organisations. (n) sketch simple score functions recommends including that re is L8 a review to EP gar evidence û on ü type, y extent = k/x, y = difficulty kx 2 y = of k/x 2, of y = k/x, mamatical y = kx 2 y requirements = k/x 2, y = sinѳ, for each y = of sciences at cosѳ, a-level y = ethat -kx. a framework is developed to regulate way mamatics is assessed within sciences to ensure parity across system. mamatics required to access y = sinѳ, sciences y = cosѳ in current a-level ûspecifications û to establish y = e -kx wher this was being appropriately met by assessments. work did not compare mamatical requirements between physics, chemistry biology as it is accepted Background se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 3 SCORE Maths in science report

31 3.1.3 methodology PHASE 3 SURVEY FINDINGS Figure groups 9: Opinions comprised from practising a-level physics teachers, online project was designed in three phases. survey teachers respondents with experience on in curriculum spread research of TYPE OF MATHEMATICS ASSESSED first was to establish nature of mamatics mamatical development content individuals areas working within for awarding a physics AT A-LEVEL PHYSICS assessed within biology, chemistry physics A-level organisations as markers, question writers or examiners. In Part A of survey, respondents were asked to a-level examinations in 21. full suite of stardisation exercises were employed throughout consider spread of mamatical content areas examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within assessed within physics A-level. Figure 9 illustrates ocr WJec were analysed using four across subject expert groups. The Key mamatical percentages of respondents that considered measures that follow: content areas were assessed second phase aimed to measure coherence spread to be good, acceptable (key mamatical 1. type of mamatics. mamatical areas between teaching learning A restricted of mamatics amount of areas were assessed), average (limited variation in mamatical content areas assessed were categorised against stated sciences. re is an assumption seemed to be that assessed type of mamatics) poor (restricted amount many times mamatical requirements for biology, chemistry mamatical concepts used to access sciences of mamatics assessed many times). physics respectively 1. are first taught within a mamatical There context, was a good i.e. spread within of different mamatical content mamatics curriculum. project areas being compared assessed Participants were also asked to comment on 2. extent of mamatics. proportion areas of mamatics y would like to feature mamatical requirements for sciences at a-level There was not enough variation of question parts within a paper that with mamatics curriculum prior in type to Key of mamatical highly in assessments, a little in assessments stage 5 content being assessed included mamatics was measured as was or not at all. The results are shown in Figure 1. using current national curriculum level descriptions proportion of marks within se questions Participants were also asked if re were any or a 212 mamatics Gcse specification 3. this work that required mamatics. areas of mamatics, not listed in requirements, was carried out by a researcher by a mamatics Prior to finding out results of analysis, 63% of that 3. y difficulty felt should of mamatics. be included in this was assessments. measured teacher. respondents felt that awarding organisations should The only against areas 3 criteria: that were number mentioned of steps repeatedly in a were use aim a framework of third to phase ensure was that to determine a broad spread nature of calculus, calculation, differentiation familiarity integration. of context mamatical of mamatics requirements that community are assessed would like to see 47% complexity of question. each category felt in a-level that all science requirements assessments. should this be was assessed achieved over Overall, had re varying was levels concern of difficulty that mamatics each was a through two- or an three-year online survey cycle for stakeholders of A-levels in to science ensure within measured physics A-level as a proportion was not of difficult total enough, number which of that community. y are Depending taught. on ir expertise, participants meant question that students parts containing lacked fluency mamatics. in mamatics it was not answered survey for biology, chemistry or physics problem-solving measured against skills. number Some of were marks. also a-level assessment. participants were chosen in concerned that students did not fully underst 4. appropriateness of mamatics. We three groups; teaching profession; higher education; mamatical concepts, which would limit ir looked at wher answer required scientific professional bodies. an online survey was completed by ability to apply what y knew. comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from number of question parts containing mamatics. industry were also consulted more generally but as most Figure science-related industries employ at a graduate level a subject 1: expert Mamatical group was established requirement for each areas that physics survey respondents would like to feature highly ir comments tended to focus more on outcomes of three in assessment, sciences. each a group little analysed in assessment full or not at all at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. Feature Highly examination Feature a papers Little included Feature Not at All all ory 35 papers (Units 1, 2, 4 5) experimental 3 practical papers (Units 3 6). calculations were based on assumption that ory 25 papers make up 8% of complete a-level 2 experimental practical papers remaining 2% 2. Number of Respondents five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 1a 1b 1c 1d 1e 1f 1g 1h 2a 2b 2c 2d 2e 3a 3b 3c 3d 3e 3f 4a 4b 4c 4d 4e 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n 5o a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical Mamatical experimental Requirements papers (Unit for 3 Physics 6) make A-Level up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 31

32 ExEcutivE In Part B, after summary receiving findings from analysis, more than 75% of respondents felt it mamatics enables students to underst was unacceptable that mamatical content describe many scientific phenomena yet re is concern areas y considered essential were hardly or that science assessments at a-level are not reflecting not at all assessed. When comparing Figure 4 subject s analytical nature. to explore wher re was Figure 1 it is clear re is a mismatch between any evidence for this concern, score investigated mamatical content areas that are assessed type, extent difficulty of mamatical questions within those that science community would like science a-levels. findings show that a large number of to be assessed (for example selecting appropriate mamatical requirements listed in biology, chemistry variables for graph plotting; underst that y = mx physics specifications are not assessed. those that + c represents a linear relationship rearrange are assessed are covered repeatedly often at a lower relationships into this form where appropriate; level than required. this is likely to have an impact on determining slope / gradient intercept of a way that subjects are taught refore on linear graph in appropriate physical units). students ability to have necessary skills to progress effectively to stem higher education employment. Furrmore nearly three quarters felt it was in addition, findings show a disparity in way inappropriate that a few mamatical requirements mamatics is assessed across different awarding were assessed repeatedly, both throughout organisations. score recommends that re is a review question papers within a qualification across of mamatical requirements for each of sciences awarding organisations, rar than a spread at a-level that a framework is developed to regulate of skills being assessed. Many acknowledged way mamatics is assessed within sciences to importance of testing some of key ensure parity across system. mamatical skills more frequently, for example, graphs using formulae, in order to improve Background mamatical fluency. However, a broader spread re was felt has to been important growing concern in order across to underst science community breadth about of physics mamatical that would dem be required of science qualifications, for progression specifically to test that Gcse deeper thinking, a-level science as qualifications opposed to are substitution not meeting formulae. needs of The students same in concern way y was assess raised again analytical that if nature topics of were science. not assessed y would not be taught. in 29 score published evidence on Gcse science examination EXTENT OF papers MATHEMATICS which reported a wide variation in In Part amount A, 59% of mamatics of respondents assessed felt that across awarding amount organisations of mamatics in confirmed paper that was not use enough of mamatics within to adequately context prepare of science for progression was examined to in higher a very limited education way. in score a physics organisations or related felt subject. that this After was unacceptable. viewing findings mamatics of Phase is integral 1, to majority teaching thought that learning percentage of sciences, of question offers parts a containing valuable aid in mamatics understing was appropriate. describing scientific However, phenomena; 4% of as respondents such it should thought be appropriately lower limit represented of 47% in of marks biology, requiring chemistry mamatics physics was too curricula low. ir assessments. No consensus was reached in Part A or B on to provide furr evidence to support se wher mamatics in ory papers concerns, score set up this project to investigate mamatics in practical papers should be mamatics found in 21 science assessments different. Those who felt that it should be same at a-level across unitary awarding organisations in felt A-level examination papers should be seen engl, Wales norrn irel. as a unified subject, two being inter-dependent. Those who felt it should be different explained that in practical units re would be more interpretation of graphs, data hling, calculation of errors, derivations, show questions. Some explained that ory papers should test rigour understing of concepts whereas practical units should be testing experimental planning, data collection, statistics analysis so mamatical element would naturally be different. DIFFICULTY OF MATHEMATICS Part A of survey showed that 1% of representatives from higher education professional bodies were not concerned if level of difficulty was perceived to go up due to aims A-levels containing more mamatics. However, only 62% of teachers agreed, largely because score s y felt that overall increasing objective for level this project of dem was to of gar mamatics evidence in on physics type, A-level extent would difficulty result in of mamatics overall A-level required being perceived to access as sciences more deming. current a-level specifications to establish wher this was In Part being A, when appropriately asked met about by difficulty assessments. in terms work of did number not compare of steps in mamatical calculations requirements on between paper, 44% physics, of respondents chemistry felt biology that re as it should is accepted se be more will multiple-step differ between calculations, disciplines. with a furr 15% wishing to see more extended questions. In findings aim to provide score with evidence to Part B, nearly two-thirds of respondents felt that inform development of policy on type, extent re should be an even spread of all three types of difficulty of mamatics in criteria calculation nearly half of respondents felt assessments for a-levels in biology, chemistry that re should be more multiple-step calculations physics. project also supports score s work on more extended calculations 13. how examinations system should operate to ensure science qualifications are fit for purpose also its When considering context as a measure of difficulty work on improving coherence between sciences in Part A of survey, two thirds of respondents mamatics. felt that number of mamatical questions set in within project, a familiar we context looked across was appropriate. all assessments In Part at B a-level respondents for a given were year, informed including that both experimental analysis had practical found that examination two awarding papers. organisations had over 7% of mamatical calculations set in a familiar context. Results were evenly split between wher this was appropriate, with half of respondents expressing view that re should be less mamatics set in familiar contexts so that students have more experience at applying mamatics in unfamiliar situations. However, overall 65% of respondents felt that high level of mamatical assessment set within a familiar context impacted adversely on students ability to apply mamatics in a novel situation. 13 Some respondents supported both statements so se percentages do not necessarily represent two different findings. 32 SCORE Maths in science report

33 Respondents methodology were asked to make a judgement on project mamatical was designed difficulty in three in phases. paper in terms of first complexity. was to establish In Part A nature no respondents of mamatics thought that assessed complexity within biology, was too chemistry difficult physics re was a-level an examinations even split between in 21. those full who suite thought of it was examinations too easy papers those from aqa, who thought ccea, edexcel, that it was appropriate. ocr WJec In Part were B, analysed when respondents using four were told measures that that vast follow: majority of questions across awarding organisations required Level 1 Level 2 complexity 1. type (i.e. of mamatics. use of straightforward mamatical familiar areas concepts assessed or required were categorised application against of one domain stated of mamatics), mamatical 88% requirements of respondents for biology, felt chemistry that recall of common physics respectively mamatical 1. procedures should be 2. assessed extent alongside of mamatics. procedures that proportion involve application of question in one or parts more within content a paper areas, that that is, that included difficulty mamatics should be was increased. measured as was proportion of marks within se questions COMPARABILITY that required mamatics. ACROSS AWARDING ORGANISATIONS In Part 3. A difficulty 88% of of respondents mamatics. agreed this was that measured it was important against that 3 criteria: A-levels number from of all steps of in awarding a organisations calculation, had familiarity same of level of context difficulty in terms of complexity mamatical of question. content. each Only category 59% of respondents had varying agreed levels that of difficulty it was important each was that all of measured awarding as a organisations proportion of assessed total number of same question mamatical parts containing content areas. mamatics. The remainder it was not considered measured it only against important number for of marks. same key areas 4. to be appropriateness assessed by of all mamatics. of awarding We organisations. looked at wher The vast majority answer (91%) required also scientific thought that comprehension proportion of in addition questions to mamatical with mamatical skill. content this should was measured be similar as across a proportion awarding of total organisations. number of 63% question of respondents parts containing felt mamatics. that awarding organisations should use a framework a subject expert group was established for each to ensure a broad spread of mamatical of three sciences. each group analysed full requirements is assessed. suite of 21 examinations papers of aqa, ccea, In edexcel, Part B ocr most respondents WJec for ir (59%) respective felt that subjects differences at a two-day across workshop. awarding examination organisations papers included in all proportion ory papers of (Units marks 1, 2, in 4 an A-level 5) with mamatical experimental content practical were papers not (Units acceptable. 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. COHERENCE groups comprised BETWEEN practising MATHEMATICS a-level teachers, AND teachers THE with SCIENCES experience in curriculum research The development appropriateness individuals of working mamatics for awarding was deemed organisations by 97% as markers, of respondents question writers to be or examiners. most important stardisation aspect exercises of mamatical were employed assessment throughout over dem analysis to verify extent reliability of mamatics. of judgements within across subject expert groups. All respondents felt that physics A-levels should second phase aimed to measure coherence contain mamatics beyond that found in between teaching learning of mamatics current mamatics GCSE. There were mixed sciences. re is an assumption that views on wher mamatics GCSE should mamatical concepts used to access sciences include se extra requirements to ensure GCSE are first taught within a mamatical context, i.e. within is adequate preparation for mamatics in a mamatics curriculum. project compared science A-level, with some agreeing that a new mamatical requirements for sciences at a-level mamatics qualification for use alongside physics with mamatics curriculum prior to Key stage 5 A-levels would support students. using current national curriculum level descriptions a 212 mamatics Gcse specification 3. this work was carried out by a researcher by a mamatics 3.2 teacher. CHEMISTRY aim PHASE of third 1: A-LEVEL phase was PAPERS to determine nature of mamatics EXTENT that community would like to see in a-level science assessments. this was achieved This measure seeks to capture how much of through an online survey for stakeholders in science A-level chemistry assessment is mamatical community. Depending on ir expertise, participants (independent of type, appropriateness or answered survey for biology, chemistry or physics difficulty). It is quantified by proportion of a-level assessment. participants were chosen in questions or question parts within a complete three groups; teaching profession; higher education; A-level that require mamatics proportion professional bodies. an online survey was completed by of marks requiring mamatics. Table 9a shows 97 participants across three groups (27 for biology; percentage of question parts containing 38 for chemistry; 32 for physics). participants from mamatics within each unit percentage industry were also consulted more generally but as most of question parts containing mamatics for science-related industries employ at a graduate level ory only practical only papers. Table 9b ir comments tended to focus more on outcomes takes into account weighting of ory papers at graduate level rar than directly referring to a-level. (8%) practical papers (2%) to calculate average percentage of question parts containing mamatics in a complete A-level. Figure 11 illustrates percentage of question parts in a complete A-level containing mamatics for five awarding organisations. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 33

34 ExEcutivE Table 9a: Percentage summary of question parts containing mamatics within each unit within set of ory practical papers across five awarding organisations mamatics enables students to underst describe many scientific phenomena yet re is concern that science assessments at a-level are not Areflecting subject s AS units analytical 1 nature. 2 to explore wher 41 re was B 6 C 41 D 35 E 5 any evidence for this concern, score investigated AS unit type, extent difficulty of mamatical questions within science A2 units a-levels. 4 5 findings show that a large 51 number of 55 mamatical A2 unit 6 requirements listed in biology, 51 chemistry 34 physics specifications are not assessed. those that Theory papers only are assessed are covered repeatedly often at a lower level Practical than required. papers this only is likely to have an 5 impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment in addition, findings show a disparity in way aims Table 9b: Percentage of questions parts weighted to take account of ory component mamatics (8%) practical is assessed component across different (2%) awarding of A-level score s assessments overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current A B C D E at a-level that a framework is developed to regulate a-level specifications to establish wher this Theory way mamatics contribution is assessed (8%) within 37sciences to 46 was being appropriately 43 met 31by assessments. 42 ensure Practical parity contribution across system. (2%) Total A-level Background work did not 6 compare mamatical 1 requirements 9 between physics, chemistry biology as it is accepted se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, Figure 11: Percentage specifically that of Gcse question a-level parts science qualifications containing are mamatics not meeting in a needs complete of students in chemistry way y A-level assess for analytical five nature awarding of science. organisations in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding Theory Practical organisations Contribution confirmed (8%) that Contribution use of mamatics (2%) within context 6 of science was examined in a very limited way. 5score organisations felt that this was unacceptable. 4 mamatics is integral to teaching learning of sciences, offers a valuable aid 3 in understing describing scientific phenomena; 2 as such it should be appropriately represented in 1 biology, chemistry physics curricula ir assessments. A B C D E Awarding Organisations to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. Percentage of question parts in a complete A level findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 34 SCORE Maths in science report

35 Table methodology 1a shows percentage of marks requiring mamatics project was for designed each unit in three for phases. ory only practical first was to only establish papers. Table nature 1b of takes mamatics into account assessed weighting within of ory biology, papers chemistry (8%) physics practical a-level examinations in 21. full suite of examinations papers from aqa, ccea, edexcel, ocr WJec were analysed using four papers groups (2%) comprised to calculate practising average a-level teachers, percentage of teachers marks with requiring experience mamatics in curriculum in a research complete A-level. development Figure 12 individuals illustrates working this as for a graph. awarding organisations as markers, question writers or examiners. stardisation exercises were employed throughout analysis to verify reliability of judgements within across subject expert groups. Table measures 1a: that Percentage follow: of marks 14 that require mamatics second within phase each aimed unit to measure within coherence set of ory practical papers across five awarding 1. type of mamatics. mamatical areas between organisations teaching learning of mamatics assessed were categorised against stated mamatical requirements for biology, A chemistry B sciences. re is an assumption that mamatical C concepts used D to access Esciences physics respectively 1. are first taught within a mamatical context, i.e. within AS units mamatics curriculum. project compared AS 2. unit extent 3 of mamatics. 49 proportion 1 mamatical 44 requirements 36 for sciences 22at a-level of question parts within a paper that A2 units with mamatics 49 curriculum 2 prior to Key 42 stage 5 included mamatics was measured as was using current national curriculum level descriptions A2 unit proportion 6 of marks within se 46 questions a 212 mamatics Gcse specification 3. this work Theory that papers required mamatics. only was carried 41out by a researcher 22 by a mamatics 4 Practical 3. difficulty papers of mamatics. this was 48 measured 2 teacher against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see complexity of question. each category Table 1b: Percentage of marks requiring mamatics in a-level within science a total assessments. A-level, weighted this was achieved to had varying levels of difficulty each was take account of ory component (8%) practical through an component online survey (2%) for stakeholders of A-level in science measured as a proportion of total number of assessments community. Depending on ir expertise, participants question parts containing mamatics. it was not answered survey for biology, chemistry or physics measured against number of marks. A B C D E a-level assessment. participants were chosen in Theory 4. contribution appropriateness (8%) of mamatics. 33We Practical looked contribution at wher (2%) answer required 1 scientific comprehension in addition to mamatical skill three groups; 33 teaching profession; 18 higher education; 32 professional 8 bodies. an online 6 survey was 4completed by 97 participants across three groups (27 for biology; Total A-level 43 this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each Figure 12: Percentage of marks requiring of three sciences. each group analysed full mamatics in a complete A-level for five suite of 21 examinations papers of aqa, ccea, awarding organisations edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers Theory (Units 1, 2, 4 Practical 5) Contribution (8%) Contribution (2%) experimental practical papers (Units 3 6). 5 calculations were based on assumption that ory papers make 4 up 8% of complete a-level experimental practical papers remaining 2% 2. Percentage of question parts in a complete A level for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, A B C D E chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level Awarding is made Organisations up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 14 A revised mark mamatics was judged Gcses. to require mamatics if part or all of mark could not be achieved without mamatics. SCORE Maths in science report 35

36 ExEcutivE TYPE summary mamatics The number enables of occurrences students to of underst each mamatical requirement listed in Chemistry A-level was measured describe to identify many scientific type of phenomena mamatics yet assessed re is concern frequency of each type of mamatics assessed. that The science results assessments are displayed at a-level in Figure are 13. not reflecting subject s analytical nature. to explore wher re was any evidence for this concern, score investigated Mamatical requirements listed in x-axis Figure 13 type, extent difficulty of mamatical questions within science 1 Arithmetic a-levels. numerical findings computation: show that a large number of (d) solve simple algebraic equations; mamatical (a) recognise requirements use expressions listed in in decimal biology, chemistry (e) use logarithms in relation to quantities which range physics stard specifications form; are not assessed. those that over several orders of magnitude. (b) use ratios, fractions percentages; are assessed are covered repeatedly often at a lower (c) make estimates of results of calculations 4 Graphs: level than (without required. using this a calculator); is likely to have an impact on (a) translate interpret information between graphical, (d) way use that calculators subjects to find are taught use power, refore exponential on numerical algebraic forms; students ability logarithmic to have functions necessary (x n, 1/x, x, skills log l x to, progress e x, log e x); (b) plot two variables from experimental or or data; effectively (e) +, -, to x,. stem higher education employment. (c) underst that y = mx + c represents a linear in addition, findings show a disparity in way aims relationship; 2 Hling data: (d) determine slope intercept of a linear graph; mamatics is assessed across different awarding (a) use an appropriate number of significant figures; (e) score s calculate overall rate of change objective from for a this graph project showing was a linear to organisations. (b) find arithmetic score means; recommends that re is a review gar relationship; evidence on type, extent difficulty of of (c) construct mamatical interpret requirements frequency for tables each of diagrams, sciences (f) mamatics draw use required slope to of access a tangent to sciences a curve as in a current at a-level bar charts that a histograms; framework is developed to regulate a-level measure specifications of rate of change; to establish wher this (d) way use mamatics an appropriate is number assessed of decimal within places. sciences to (g) interpret a spectrum. was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements 3 Algebra: 5 Geometry trigonometry: (a) underst use symbols: =, <, <<, >>, >,, a) between appreciate physics, angles chemistry shapes in regular biology 2-D as it is 3-D accepted Background ~, μ; se structures; will differ between disciplines. (b) change subject of an equation; b) visualise represent 2-D 3-D forms including re has been growing concern across science (c) substitute numerical values into algebraic equations two-dimensional findings aim to representations provide score of 3-D with objects; evidence to community about mamatical dem of science using appropriate units for physical quantities; c) inform underst development symmetry of of policy 2-D on 3-D shapes. type, extent qualifications, specifically that Gcse a-level science difficulty of mamatics in criteria qualifications are not meeting needs of students in assessments for a-levels in biology, chemistry way y assess analytical nature of science. Figure 13: The number of occurrences for each mamatical physics. project requirement also supports in a full score s suite work of on examination 29 score papers published for evidence a complete on Gcse chemistry science A-level how in each examinations of awarding system should organisations. operate to ensure examination papers which reported a wide variation in science qualifications are fit for purpose also its It has no relation to number of marks awarded for each mamatical requirement. amount of mamatics assessed across awarding work on improving coherence between sciences organisations confirmed that use of mamatics mamatics. within context Awarding of science Organisations was examined in a very A B C D E limited way. score organisations felt that this was 8 unacceptable. mamatics is integral to teaching 7 learning of sciences, offers a valuable aid in understing 6 describing scientific phenomena; as such it should 5 be appropriately represented in biology, chemistry 4 physics curricula ir assessments. Number of Occurrences 3 2 to provide furr evidence to support se concerns, score 1 set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in Arithmetic Hling Algebra Graphs engl, Wales Numerical norrn irel. Data Computation Mamatical Requirements for Chemistry A-Level in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 1a 1b 1c 1d 1e 2a 2b 2c 2d 3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 4f 4g 4h 5a 5b 5c 5d Geometry Trigonometry 36 SCORE Maths in science report

37 methodology DIFFICULTY Table groups 11a shows comprised practising percentage a-level of mamatical teachers, project was designed in three phases. question teachers with parts experience classified in as curriculum containing research single For each of following measures, percentages first was to establish nature of mamatics step development (S), multiple individuals step (M) working extended for awarding step (E) are stated as number of question parts assessed within biology, chemistry physics calculations organisations within as markers, each question A-level unit writers or as examiners. an containing mamatics. The percentages do not a-level examinations in 21. full suite of average stardisation for ory exercises only were practical employed only throughout papers. relate in any way to number of marks awarded examinations papers from aqa, ccea, edexcel, These analysis figures to verify are calculated reliability of as judgements a percentage within for mamatical understing. ocr WJec were analysed using four of across question subject parts expert identified groups. as containing NUMBER measures that OF follow: STEPS mamatics. second phase Table aimed 11b to shows measure se coherence percentages The 1. number type of of steps mamatics. involved in a mamatical calculation areas was of between total number teaching of question learning parts of mamatics Table 11c used assessed one measure were categorised of difficulty against based on stated takes into sciences. account re is weighting an assumption of ory that papers assumption mamatical that questions requirements containing for biology, mamatics (8%) chemistry mamatical practical concepts papers used to (2%) access to calculate sciences that required physics multiple respectively step or 1. extended calculation average are first taught percentage within a of mamatical single step, context, multiple i.e. step within (e.g. value x had to be found used in a mamatics extended step curriculum. calculations project in a complete compared 2. extent of mamatics. proportion subsequent calculation in order to find solution A-level. mamatical Figure requirements 14a illustrates for sciences percentage at a-level of of question parts within a paper that to problem, y) were more difficult than single single, with multiple mamatics extended curriculum step prior to calculations Key stage 5 in included mamatics was measured as was step calculations, as y require students to a using complete current A-level national for each curriculum of level five awarding descriptions proportion of marks within se questions use higher order skills extended reasoning. organisations. a 212 mamatics Figures 14b Gcse specification 14c illustrate 3. this se work that required mamatics. Appendix 5a shows an example of each type of percentages was carried out for by ory a researcher only practical by a mamatics only calculation. 3. difficulty of mamatics. this was measured papers teacher. respectively. against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see Table 11a: complexity Percentage of question. of single, each multiple category extended step calculations in chemistry A-level, in a-level science assessments. this was achieved calculated had varying as a levels percentage of difficulty of question each was parts identified as containing mamatics through an online survey for stakeholders in science measured as a proportion of total number of community. Depending on ir expertise, participants question parts containing A mamatics. it Bwas not C D E answered survey for biology, chemistry or physics measured against number of marks. Number of steps E M S E M S a-level E assessment. M S E participants M S were E chosen M in S 4. appropriateness of mamatics. We three groups; teaching profession; higher education; AS units looked at wher answer required scientific professional bodies. an online survey was completed by AS unit comprehension in addition to mamatical skill. 97 participants across 53 three groups 48 (27 for 56 biology; 44 A2 units this was 4 measured 5 as a 14proportion of 32 total for chemistry; for 12 physics). 81 participants 42 2 from 57 number of question parts containing mamatics. industry were also consulted more generally but as most A2 unit science-related industries employ at a graduate level a Theory subject papers expert group onlywas established for 57each ir 17comments 9 76 tended 12to focus 35 more 55 on 35 outcomes 5 62 of three sciences. each group analysed full Practical papers only at graduate 9 16level 76rar 68than directly 33referring to 45a-level. 56 suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included Table all ory 11b: Percentage papers (Units 1, of 2, single, 4 5) multiple extended step calculations in chemistry A-level, calculated experimental as a practical percentage papers of (Units 3 total 6). number of question parts in a complete A-level calculations were based on assumption that ory papers make up 8% of Acomplete a-level B C D E experimental Number of steps practical papers E M remaining S E 2% M 2. S E M S E M S E M S AS units AS unit A2 units five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. A2 unit Theory papers only Practical papers only SCORE Maths in science report 37

38 ExEcutivE Table 11c: Percentage summary of single, multiple extended step calculations in chemistry A-level, mamatics weighted to enables take students account to of underst ory component (8%) practical component (2%) of describe A-level many assessments scientific phenomena yet re is concern that science assessments at a-level are not reflecting A B subject s analytical nature. to explore wher re was any Number evidence of for steps this concern, Escore M investigated S E M type, Theory extent papers difficulty only of mamatical 8 7 questions within 1 science (8%) a-levels. findings show that a large number of S 34 C E 7 M 3 S 33 D E 3 M 1 S 18 E E 15 M 2 S 26 mamatical requirements listed in biology, chemistry Practical papers only physics specifications are 2 not assessed. 1 8 those 1 that (2%) are assessed are covered repeatedly often at a lower A-level than required. total this is likely 1to have 8 an 3 impact 13on 2 (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment in Figure addition, 14a: Percentage findings show a of disparity mamatical in way aims Figure 14c: Percentage of mamatical mamatics question parts is assessed identified across as containing different awarding single, score s question overall parts objective identified for this as project containing was to single, organisations. multiple score extended recommends step calculations that re is a in review a gar multiple evidence extended on type, step extent calculations difficulty of in of complete mamatical A-level requirements for each of for each five of awarding sciences mamatics practical examination required to access papers sciences for chemistry in current at organisations a-level that a framework is developed to regulate a-level A-level specifications to establish wher this way mamatics is assessed within sciences to ensure parity across TOTAL system. was being appropriately met by assessments. work did not compare PRACTICAL mamatical requirements Extended Multiple Single Extended Multiple Single between physics, chemistry biology as it is accepted Background 6 se will differ 6 between disciplines. 5 5 re has been growing concern across science findings aim to provide score with evidence to community 4about mamatical dem of science 4 inform development of policy on type, extent qualifications, 3 specifically that Gcse a-level science 3 difficulty of mamatics in criteria qualifications 2 are not meeting needs of students in 2 assessments for a-levels in biology, chemistry way y 1 assess analytical nature of science. 1 physics. project also supports score s work on in 29 score Apublished B evidence C on DGcse Escience how examinations A system B should C operate D Eto ensure examination papers which Awarding reported Organisations a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics science qualifications Awarding are fit for Organisations purpose also its work on improving coherence between sciences mamatics. within Figure 14b: context Percentage of science was of mamatical examined in a very in project, we looked across all assessments at limited question way. parts score identified organisations as containing felt that this was single, a-level for a given year, including both experimental unacceptable. multiple mamatics extended step is integral calculations to teaching practical examination papers. ory learning examination of sciences, papers for offers Chemistry a valuable A-level aid in understing describing scientific phenomena; as such it should be appropriately THEORY represented in biology, chemistry Extended physics Multiplecurricula Single ir assessments. 6 Percentage of question parts in a complete A level Percentage of question parts in a complete A level 5 to provide furr evidence to support se 4 concerns, score set up this project to investigate 3 mamatics found in 21 science assessments 2 at a-level across unitary awarding organisations in engl, Wales 1 norrn irel. A B C D E Awarding Organisations Percentage of question parts in a complete A level 38 SCORE Maths in science report

39 COMPLEXITY methodologyof TASK Question project parts was that designed contained three mamatics phases. within a first full was suite to of establish A-level examinations nature of were mamatics measured against assessed four within levels of biology, complexity, chemistry with Level physics 4 being considered a-level examinations most in difficult. 21. These full suite levels of included Level examinations 1 (straight papers forward/routine), from aqa, ccea, Level edexcel, 2 (requires understing ocr WJec were application analysed using of mamatics four complexity groups comprised within each practising A-level a-level unit teachers, as an average teachers with for ory experience only in curriculum practical research only papers. These development figures are individuals calculated working as a percentage for awarding of organisations question as markers, parts identified question as writers containing or examiners. mamatics. stardisation Table exercises 12b were shows employed se percentages throughout of analysis total verify number reliability of question of judgements parts within Table 12c takes across into subject account expert weighting groups. of ory papers within measures one that domain), follow: Level 3 (requires understing (8%) practical papers (2%) to calculate second phase aimed to measure coherence application of mamatics across domains) average percentage of Level 1, 2 3 complexity 1. type of mamatics. mamatical areas between teaching learning of mamatics Level 4 (requires synsis application in a complete A-level. Figure 15a illustrates assessed were categorised against stated sciences. re is an assumption that of mamatics across a number of domains). percentage of Level 1, 2 3 complexity type mamatical requirements for biology, chemistry mamatical concepts used to access sciences Appendix 5b shows an example of each level of calculations in a complete A-level for each of physics respectively 1. are first taught within a mamatical context, i.e. within complexity. five awarding organisations. Figures 15b 15c mamatics curriculum. project compared 2. extent of mamatics. proportion illustrate se percentages for ory only mamatical requirements for sciences at a-level Table of 12a shows question parts percentage within a paper of mamatical that practical only papers respectively. with mamatics curriculum prior to Key stage 5 question included parts mamatics classified as was Level measured 1, 2 or as 3 was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics Table 3. 12a: difficulty Percentage of mamatics. of Level this 1, was 2 measured 3 complexity teacher. type calculations in chemistry A-level, calculated against as 3 criteria: a percentage number of of question steps in a parts identified as containing mamatics aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see complexity of question. A each category B C D E in a-level science assessments. this was achieved Complexity had varying levels of difficulty 3 2 each 1 was through 3 an 2 online 1 survey 3 for 2stakeholders 1 3 in 2 science 1 measured as a proportion of total number of AS units community Depending 38 on ir 35 expertise, 66 participants question parts containing mamatics. it was not answered survey for biology, chemistry or physics AS unit measured 3 against number of marks a-level assessment. participants were chosen in A2 4. units appropriateness 4 5 of mamatics We three 11groups; 12 teaching 76 7profession; higher 5education; A2 unit looked 6 at wher answer required 14 scientific 38 62professional 38bodies. 62 an online 71survey 29 was completed 74 26by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Theory papers only this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from Practical number papers of question only parts 15containing 6 26 mamatics industry were 4 also 6consulted 66 more 35 generally but 67as most 34 science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full at graduate level rar than directly referring to a-level. Table suite of 12b: 21 Percentage examinations of papers Level of aqa, 1, 2 ccea, 3 complexity type calculations in chemistry A-level, calculated edexcel, ocr as a percentage WJec for ir of respective total subjects number of question parts in a complete A-level at a two-day workshop. examination papers included all ory papers (Units 1, A2, 4 5) B C D E experimental practical papers (Units 3 6). Complexity calculations were based on assumption that ory papers AS units make 1 up 8% 2 of complete 2 a-level experimental AS unit 3 practical papers 9 21 remaining 19 2% A2 units A2 unit Theory papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 15 Level revised 4 mamatics was omitted Gcses. from findings as very few examination papers included questions of this complexity. Practical papers only SCORE Maths in science report 39

40 ExEcutivE Table 12c: Percentage summary of Level 1, 2 3 complexity type calculations in chemistry A-level, weighted to take account of ory component (8%) practical component (2%) of mamatics enables students to underst A-level assessments describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting A B C D E subject s analytical nature. to explore wher re was any Complexity evidence for this concern, 3score 2 investigated type, Theory extent papers difficulty only of mamatical 13 questions 25 within 8 science (8%) a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry Practical papers only physics specifications are not assessed. those that (2%) are assessed are covered repeatedly often at a lower level A-level than required. total this is likely 1 to have 19 an 28 impact on 9 (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively Figure 15a: to stem Percentage higher education of mamatical employment. in addition, findings show a disparity way aims Figure 15c: Percentage of mamatical question parts identified as containing question parts identified as containing mamatics is assessed across different awarding Level 1, Level 2 Level 3 complexity type score s Level 1, overall Level objective 2 Level for this 3 project complexity was to type organisations. score recommends that re is a review calculations in a complete A-level for each of gar calculations evidence in on practical type, extent examination difficulty papers of of mamatical requirements for each of sciences five awarding organisations mamatics for chemistry required A-level to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is TOTAL assessed within sciences to was being appropriately PRACTICAL met by assessments. ensure parity across Level 3 system. Level 2 Level 1 work did not compare Level 3 Level mamatical 2 Level 1 requirements 6 between physics, 6 chemistry biology as it is accepted Background se will differ between disciplines. 5 5 re has 4 been growing concern across science 4 findings aim to provide score with evidence to community about mamatical dem of science 3 inform 3 development of policy on type, extent qualifications, specifically that Gcse a-level science 2 difficulty 2 of mamatics in criteria qualifications are not meeting needs of students in 1 assessments 1 for a-levels in biology, chemistry way y assess analytical nature of science. physics. project also supports score s work on A B C D E A B C D E in 29 score published evidence on Gcse science how examinations system should operate to ensure Awarding Organisations Awarding Organisations examination papers which reported a wide variation in science qualifications are fit for purpose also its amount of mamatics assessed across awarding organisations Figure 15b: Percentage confirmed that of mamatical use of mamatics work on improving coherence between sciences mamatics. Percentage of question parts in a complete A level within question context parts of identified science was examined containing a very limited Level way. 1, Level score 2 organisations Level 3 complexity felt that this was type unacceptable. calculations mamatics in ory examination is integral to papers teaching for chemistry learning of A-level sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately THEORY represented in biology, chemistry Level 3 physics Level 2 curricula Level 1 ir assessments. 6 Percentage of question parts in a complete A level 5 to provide furr evidence to support se 4 concerns, score set up this project to investigate 3 mamatics found in 21 science assessments 2 at a-level across unitary awarding organisations in engl, Wales 1 norrn irel. A B C D E Awarding Organisations Percentage of question parts in a complete A level in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 4 SCORE Maths in science report

41 CONTEXT methodology The question project was parts designed that contained three phases. mamatics within first was a full to establish suite of A-level nature examinations of mamatics were classified assessed within as Level 1, biology, Level chemistry 2 or Level 3, physics with Level 1 a-level most examinations familiar context. in 21. Level full 1 suite is a of context typically examinations met papers through from aqa, learning ccea, programme, edexcel, Level ocr 2 is WJec a context were that analysed contains using some four novel average groups for comprised ory only practising practical a-level only teachers, papers. These teachers figures with experience are calculated in curriculum as a percentage research of development question parts individuals identified working as containing for awarding mamatics. organisations as Table markers, 13b question shows se writers percentages or examiners. of stardisation total number exercises of question were employed parts throughout Table 13c takes analysis into verify account reliability weighting of judgements of ory within papers (8%) across subject practical expert papers groups. (2%) to calculate aspects measures that Level follow: 3 is an unfamiliar context unlikely average percentage of Level 1, 2 3 context second phase aimed to measure coherence to have been met before. Appendix 5c shows an in a complete A-level. Figure 16a illustrates 1. type of mamatics. mamatical areas between teaching learning of mamatics example of levels of familiarity. percentage of Level 1, 2 3 context calculations assessed were categorised against stated sciences. re is an assumption that in a complete A-level for each of five awarding mamatical requirements for biology, chemistry mamatical concepts used to access sciences Table 13a shows percentage of mamatical organisations. Figures 16b 16c illustrate se physics respectively 1. are first taught within a mamatical context, i.e. within question parts classified as Level 1, 2 or 3 percentages for ory only practical only mamatics curriculum. project compared context 2. within extent each of A-level mamatics. unit as proportion an papers respectively. mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions Table a 212 mamatics Gcse specification 3. this work that 13a: required Percentage mamatics. of Level 1, 2 3 context-type calculations in chemistry A-level, calculated as a percentage of question parts identified was carried as containing out by a researcher mamatics by a mamatics 3. difficulty of mamatics. this was measured teacher. against 3 criteria: number of steps in a A B Caim of third phase D was to determine E nature calculation, familiarity of context of mamatics that community would like to see Context complexity of question. 3 2 each 1 category in a-level science assessments. this was achieved AS units had varying 1 levels 2 of difficulty each 1 was 2 99 through an online 1survey for stakeholders 1 in science 1 measured as a proportion of total number of AS unit 3 1 1community. Depending 1 on ir expertise, 1 participants question parts containing mamatics. it was not answered survey for biology, chemistry or physics A2 units measured 4 against 5 number 7 of marks a-level assessment. participants were chosen in A2 4. unit appropriateness 6 of mamatics. 1We three groups; 33 teaching 66 profession; 1 higher education; 1 Theory looked papers at wher only answer 4required 97 scientific 1 1professional bodies. 1 an online survey 1 was completed 1 by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Practical papers only this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from number of question parts containing mamatics. industry were also consulted more generally but as most science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes Table of three 13b: sciences. Percentage each of group Level analysed 1, 2 full 3 context-type calculations in chemistry A-level, at graduate level rar than directly referring to a-level. calculated suite of 21 as examinations a percentage papers of of aqa, total ccea, number of question parts in a complete A-level edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination A papers included B C D E all ory papers (Units 1, 2, 4 5) Context experimental practical papers (Units 3 6). calculations AS units 1 were based 2 on assumption 41 that ory papers AS unit make 3 up 8% of complete a-level 49 experimental practical papers remaining 2% 2. A2 units A2 unit Theory papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. Practical papers only SCORE Maths in science report 41

42 ExEcutivE Table 13c: Percentage summary of Level 1, 2 3 context-type calculations in chemistry A-level, weighted to take account of ory component (8%) practical component (2%) of mamatics enables students to underst A-level assessments describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting A B C D E subject s analytical nature. to explore wher re was any Context evidence for this concern, 3score 2 investigated type, Theory extent papers difficulty only of mamatical 1 questions 36 within science (8%)) a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry Practical papers only physics specifications are not assessed. those that (2%) are assessed are covered repeatedly often at a lower level A-level than required. total this is likely to have 1 an 46 impact on 1 (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively Figure 16a: to stem Percentage higher education of mamatical employment. question in addition, findings show a disparity in way aims Figure 16c: Percentage of mamatical question parts identified as containing calculations set parts identified as containing calculations set mamatics is assessed across different awarding in a Familiar, with Some Novel Aspects, score s in a Familiar, overall with objective Some for this Novel project Aspects, was to organisations. score recommends that re is a review Unfamiliar context in a complete A-level for gar Unfamiliar evidence context in type, practical extent examination difficulty of of mamatical requirements for each of sciences each of five awarding organisations mamatics papers for chemistry required to access A-level sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is TOTAL assessed within sciences to was being appropriately PRACTICAL met by assessments. ensure parity across Unfamiliar system. Some Novel Familiar work did not compare Unfamiliar mamatical Some Novel Familiar requirements 6 between physics, 6 chemistry biology as it is accepted Background se will differ between disciplines. 5 5 re has 4 been growing concern across science 4 findings aim to provide score with evidence to community about mamatical dem of science 3 inform 3 development of policy on type, extent qualifications, specifically that Gcse a-level science 2 difficulty 2 of mamatics in criteria qualifications are not meeting needs of students in 1 assessments 1 for a-levels in biology, chemistry way y assess analytical nature of science. physics. project also supports score s work on A B C D E A B C D E in 29 score published evidence on Gcse science how examinations system should operate to ensure Awarding Organisations Awarding Organisations examination papers which reported a wide variation in science qualifications are fit for purpose also its amount of mamatics assessed across awarding organisations Figure 16b: Percentage confirmed of that mamatical use of mamatics question work on improving coherence between sciences mamatics. Percentage of question parts in a complete A level within parts identified context of as science containing was examined calculations in a very limited set in way. a Familiar, score organisations with Some felt Novel that Aspects, this was unacceptable. Unfamiliar mamatics context is in integral ory to examination teaching papers learning for of chemistry sciences, A-level offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately THEORY represented in biology, chemistry Unfamiliar physics Some curricula Novel Familiar ir assessments. 6 Percentage of question parts in a complete A level 5 to provide furr evidence to support se 4 concerns, score set up this project to investigate 3 mamatics found in 21 science assessments 2 at a-level across unitary awarding organisations in engl, Wales 1 norrn irel. A B C D E Awarding Organisations Percentage of question parts in a complete A level in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 42 SCORE Maths in science report

43 methodology APPROPRIATENESS addition groups to comprised mamatical practising skill it a-level was classified teachers, as project was designed in three phases. some teachers scientific with experience comprehension in curriculum research question parts APPLICATION first was to establish nature of mamatics where development all marks required individuals scientific working for comprehension awarding Judgements were made as to wher content assessed within biology, chemistry physics were organisations classified as markers, scientific question comprehension. writers or examiners. of question part reflected how mamatics a-level examinations in 21. full suite of Appendix stardisation 5d shows exercises an example were employed of each throughout category. is used real world in scientific context. examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within All of question parts with mamatics were Table ocr WJec were analysed using four across 14a subject shows expert percentage groups. of mamatical judged to reflect an appropriate way in which question parts classified as all marks (S), some mamatics measures that could follow: be used in a real scientific second phase aimed to measure coherence marks (B) or no marks (M) requiring scientific context. 1. type of mamatics. mamatical areas between teaching learning of mamatics comprehension within each A-level unit as an assessed were categorised against stated sciences. re is an assumption that average for ory only practical only papers. STRUCTURAL OR TAGGED ON mamatical requirements for biology, chemistry mamatical concepts used to access sciences These figures are calculated as a percentage One of measures was to ascertain wher physics respectively 1. are first taught within a mamatical context, i.e. within of question parts identified as containing mamatics was a structural part of question mamatics curriculum. project compared 2. extent of mamatics. proportion mamatics. Table 14b shows se percentages or wher mamatics was purely tagged mamatical requirements for sciences at a-level of parts within a paper that of total number of question parts Table 14c on to question. In all of question parts with with mamatics curriculum prior to Key stage 5 included mamatics was measured was takes into account weighting of ory papers mamatical content mamatics was judged using current national curriculum level descriptions proportion of marks within se questions (8%) practical papers (2%) to calculate to be a structural part of question. a 212 mamatics Gcse specification 3. this work that required mamatics. average percentage of mamatical question was carried out by a researcher by a mamatics MATHEMATICS SKILLS OR SCIENTIFIC parts where all marks, some marks or no marks 3. difficulty of mamatics. this was measured teacher. COMPREHENSION require scientific comprehension in a complete against 3 criteria: number of steps in a Mamatical question parts within a full suite of A-level. aim Figure of third 17a phase illustrates was to determine percentage nature of calculation, familiarity of context A-level examinations were measured against mamatical of mamatics question that community parts where would all, like some to see complexity of question. each category extent to which scientific comprehension was no in a-level marks science require assessments. scientific comprehension this was achieved in a had varying levels of difficulty each was required to achieve full marks. If a question part complete through an A-level online survey for each for stakeholders of five awarding science measured as a proportion of total number of required no scientific comprehension to acquire organisations. community. Depending Figures on 17b ir expertise, 17c illustrate participants se question parts containing mamatics. it was not full marks it was classified as no scientific percentages answered survey for ory for biology, only chemistry practical or physics only measured against number of marks. comprehension (mamatical skill only), if some papers a-level assessment. respectively. participants were chosen in of 4. marks appropriateness required scientific of mamatics. comprehension We in looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from Table number 14a: Percentage of question parts of mamatical containing mamatics. question parts industry classified were also as consulted all marks more (S), generally some but marks as most (B) science-related industries employ at a graduate level a subject no expert marks group (M) was requiring established scientific for each comprehension in chemistry A-level, calculated as a percentage ir comments tended to focus more on outcomes of three sciences. of question each group parts analysed identified full as containing mamatics at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for Air respective subjects B at Context a two-day workshop. examination S B papers M included S B M C S B M D S B M E S B M all ory papers (Units 1, 2, 4 5) AS units experimental practical papers (Units 3 6) calculations AS unit 3 were based on assumption that ory 67 papers make up 8% of complete a-level A2 units experimental practical papers remaining 2% A2 unit Theory papers only Practical papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 43

44 ExEcutivE Table 14b: Percentage summary of mamatical type question parts where all marks (S), some marks (B) or no marks (M) require scientific comprehension in chemistry A-level, calculated as a mamatics enables students to underst percentage of total number of question parts in a complete A-level describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical nature. to explore A wher re B was any Context evidence for this concern, Sscore B investigated M S B type, extent difficulty of mamatical questions within AS units science a-levels. findings show that a large number of mamatical AS unit 3 requirements listed in 32 biology, 17 chemistry 18 A2 physics units 4 specifications 5 are 51 not assessed. those 54 that 1 are assessed are covered repeatedly often at a lower A2 unit level than required. this is likely to have an impact on Theory way that papers subjects only are taught 45 1 refore 57on 1 M 9 9 C S B M 4 4 D S B M E S B M students ability to have necessary skills to progress Practical papers only effectively to stem higher education employment. in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. Table 14c: Percentage score recommends of mamatical that re is type a review question gar parts evidence where on all marks type, extent (S), some difficulty marks of (B) of no mamatical marks (M) requirements scientific for each of comprehension sciences in mamatics chemistry required A-level, to access weighted sciences to take in account current at of a-level ory that component a framework (8%) is developed practical to regulate component a-level (2%) specifications of A-level to establish assessments wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. A B work C did not compare D mamatical Erequirements between physics, chemistry biology as it is accepted Context S B M S B M S B M S B M S B M Background se will differ between disciplines. Theory papers only re has been growing concern across science (8%) findings aim to provide score with evidence to community about mamatical dem of science inform development of policy on type, extent qualifications, Practical papers specifically only that Gcse 7 3a-level science difficulty of mamatics in criteria qualifications (2%) are not meeting needs of students in assessments for a-levels in biology, chemistry A-level way y total assess analytical 36 nature 7 3of science physics project 1 also 27 supports 12 2score s 42 work 6 on 4 in 29 score published evidence on Gcse science examination papers which reported a wide variation in Figure amount 17a: of Percentage mamatics assessed of mamatical across awarding organisations question parts confirmed requiring that scientific use of mamatics how examinations system should operate to ensure science qualifications are fit for purpose also its work Figure on 17b: improving Percentage coherence of mamatical between sciences question mamatics. parts requiring scientific within comprehension context of in science addition was to examined mamatical in a very comprehension in addition to mamatical in project, we looked across all assessments at limited skill to way. achieve score all organisations marks, some felt that of this was marks skill to achieve all marks, some of marks a-level for a given year, including both experimental unacceptable. or no marks mamatics in a complete is integral A-level to for teaching each of or no marks in ory examination papers for practical examination papers. learning five awarding of sciences, organisations offers a valuable aid chemistry A-level in understing describing scientific phenomena; as such it should be appropriately TOTAL represented in THEORY biology, chemistry Scientific physics Some curricula Scientific ir Comprehension Comprehension assessments. Percentage of question parts in a complete A level 6 5 to provide furr evidence to support se 4 concerns, score set up this project to investigate 3 mamatics found in 21 science assessments at a-level across 2 unitary awarding organisations in engl, Wales 1 norrn irel. A B C D E Awarding Organisations No Scientific Comprehension Percentage of question parts in a complete A level Scientific Comprehension Some Scientific Comprehension A B C D E Awarding Organisations No Scientific Comprehension 44 SCORE Maths in science report

45 Figure methodology 17c: Percentage of mamatical question project parts was designed requiring in three scientific phases. comprehension first was to establish in addition nature of to mamatical mamatics skill assessed to achieve within all biology, marks, chemistry some of physics marks or a-level no marks examinations practical in 21. examination full suite of papers for examinations chemistry papers A-level from aqa, ccea, edexcel, ocr WJec were analysed using four measures that follow: PRACTICAL 1. type Comprehension of mamatics. Comprehension mamatical Comprehension areas 6 assessed were categorised against stated 5 mamatical requirements for biology, chemistry physics 4 respectively 1. Percentage of question parts in a complete A level 3 Scientific Some Scientific No Scientific 2. extent of mamatics. proportion 2 of question parts within a paper that 1 included mamatics was measured as was proportion Aof marks B within C se D questions E that required mamatics. Awarding Organisations groups PHASE comprised 2 CHEMISTRY practising a-level A-LEVEL teachers, IN COMPARISON teachers with experience WITH in GCSE curriculum MATHEMATICS research AND development NATIONAL individuals CURRICULUM working for LEVEL awarding DESCRIPTORS organisations as markers, question writers or examiners. stardisation exercises were employed throughout Two comparisons were used to establish analysis to verify reliability of judgements within coherence of chemistry A-level across subject expert groups. mamatics accessed up to Key Stage 4: comparison second phase with National aimed to measure Curriculum level coherence descriptors between teaching comparison learning with of mamatics 212 mamatics sciences. GCSE re specification. is an assumption These that comparisons mamatical concepts are displayed used to in access Table 15. sciences are first taught within a mamatical context, i.e. within mamatics curriculum. project compared mamatical requirements for sciences at a-level with mamatics curriculum prior to Key stage 5 using current national curriculum level descriptions a 212 mamatics Gcse specification 3. this work was carried out by a researcher by a mamatics teacher. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see Table 15: complexity Comparison of question. of mamatical each category requirements in a-level for chemistry science assessments. A-level with this mamatics was achieved found had in varying National levels of Curriculum difficulty each Level was Descriptors through GCSE an online mamatics survey for stakeholders specification in science measured as a proportion of total number of community. Depending on ir expertise, participants Mamatical question parts requirements containing mamatics. as it Corresponding was not answered Found survey in for biology, Comment chemistry or physics listed measured in Chemistry against number A-level of marks. NC level(s) for a-level Edexcel assessment. GCSE participants were chosen in specification 4. appropriateness of mamatics. We mamaticsthree groups; specification teaching profession; higher education; looked at wher answer required scientific professional Foundation bodies. an (F) online survey was completed by comprehension in addition to mamatical skill. 97 participants Higher across (H) three groups (27 for biology; this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from 1 Arithmetic number of question numerical parts containing mamatics. industry Fwere also Hconsulted more generally but as most computation: science-related industries employ at a graduate level a subject expert group was established for each (a) recognise use expressions in L5 (decimals) ir comments ü tended ü to focus Decimals more on outcomes of three sciences. each group analysed full decimal stard form; to L8 (stard at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, form) edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers (b) use make ratios, up fractions 8% of complete a-level L5 (AS) to L6 (A2) experimental percentages; practical papers remaining 2% 2. û ü ü ü Stard Form: this will be taken off new 212 Foundation level specification Percentages: reverse ü ü Ratios ü ü Fractions percentages are exclusive to Higher level 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 (c) make estimates of results of L5 to 6 (NB ü ü a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete calculations a-level assessment (without marks using from a calculator); practical experimental always have papers a (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation calculator) but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 45

46 ExEcutivE Table 15: continued summary mamatics enables students to underst (d) use calculators to find use power, L7 to EP û û Power functions describe many scientific phenomena yet re is concern exponential logarithmic functions ( x n, (power that science assessments at a-level are not reflecting 1/x, x, log subject s analytical l x, e x, log nature. to e x ); exponentials explore wher re was unlikely to be û ü any evidence for this concern, score investigated Degrees found). type, extent difficulty of mamatical questions within Theory of science a-levels. findings show that a large number of logs is EP. In mamatical requirements listed in biology, chemistry ü ü context pupils Radians appear in physics specifications are not assessed. those that calculate ph AS level mamatics are assessed are covered repeatedly often at a lower using calculator specification level than required. this is likely to have an impact on minus log way that subjects are taught refore on button or shift ü ü Exponential functions students ability to have necessary skills to progress log button, so effectively to stem higher education employment. re are some in addition, findings show a disparity in way aims mamatical mamatics is assessed across different awarding û û score s overall objective for Logarithmic this project was functions to decisions to be organisations. score recommends that re is a review gar evidence on type, extent difficulty of made. of mamatical requirements for each of sciences mamatics required to access sciences in current at (e) a-level +, -, x,. that a framework is developed to regulate L1 to L7 (due a-level üspecifications ü to establish wher this way mamatics is assessed within sciences to number to of was being appropriately met by assessments. ensure parity across system. decimal places work did not compare mamatical requirements significant between physics, chemistry biology as it is accepted Background figures) se will differ between disciplines. re 2 Hling has been data: growing concern across science NC levels findings F aim to Hprovide score Comment with evidence to community about mamatical dem of science (a) use an appropriate number of L8 inform ü development ü of policy on type, extent qualifications, specifically that Gcse a-level science significant figures; difficulty of mamatics in criteria qualifications are not meeting needs of students in assessments for a-levels in biology, chemistry (b) way find y arithmetic assess means; analytical nature of science. L7 to EP (involves ü ü physics. project also supports score s work on % calculation in 29 score published evidence on Gcse science how examinations system should operate to ensure inverse means) examination papers which reported a wide variation in science qualifications are fit for purpose also its (c) amount construct of mamatics interpret assessed frequency across awarding L4 to L6 (L4 work on üimproving ü coherence Tables, between frequency sciences organisations tables diagrams, confirmed bar that charts use of mamatics collect record mamatics. tables, diagrams, bar within histograms; context of science was examined in a discrete very data, L6 charts in project, we looked across all assessments at limited way. score organisations felt that this was for continuous a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching data) practical examination papers. learning of sciences, offers a valuable aid û ü Histograms in understing describing scientific phenomena; (d) use an appropriate number of L5 ü ü Students are expected as such it should be appropriately represented in decimal places. biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. to underst how to round off to an appropriate number of decimal places 46 SCORE Maths in science report

47 Table methodology 15: continued project was designed in three phases. first 3 Algebra: was to establish nature of mamatics NC levels assessed (a) underst within biology, use chemistry symbols: =, physics L5 to L7 a-level <, <<, examinations >>, >,, ~, in μ; 21. full suite of examinations papers from aqa, ccea, edexcel, groups comprised practising a-level teachers, teachers with experience in curriculum research development F Hindividuals Comment working for awarding organisations ü as markers, ü question =, <,>,~ writers or examiners. stardisation exercises were employed throughout analysis to verify reliability of judgements within ocr WJec were analysed using four across subject expert groups. û û <<, >> These symbols measures that follow: second phase aimed to measure are not used coherence in 1. type of mamatics. mamatical areas assessed were categorised against stated between teaching learning mamatics of mamatics GCSE or sciences. re is an A-level assumption that mamatical requirements for biology, chemistry mamatical concepts used to access sciences û ü physics respectively 1. are first taught within a mamatical context, i.e. within mamatics û curriculum. û μ appears project in compared A-level 2. extent of mamatics. proportion mamatical requirements for mamatics sciences at a-level of question parts within a paper that with mamatics curriculum specification prior to Key stage 5 included mamatics was measured as was (b) change proportion of subject marks of an within equation; se questions L8 using ü current national ü curriculum In Foundation level descriptions level a 212 mamatics Gcse that required mamatics. students specification are required 3. this work to was carried out by a researcher change by a mamatics subject of a 3. difficulty of mamatics. this was measured teacher. formula. against 3 criteria: number of steps in a aim of third phase was In to Higher determine level this nature calculation, familiarity of context of mamatics that community includes would cases like where to see complexity of question. each category in a-level science assessments. this subject was achieved is on both had varying levels of difficulty each was through an online survey for stakeholders sides of in original science measured as a proportion of total number of community. Depending on ir formula expertise, or where participants question parts containing mamatics. it was not answered survey for biology, power chemistry of a subject or physics measured against number of marks. a-level assessment. participants appears. were chosen in (c) 4. substitute appropriateness numerical of values mamatics. into We L8 to EP algebraic looked equations wher using answer appropriate required scientific units comprehension for physical quantities; in addition to mamatical skill. three groups; ü teaching ü profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from (d) solve simple algebraic equations; L7 to L8 ü ü number of question parts containing mamatics. industry were also consulted more generally but as most (e) use logarithms in relation to EP (see 1(d) science-related û industries û employ at a graduate level a subject expert group was established for each quantities which range over several above) ir comments tended to focus more on outcomes of three sciences. each group analysed full orders of magnitude. at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, edexcel, 4 Graphs: ocr WJec for ir respective subjects NC level at (a) a translate two-day workshop. interpret examination information papers included L5 to L6 all between ory graphical, papers (Units numerical 1, 2, 4 5) experimental algebraic forms; practical papers (Units 3 6). F ü H ü Comment calculations were based on assumption that ory (b) plot two variables from experimental L6 ü ü papers make up 8% of complete a-level or or data; experimental practical papers remaining 2% 2. (c) underst that y = mx + c L8 ü ü represents a linear relationship; (d) determine slope intercept of a linear graph; EP ü ü slope 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit û 1, 2, 4 ü5) make up 8% intercept of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, (e) question calculate parts rar rate than of marks change were from used in a calculation but we maintained 8:2 weighting. 3 graph edexcel showing 212 a specification a linear relationship; was used for purpose of analysis as it was considered representative of typical out a content gradient found in revised mamatics Gcses. EP ü ü Taken to mean working SCORE Maths in science report 47

48 ExEcutivE Table 15: continued summary mamatics enables students to underst (f) draw use slope of a tangent EP û û Taken out of describe many scientific phenomena yet re is concern to a curve as a measure of rate of GCSE mamatics that science assessments at a-level are not reflecting change; specification subject s analytical nature. to explore wher re was any (g) evidence interpret for a spectrum. this concern, score investigated L6 to L8 (involves type, extent difficulty of mamatical questions identifying within science a-levels. findings show that a large number peaks, of reading mamatical requirements listed in biology, chemistry off scales, physics specifications are not assessed. those interpreting that data are assessed are covered repeatedly often at a lower using tables. level than required. this is likely to have an impact L6 on compares to way that subjects are taught refore reading on scatter students ability to have necessary skills to progress diagrams effectively to stem higher education employment. L8 compares to in addition, findings show a disparity in way interpreting data aims ü ü While a spectrum is not in mamatics specification, skills of interpreting a spectrum are mamatics is assessed across different awarding from it) score s overall objective for this project was to organisations. 5 Geometry score Trigonometry: recommends that re is NB a review shapes of gar evidence F on H type, Comment extent difficulty of of mamatical requirements for each of molecules sciences relates mamatics required to access sciences in current at a-level that a framework is developed to regulate to drawing 2D a-level specifications to establish wher this way mamatics is assessed within sciences 3D to shapes was being appropriately met by assessments. ensure parity across system. Background although some work did not compare mamatical requirements different notations between physics, chemistry biology as it is accepted are used in se will differ between disciplines. re has been growing concern across science chemistry findings aim to provide score with evidence to community about mamatical dem of mamatics. science inform development of policy on type, extent qualifications, specifically that Gcse a-level Mamatics science difficulty of mamatics in criteria qualifications are not meeting needs of students can help in assessments for a-levels in biology, chemistry way y assess analytical nature of science. understing, physics. project also supports score s work on but se in 29 score published evidence on Gcse science how examinations system should operate to ensure questions can examination papers which reported a wide variation in science qualifications are fit for purpose also its be done without amount of mamatics assessed across awarding work on improving coherence between sciences mamatics. organisations confirmed that use of mamatics mamatics. within a) appreciate context angles of science was shapes examined in in a L6 ü ü very in project, we looked across all assessments at limited regular way. 2-D score 3-D organisations structures; felt that this was a-level for a given year, including both experimental unacceptable. b) visualise mamatics represent is 2-D integral to teaching L6 ü ü practical examination papers. 3-D learning forms of including sciences, two-dimensional offers a valuable aid in representations understing of describing 3-D objects; scientific phenomena; as such it should be appropriately represented in c) underst symmetry of 2-D L6 ü ü biology, chemistry physics curricula ir 3-D shapes assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 48 SCORE Maths in science report

49 3.2.3 methodology PHASE 3 SURVEY FINDINGS Overall, groups participants comprised were practising concerned a-level teachers, about project was designed in three phases. teachers levels with of mamatical experience in curriculum content in research chemistry TYPE OF MATHEMATICS ASSESSED first was to establish nature of mamatics A-levels, development with many individuals feeling working that students for awarding were AT A-LEVEL CHEMISTRY assessed within biology, chemistry physics being organisations misled as about markers, mamatical question writers requirements or examiners. In Part A respondents were asked to consider a-level examinations in 21. full suite of of stardisation chemistry as exercises a subject. were Concern employed was throughout also spread of mamatical content areas assessed examinations papers from aqa, ccea, edexcel, expressed analysis to verify that downgrading reliability of judgements mamatical within within chemistry A-level. Figure 18 illustrates ocr WJec were analysed using four requirements across subject would expert also groups. lead to a restriction in percentages of respondents that considered measures that follow: chemistry content that could be assessed. Algebra, second phase aimed to measure coherence spread to be good, acceptable (key mamatical problem solving, calculus, data manipulation 1. type of mamatics. mamatical areas between teaching learning of mamatics areas were assessed), average (limited variation in units were all mentioned as areas with which many assessed were categorised against stated sciences. re is an assumption that type of mamatics) poor (restricted amount chemistry students struggled. mamatical requirements for biology, chemistry mamatical concepts used to access sciences of mamatics assessed many times). physics respectively 1. are first taught within a mamatical context, i.e. within 63% of repondents felt that awarding organisations mamatics curriculum. project compared 2. extent of mamatics. proportion should use a framework to ensure a broad spread Figure 18: Opinions from chemistry mamatical requirements for sciences at a-level of question parts within a paper that of mamatical requirements are assessed online survey respondents on spread with mamatics curriculum prior to Key stage 5 included mamatics was measured as was 58% felt that all requirements should be assessed of mamatical content areas within a using current national curriculum level descriptions proportion of marks within se questions over a two- or three-year cycle of A-levels to chemistry A-level a 212 mamatics Gcse specification 3. this work that required mamatics. ensure y are taught. 63% also felt that if areas was carried out by a researcher by a mamatics were not assessed n it would mean y would 3. difficulty of mamatics. this was measured teacher. not be taught. Very few (16%) felt that only key against 3 criteria: number of steps in a The Key mamatical requirements aim of should third phase be assessed was to determine as opposed nature calculation, familiarity of content context areas were assessed to of mamatics all requirements. that community would like to see complexity of question. each category A restricted amount of in a-level science assessments. this was achieved had varying levels of difficulty mamatical each content was areas In through Part B, an after online receiving survey for stakeholders findings from in seemed to be assessed science measured as a proportion of many times total number of analysis, community. three-quarters Depending on of ir respondents expertise, participants felt it was question parts containing mamatics. There was a good it spread was of not unacceptable answered survey that essential for biology, mamatical chemistry or content physics different mamatical content measured against number of marks. areas being assessed areas a-level were assessment. hardly or not participants at all assessed. were chosen The quarter in 4. appropriateness of mamatics. We that three found groups; it acceptable teaching profession; was almost higher exclusively education; There was not enough variation in type of mamatical looked at wher answer required scientific made professional up of bodies. teachers. an online When survey comparing was completed Figure 13 by content being assessed comprehension in addition to mamatical skill. 97 participants Figure 19 it across is clear re three is groups a mismatch (27 for between biology; this was measured as a proportion of total mamatical 38 for chemistry; content 32 areas for physics). that are participants assessed from number of question parts containing mamatics. industry those were that also consulted science more community generally would but as like most Participants were also asked to comment on to science-related be assessed industries (for example, employ recognise at a graduate level use areas a subject of mamatics expert group was y established would like for to each feature expressions ir comments in tended decimal to focus stard more on form). outcomes More highly of three in assessment, sciences. each a little group or not analysed at all. These full positively, at graduate re level were rar some than directly areas that referring to science a-level. results suite of are 21 displayed examinations in Figure papers 19. of aqa, Participants ccea, community thought should feature highly did in were edexcel, asked ocr if re WJec were for any ir or respective areas of subjects fact feature highly across all awarding organisations mamatics, a two-day workshop. not listed examination in requirements papers included that (for example, substituting numerical vales into y all felt ory should papers be included (Units 1, 2, in 4 assessments. 5) algebraic equations using appropriate physical Content experimental areas suggested practical papers by more (Units than 3 one 6). quantities). Most of comments related to this respondent calculations were: based on assumption that ory section of survey indicated that missing papers calculus make (mentioned up 8% of by 2% complete of respondents) a-level topics from assessment were central experimental logarithms practical papers remaining 2% 2. to chemistry. statistics first order, second order equations quadratic equations 1 powers five awarding / manipulation organisations use of indices mamatical probability. requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 49

50 ExEcutivE Figure 19: Mamatical summary requirement areas that chemistry survey respondents would like to mamatics feature highly enables in assessment, students to underst a little in assessment or not at all describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical Feature nature. Highlyto explore Feature wher a Little re Feature was Not At All any evidence 4 for this concern, score investigated type, extent 35 difficulty of mamatical questions within science a-levels. 3 findings show that a large number of mamatical requirements listed in biology, chemistry 25 physics specifications are not assessed. those that 2 are assessed are covered repeatedly often at a lower 15 level than required. this is likely to have an impact on way that 1 subjects are taught refore on students ability 5 to have necessary skills to progress effectively to stem higher education employment. 1a 1b 1c 1d 1e 2a 2b 2c 2d in addition, findings show a disparity in way 3a 3b 3caims 3d 3e 4a 4b 4c 4d 4e 4f 4g 5a 5b 5c Mamatical Requirements for Chemistry A-Level mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review of mamatical requirements for each of sciences at Furrmore, a-level that over a framework two-thirds is felt developed it was to regulate inappropriate way mamatics that a is few assessed mamatical within requirements sciences to ensure were assessed parity across repeatedly, system. rar than a spread of skills being assessed. While re was broad Background agreement that many key skills would should gar evidence on type, extent difficulty of mamatics required to access sciences in current a-level Respondents specifications were told to that establish in analysis wher it this was was found being that appropriately percentage met of by marks assessments. that required work mamatics did not compare varied across mamatical awarding organisations requirements between physics, 24% chemistry 43%. 6% biology of respondents as it is accepted se thought will differ lower between limit of marks disciplines. was too low re be assessed has been repeatedly growing concern as y across are linked science to re was no consensus reached on higher limit. findings aim to provide score with evidence to community different content about areas mamatical of chemistry, dem y of felt science that inform development of policy on type, extent qualifications, re was an specifically absence of that some Gcse or a-level important science No consensus was found on wher difficulty of mamatics in criteria qualifications skills re are not was meeting a danger that needs of repetition students in mamatics in ory papers assessments for a-levels in biology, chemistry encourages way y assess more rote analytical learning nature rar of than science. a deeper mamatics in practical papers should be understing of material. It was felt that a physics. different. However, project also re supports was some score s consensus work on in broader 29 score range of published mamatical evidence skills on Gcse needed science to be examination assessed to papers check which more reported in-depth a wide understing, variation to give amount a more of mamatics meaningful assessed assessment across of awarding students organisations skills to show confirmed skills that of use more of mamatics able how when asked examinations ir reasons system for should ir operate opinions. to ensure It was science widely agreed qualifications that some are fit types for purpose of mamatics also its work were on more improving suitable for coherence use in between practical sciences papers, mamatics. for example, data hling, processing within students. context Many felt of science that a chemistry was examined examination a very experimental results, measurement in-depth in project, we looked across all assessments at limited should way. only score be concerned organisations with felt chemistry that this content was analysis that assessments should draw on a-level for a given year, including both experimental unacceptable. that mamatics is should integral be to assessed teaching in appropriate mamatics to support chemistry practical examination papers. context learning of chemistry. sciences, offers a valuable aid content. It was thought to be important across in understing describing scientific phenomena; as EXTENT such it should OF MATHEMATICS be appropriately represented in biology, In Part A chemistry 56% of respondents physics curricula felt that ir amount assessments. of mamatics in paper was not enough whole course to use apply appropriate mamatics skills to appreciate chemistry. It was felt that mamatical content should not be stipulated for inclusion in eir ory or practical to adequately prepare for progression to higher papers as that would lead to convoluted questions. to provide furr evidence to support se education in chemistry or a related subject. However, Ors felt that linking certain mamatical concerns, score set up this project to investigate after viewing findings of analysis, majority concepts to only one type of paper could lead mamatics found in 21 science assessments (88%) thought that percentage of question parts to compartmentalisation of mamatics at a-level across unitary awarding organisations in containing mamatics was appropriate. ors felt mamatics should be found in both engl, Wales norrn irel. types of paper so that students could apply ir knowledge in a variety of settings. Number of Respondents 5 SCORE Maths in science report

51 DIFFICULTY methodology OF MATHEMATICS appropriate. groups comprised When considering practising a-level a set of teachers, questions, In Part project A 1% was designed of representatives in three phases. from higher two teachers thirds with felt experience that questions in curriculum were research appropriate education first was to felt establish that it did nature not matter of mamatics if level of in development terms of complexity individuals while working remaining for awarding third difficulty assessed was within perceived biology, to chemistry go up due to physics A-levels felt organisations it was too as easy. markers, In Part question B, when writers respondents or examiners. containing a-level examinations more mamatics, in 21. while full suite only of 71% of were stardisation told that exercises vast majority were employed of questions throughout across respondents examinations papers overall from agreed aqa, with ccea, this. edexcel, awarding analysis to organisations verify reliability required of judgements Level 1 within Level ocr WJec were analysed using four 2 across complexity subject (i.e. expert use of groups. straightforward familiar In Part A, when asked about difficulty in terms measures that follow: concepts or required application of one domain of second phase aimed to measure coherence of number of steps in calculations on mamatics), 72% of participants felt that 1. type of mamatics. mamatical areas between teaching learning of mamatics paper, most respondents felt that balance recall of common mamatical procedures should assessed were categorised against stated sciences. re is an assumption that on sample paper seemed appropriate, with be assessed alongside procedures that involve mamatical requirements for biology, chemistry mamatical concepts used to access sciences quite a number of respondents (mostly from HE) application in one or more content areas, that is physics respectively 1. are first taught within a mamatical context, i.e. within feeling that it was not an important issue. In Part B that difficulty should be increased in terms of mamatics curriculum. project compared 2. participants extent of were mamatics. told that analysis proportion found complexity. mamatical requirements for sciences at a-level that of majority question of parts calculations within a were paper single that step. with mamatics curriculum prior to Key stage 5 42% included felt that mamatics re should was be an measured even spread as was of COMPARABILITY ACROSS AWARDING using current national curriculum level descriptions all three proportion types of of calculation marks within se nearly questions half of ORGANISATIONS a 212 mamatics Gcse specification 3. this work respondents that required felt that mamatics. re should be more multiple In Part A 1% of respondents agreed that it was was carried out by a researcher by a mamatics step calculations (42%) more extended important that A-levels from all of awarding 3. difficulty of mamatics. this was measured teacher. calculations (34%) 16. organisations had same level of difficulty against 3 criteria: number of steps in a in terms aim of third mamatical phase was content. to determine 37% of nature When calculation, considering context familiarity as of a measure context of respondents of mamatics also that agreed community that was would important like to see that difficulty, complexity three-quarters of of question. respondents each category in all in a-level of awarding science assessments. organisations this assessed was achieved same Part A had felt varying that levels number of difficulty of questions each with was mamatical through an online content survey areas, for stakeholders with 61% thinking science only mamatical measured content as a proportion set in a of familiar total context number was of that community. was important Depending that on ir same expertise, key participants areas were appropriate. question In parts Part containing B respondents mamatics. were told it was that not assessed answered by all survey of for awarding biology, chemistry organisations. physics The vast measured majority against of mamatics number of marks. in A-levels vast a-level majority assessment. (97%) thought participants that were proportion chosen in of was 4. set in appropriateness contexts typically of mamatics. met through We questions three groups; with teaching mamatical profession; content higher should education; be learning looked programme, at wher that answer is, it was required set in scientific a familiar similar professional across bodies. awarding an online organisations. survey was completed 63% of by context comprehension (92%-1%). in addition Two-thirds to mamatical of respondents skill. respondents 97 participants felt across that awarding three groups organisations (27 for biology; should felt that this re was measured should be as less a proportion mamatics of set total use 38 for a framework chemistry; to ensure 32 for physics). that a broad participants spread from of in familiar number contexts of question so that parts students containing would mamatics. have mamatical industry were also requirements consulted more is assessed. generally Lastly, but most re more experience of applying mamatics in were science-related requests that industries mamatical employ a graduate requirements level unfamiliar a subject expert situations; group thus was established majority for wanted each across ir comments all of tended awarding to focus organisations more on should outcomes be an of increase three sciences. in difficulty each in terms group analysed of familiarity full of at graduate same. level rar than directly referring to a-level. context. suite of 21 Respondents examinations were papers asked of aqa, wher ccea, or not edexcel, familiarity ocr of WJec context for ir respective in majority subjects In Part B most respondents (89%) felt that of at a two-day assessments workshop. was examination creating a papers problem included with differences across awarding organisations in progression all ory to papers higher (Units education 1, 2, 4 or industry 5) proportion of marks at A-level that are for students experimental ability to practical apply papers mamatics (Units 3 in a novel 6). mamatical content were not acceptable. situation. calculations Two-thirds were based did on feel that assumption this was that causing ory a papers problem. make up 8% of complete a-level COHERENCE BETWEEN MATHEMATICS experimental practical papers remaining 2% 2. AND THE SCIENCES Respondents were asked to make a judgement on Respondents were asked which was most mamatical difficulty in terms of complexity important feature of mamatics in chemistry in paper. In Part A no respondents thought A-levels: proportion, appropriateness or difficulty that 1 five awarding complexity organisations was use too difficult mamatical requirements re defined by of ofqual mamatical in developing ir content. specifications 83% for of biology, respondents was chemistry an even physics. split between mamatical those requirements who thought are available it in full felt report. that appropriateness of mamatical 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete was a-level too assessment easy those marks who from thought practical that experimental it was papers content (Unit 3 was 6) make up most remaining significant, 2%. in with analysis, 14% question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 16 Some revised respondents mamatics Gcses. supported both statements so se percentages do not necessarily represent two different findings. SCORE Maths in science report 51

52 3.3 BIOLOGY ExEcutivE of respondents summary feeling that difficulty of mamatics was most important aspect. mamatics enables students to underst PHASE 1: A-LEVEL PAPERS describe many scientific phenomena yet re is concern All respondents felt that chemistry A-levels should EXTENT that science assessments at a-level are not reflecting contain mamatics that is not found in current subject s analytical nature. to explore wher re was This measure seeks to capture how much mamatics GCSE. A third of respondents agreed any evidence for this concern, score investigated mamatics is in biology A-level assessments that mamatics GCSE should be adequate type, extent difficulty of mamatical questions within (independent of type, appropriateness or preparation for mamatics in a science A-level science a-levels. findings show that a large number of difficulty). It is quantified by number of questions two-thirds agreed that introduction of a mamatical requirements listed in biology, chemistry question parts within a complete A-level that new mamatics qualification for use alongside physics specifications are not assessed. those that require mamatics number of marks chemistry A-levels would support students. are assessed are covered repeatedly often at a lower within those questions requiring mamatics. level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress Table 16a shows percentage of question parts containing mamatics within each unit percentage of question parts containing effectively to stem higher education employment. mamatics for ory only practical only in addition, findings show a disparity in way aims papers. Table 16b takes into account weighting mamatics is assessed across different awarding organisations. score recommends that re is a review of mamatical requirements for each of sciences at a-level that a framework is developed to regulate way mamatics is assessed within sciences to ensure parity across system. score s of ory overall papers objective (8%) for this practical project papers was to (2%) gar to calculate evidence on average type, percentage extent difficulty of question of mamatics parts containing required mamatics to access in a sciences complete in current A-level. a-level Figure specifications 2 illustrates to percentage establish wher of question this was parts being a appropriately complete A-level met by containing assessments. mamatics work for did five not awarding compare organisations. mamatical requirements between physics, chemistry biology as it is accepted Background se will differ between disciplines. re Table has 16a: been Percentage growing concern of question across parts science containing mamatics findings aim to within provide each score unit with evidence within to community set of ory about practical mamatical papers dem across of science five awarding inform development organisations of policy on type, extent qualifications, specifically that Gcse a-level science difficulty of mamatics in criteria qualifications are not meeting needs of students in A B assessments C for a-levels in Dbiology, chemistry E way y assess analytical nature of science. AS units physics. 11 project also supports 18 score s 4 work on in 29 score published evidence on Gcse science how examinations system should operate to ensure AS unit 3 59 examination papers which reported a wide variation in science qualifications 55 are fit 1 for purpose 53 also its A2 amount units 4 of mamatics 5 assessed across 27 awarding 7 work on improving 3 coherence 22 between 3 sciences organisations A2 unit 6 confirmed that use of 58mamatics 5 mamatics within context of science was examined in a very Theory papers only in project, 7 we looked across 2 all assessments 4 at limited way. score organisations felt that this was a-level for a given year, including both experimental unacceptable. Practical papers mamatics only is integral to 59 teaching practical examination papers. learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in Table 16b: Percentage of question parts weighted to take account of ory component biology, chemistry physics curricula ir (8%) practical component (2%) of A-level assessments assessments. to provide furr evidence to support se A concerns, score set up this project to investigate Theory contribution (8%) 18 mamatics found in 21 science assessments at Practical a-level across contribution unitary (2%) awarding organisations 12 in B 12 5 C 6 11 D E 3 12 engl, Total A-level Wales norrn irel SCORE Maths in science report

53 Table methodology 17a shows percentage of marks requiring mamatics project was for designed each unit in three for phases. ory only practical first was to only establish papers. Table nature 17b of takes mamatics into account assessed weighting within of ory biology, papers chemistry (8%) physics practical a-level examinations in 21. full suite of examinations papers from aqa, ccea, edexcel, Figure ocr 2: WJec Percentage were analysed of question using parts four in a complete measures that A-level follow: containing mamatics for 1. five awarding type of mamatics. organisations mamatical areas assessed were categorised against stated mamatical requirements for biology, chemistry Theory physics respectively 1 Practical Contribution (8%). Contribution (2%) Percentage of question parts in a complete A level 4 2. extent of mamatics. proportion 35 of question parts within a paper that 3 included 25 mamatics was measured as was proportion 2 of marks within se questions that required 15 mamatics difficulty 5 of mamatics. this was measured against 3 criteria: A B number C of steps D in Ea calculation, Awarding familiarity Organisations of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of papers groups (2%) comprised to calculate practising average a-level teachers, percentage of teachers marks with requiring experience mamatics in curriculum in a research complete A-level. development Figure 21 individuals illustrates working this as for a graph. awarding organisations as markers, question writers or examiners. stardisation exercises were employed throughout analysis to verify reliability of judgements within across subject expert groups. Figure 21: Percentage of marks requiring mamatics second phase in aimed a complete to measure A-level coherence for five awarding between organisations teaching learning of mamatics sciences. re is an assumption that mamatical concepts used to access sciences Theory Practical are first taught within a mamatical context, i.e. within Contribution (8%) Contribution (2%) mamatics curriculum. project compared 3 mamatical requirements for sciences at a-level 25 with mamatics curriculum prior to Key stage 5 2 using current national curriculum level descriptions 15 a 212 mamatics Gcse specification 3. this work 1 was carried out by a researcher by a mamatics teacher. 5 aim of third A phase B was Cto determine D E nature of mamatics that Awarding community Organisations would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants question parts containing mamatics. it was not Table 17a: Percentage of marks 17 that require mamatics answered within survey each for biology, unit chemistry within or physics set measured against number of marks. of ory practical papers across five awarding a-level organisations assessment. participants were chosen in 4. appropriateness of mamatics. We looked at wher answer required A scientific B three groups; teaching profession; higher education; professional Cbodies. an online D survey was Ecompleted by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; AS units this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from AS unit number 3 of question parts containing 46 mamatics. industry were 38 also consulted 56more generally 41but as most science-related industries employ at a graduate level a A2 subject units expert 4 group 5 was established for 21each ir comments tended to focus more on outcomes of A2 unit three 6 sciences. each group analysed 48 full 48 at graduate 4level rar than 45directly referring 68to a-level. suite of 21 examinations papers of aqa, ccea, Theory papers only edexcel, ocr WJec for ir respective subjects at Practical a two-day papers workshop. onlyexamination papers 47 included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6) calculations were based on assumption that ory Table 17b: Percentage of marks requiring mamatics within a total A-level, weighted to take papers make up 8% of complete a-level account of ory component (8%) practical component (2%) of A-level assessments experimental practical papers remaining 2% 2. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 Total a complete A-level science a-level is made up of 6 units. 24marks from ory 16 papers (Unit 1, 14 2, 4 5) make up 21 8% of complete 13 a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 17 A revised mark mamatics was judged Gcses. to require mamatics if part or all of mark could not be achieved without mamatics. Percentage of question parts in a complete A level A B C D E Theory contribution (8%) Practical contribution (2%) SCORE Maths in science report 53

54 ExEcutivE TYPE summary mamatics The number enables of occurrences students to of underst each mamatical requirement listed in Biology A-level was measured describe to identify many scientific type of phenomena mamatics yet assessed re is concern frequency of each type of mamatics assessed. that The science results assessments are displayed at a-level in Figure are 22. not reflecting subject s analytical nature. to explore wher re was any Mamatical evidence for this requirements concern, score listed in investigated x-axis on Figure 22 type, 1 Arithmetic extent difficulty numerical of mamatical computation: questions within (k) underst probability in order to underst how science (a recognise a-levels. use findings expressions show in that decimal a large number of genetic ratios arise; mamatical stard requirements form; listed in biology, chemistry (l) frame null hyposis. (b) calculate or use ratios, fractions percentages; physics specifications are not assessed. those that (c) make estimates of results of calculations (without 3 Algebra: are assessed are covered repeatedly often at a lower using a calculator); (a) change subject of an equation; level (d) than use required. calculators this to find is likely use to have mean, an stard impact on (b) substitute numerical values into algebraic equations way deviations, that power, subjects exponential are taught logarithmic refore functions; using appropriate units for physical quantities; students (e) use ability calculations to have involving necessary simple arithmetic skills to progress algebraic (c) underst use of logarithms in relation to quantities effectively transformations: that range over several orders of magnitude; to stem higher education employment. (f) underst use correlations; (d) derive an equation; in addition, findings show a disparity in way aims (g) +, -, x,. (e) =, <, >. mamatics is assessed across different awarding score s overall objective for this project was to organisations. 2 Hling data: 4 Graphs: score recommends that re is a review gar evidence on type, extent difficulty of of (a) use mamatical an appropriate requirements number of significant for each of figures; (a) translate information between graphical, numerical sciences mamatics required to access sciences in current (b) find arithmetic means; algebraic forms; at a-level that a framework is developed to regulate (c) construct or interpret tables, frequency tables (b) a-level plot two specifications variables from experimental to establish or or wher data; this way diagrams, mamatics bar charts is assessed histograms; within sciences to (c) was calculate being rate appropriately of change from met a by graph assessments. showing a linear ensure (d) underst parity across simple probability; system. relationship; work did not compare mamatical requirements (e) underst principles of sampling as applied to (d) draw use slope of a tangent to a curve as a between physics, chemistry biology as it is accepted Background scientific data; measure of rate of change; se will differ between disciplines. (f) underst terms mean, median mode (e) construct / or interpret line graphs. re stard has been deviation; growing concern across science 5 Geometry: findings aim to provide score with evidence to community (g) use a scatter about diagram mamatical to identify positive dem of negative science (a) inform visualise three development dimensional of forms policy from on two type, dimensional extent qualifications, correlation specifically between two that variables; Gcse a-level science representations of three dimensional objects; difficulty of mamatics in criteria qualifications (h) select are use not a meeting simple statistical needs test; of students in (b) calculate circumferences areas of circles, surface (i) make order of magnitude calculations; assessments for a-levels in biology, chemistry way y assess analytical nature of science. areas volumes of regular blocks cylinders when (j) determine interpret population variance, stard physics. provided with project appropriate also formulae. supports score s work on deviation stard deviation (error) of mean; in 29 score published evidence on Gcse science how examinations system should operate to ensure examination papers which reported a wide variation in science qualifications are fit for purpose also its Figure 22: The number of occurrences for each mamatical requirement in a full suite of amount of mamatics assessed across awarding work on improving coherence between sciences examination papers for a complete biology A-level in each of awarding organisations. organisations confirmed that use of mamatics mamatics. It has no relation to number of marks awarded for each mamatical requirement. within context of science was examined in a very in project, we looked across all assessments at limited way. score organisations felt that this was Awarding Organisations a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching A B C D E practical examination papers. learning 4of sciences, offers a valuable aid in understing describing scientific phenomena; 35 as such it should be appropriately represented in 3 biology, chemistry physics curricula ir 25 assessments. Number of Occurrences 2 to provide furr 15 evidence to support se concerns, score set up this project to investigate 1 mamatics found in 21 science assessments 5 at a-level across unitary awarding organisations in engl, Wales norrn irel. 1a 1b 1c 1d 1e 1f 1g 2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 5a 5b Arithmetic Computation Hling Data Algebra Graphs Mamatical Requirements for Biology A-Level Geometry Trigonometry 54 SCORE Maths in science report

55 methodology DIFFICULTY Table groups 18a shows comprised practising percentage a-level of mamatical teachers, project was designed in three phases. question teachers with parts experience classified in as curriculum containing research single For each of following measures, percentages first was to establish nature of mamatics step development (S), multiple individuals step (M) working extended for awarding step (E) are stated as a proportion of number of assessed within biology, chemistry physics calculations organisations within as markers, each question A-level unit writers or as examiners. an question parts containing mamatics. The a-level examinations in 21. full suite of average stardisation for ory exercises only were practical employed only throughout papers. percentages do not relate in any way to number examinations papers from aqa, ccea, edexcel, These analysis figures to verify are calculated reliability of as judgements a percentage within of marks awarded for mamatical understing. ocr WJec were analysed using four of across question subject parts expert identified groups. as containing NUMBER measures that OF follow: STEPS mamatics. Table 18b shows se percentages second phase aimed to measure coherence The number of steps involved in a calculation was of total number of question parts Table 18c 1. type of mamatics. mamatical areas between teaching learning of mamatics used as one measure of difficulty, based on takes into account weighting of ory papers assessed were categorised against stated sciences. re is an assumption that assumption that questions containing mamatics (8%) practical papers (2%) to calculate mamatical requirements for biology, chemistry mamatical concepts used to access sciences that required multiple step or extended calculation average percentage of single step, multiple step physics respectively 1. are first taught within a mamatical context, i.e. within (e.g. value x had to be found used in a extended step calculations in a complete mamatics curriculum. project compared subsequent 2. extent calculation of mamatics. in order to find proportion solution A-level. Figure 23a illustrates percentage of mamatical requirements for sciences at a-level to of problem, question y) were parts more within difficult a paper than that single single, multiple extended step calculations in with mamatics curriculum prior to Key stage 5 step calculations, included mamatics as y was require measured students as was to a complete A-level for each of five awarding using current national curriculum level descriptions use higher proportion order of skills marks extended within se reasoning. questions organisations. Figures 23b 23c illustrate se a 212 mamatics Gcse specification 3. this work Appendix that required 5a shows mamatics. an example of each type of percentages for ory only practical only was carried out by a researcher by a mamatics calculation. papers respectively. 3. difficulty of mamatics. this was measured teacher. against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity of context Table 18a: Percentage of single, multiple extended of mamatics step calculations that community in biology would A-level, like to see complexity of question. each category calculated as a percentage of question parts identified in a-level as containing science assessments. mamatics this was achieved had varying levels of difficulty each was through an online survey for stakeholders in science measured as a proportion of total number of community. Depending on ir expertise, participants question parts containing A mamatics. it Bwas not C D E answered survey for biology, chemistry or physics Number measured of steps against number E Mof marks. S E M S a-level E assessment. M S E participants M S were E chosen M in S AS 4. units appropriateness 1 2 of mamatics We three 17groups; 29 teaching 54 6 profession; 35 6higher education; 1 looked at wher answer required scientific professional bodies. an online survey was completed by AS unit comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; A2 units this was 4 measured 5 as a proportion 9 92 of total for chemistry; for 62 physics). 32 participants 5 5 from A2 unit number 6 of question parts 21containing 12 67mamatics industry 8 were 46 also 46 consulted 13 43more 43generally 7 but 15as most 78 science-related industries employ at a graduate level a Theory subject papers expert group onlywas established 11 for 9each ir comments tended to focus more on outcomes of three sciences. each group analysed full Practical papers only at graduate 13 32level 57rar 7 than 42 directly 52referring 4 to 17a-level. 8 suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included Table all ory 18b: Percentage papers (Units 1, of 2, single, 4 5) multiple extended step calculations in biology A-level, calculated experimental as a practical percentage papers of (Units 3 total 6). number of question parts in a complete A-level calculations were based on assumption that ory papers make up 8% of Acomplete a-level B experimental Number of steps practical papers E M remaining S E 2% M 2. S C E M S D E M S E E M S AS units AS unit A2 units five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. A2 unit Theory papers only Practical papers only SCORE Maths in science report 55

56 ExEcutivE Table 18c: Percentage summary of single, multiple extended step calculations in biology A-level, weighted to take account of ory component (8%) practical component (2%) mamatics enables students to underst of A-level assessments describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting A B subject s analytical nature. to explore wher re was any Number evidence of for steps this concern, Escore M investigated S E M type, Theory extent papers difficulty only of mamatical 2 questions 17 within 5 science (8%) a-levels. findings show that a large number of S 7 C E 1 M 2 S 3 D E 1 M 8 S 7 E E 1 M 1 S 2 mamatical requirements listed in biology, chemistry Practical papers only physics specifications are 1 not assessed. 1 9 those 1 that (2%) are assessed are covered repeatedly often at a lower A-level than required. total this is likely 1 to have 3 an 26 impact 1 on 8 (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment in Figure addition, 23a: Percentage findings show a of disparity mamatical in way aims Figure 23c: Percentage of mamatical mamatics question parts is assessed identified across as containing different awarding single, score s question overall parts objective identified for this as project containing was to single, organisations. multiple score extended recommends step calculations that re is a in review a gar multiple evidence extended on type, step extent calculations difficulty of in of complete mamatical A-level requirements for each of for each five of awarding sciences mamatics practical examination required to access papers sciences for biology in current at organisations a-level that a framework is developed to regulate a-level A-level specifications to establish wher this way mamatics is assessed within sciences to ensure parity across TOTAL system. was being appropriately met by assessments. work did not compare PRACTICAL mamatical requirements Extended Multiple Single Extended Multiple Single between physics, chemistry biology as it is accepted Background 4 se will 1 differ between disciplines re has been growing concern across science 8 3 findings 7 aim to provide score with evidence to community 25about mamatical dem of science inform 6 development of policy on type, extent qualifications, 2 specifically that Gcse a-level science 5 difficulty of mamatics in criteria 15 4 qualifications are not meeting needs of students in assessments 3 1 for a-levels in biology, chemistry way y assess analytical nature of science. 2 5 physics. 1 project also supports score s work on in 29 score Apublished B evidence C on DGcse Escience examination papers which Awarding reported Organisations a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics how examinations A system B should C operate D Eto ensure science qualifications Awarding are fit for Organisations purpose also its work on improving coherence between sciences mamatics. within Figure 23b: context Percentage of science was of mamatical examined in a very in project, we looked across all assessments at limited question way. parts score identified organisations as containing felt that this was single, a-level for a given year, including both experimental unacceptable. multiple mamatics extended step is integral calculations to teaching practical examination papers. ory learning examination of sciences, papers offers for biology a valuable A-level aid in understing describing scientific phenomena; as such it should be appropriately THEORY represented in biology, chemistry Extended physics Multiplecurricula Single ir assessments. 25 Percentage of question parts in a complete A level Percentage of question parts in a complete A level 2 to provide furr evidence to support se concerns, 15 score set up this project to investigate mamatics 1 found in 21 science assessments at a-level across unitary awarding organisations in 5 engl, Wales norrn irel. A B C D E Awarding Organisations Percentage of question parts in a complete A level 56 SCORE Maths in science report

57 COMPLEXITY methodologyof TASK Question project parts was that designed contained three mamatics phases. within a first full was suite to of establish A-level examinations nature of were mamatics measured against assessed four within levels of biology, complexity, chemistry with Level physics 4 being considered a-level examinations most in difficult. 21. These full suite levels of included Level examinations 1 (straight papers forward/routine), from aqa, ccea, Level edexcel, 2 (requires understing ocr WJec were application analysed using of mamatics four average groups for comprised ory only practising practical a-level only teachers, papers. These teachers figures with experience are calculated in curriculum as a percentage research of development question parts individuals identified working as containing for awarding mamatics. organisations as Table markers, 19b question shows se writers percentages or examiners. of stardisation total number exercises of question were employed parts throughout Table 19c takes analysis into verify account reliability weighting of judgements of ory within papers (8%) across subject practical expert papers groups. (2%) to calculate within measures one that domain), follow: Level 3 (requires understing average percentage of Level 1, 2 3 complexity second phase aimed to measure coherence application of mamatics across domains) in a complete A-level. Figure 24a illustrates 1. type of mamatics. mamatical areas between teaching learning of mamatics Level 4 (requires synsis application of percentage of Level 1, 2 3 complexity type assessed were categorised against stated sciences. re is an assumption that mamatics across a number of domains). Appendix calculations in a complete A-level for each of mamatical requirements for biology, chemistry mamatical concepts used to access sciences 5b shows an example of each level of complexity. five awarding organisations. Figures 24b 24c physics respectively 1. are first taught within a mamatical context, i.e. within illustrate se percentages for ory only mamatics curriculum. project compared Table 2. 19a extent shows of mamatics. percentage of mamatical proportion practical only papers respectively. mamatical requirements for sciences at a-level question of parts question classified parts within as Level a paper 1, 2 that or 3 with mamatics curriculum prior to Key stage 5 complexity included within mamatics each A-level was measured unit as as was an using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics Table 3. 19a: difficulty Percentage of mamatics. of Level this 1, was 2 measured 3 complexity teacher. type calculations in biology A-level, calculated against as 3 criteria: a percentage number of of question steps in a parts identified as containing mamatics aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see complexity of question. A each category B C D E in a-level science assessments. this was achieved Complexity had varying levels of difficulty 3 2 each 1 was through 3 an 2 online 1 survey 3 for 2stakeholders 1 3 in 2 science 1 measured as a proportion of total number of AS units community. Depending 1 on ir expertise, 1 participants 1 question parts containing mamatics. it was not answered survey for biology, chemistry or physics AS unit measured 3 against number of marks a-level assessment. participants were chosen in A2 4. units appropriateness 4 5 of mamatics We 1three groups; teaching 1 profession; 1 higher education; 1 A2 unit looked 6 at wher answer required 1scientific professional 33 bodies. 66 an online survey 1 was completed 1 by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Theory papers only this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from Practical number papers of question only parts containing 1 mamatics industry were 17 also 83 consulted more 1 generally but 6 as 95 most science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full at graduate level rar than directly referring to a-level. Table suite of 19b: 21 Percentage examinations of papers Level of aqa, 1, 2 ccea, 3 complexity type calculations in biology A-level, calculated edexcel, ocr as a percentage WJec for ir of respective total subjects number of question parts in a complete A-level at a two-day workshop. examination papers included all ory papers (Units 1, A 2, 4 5) B C D E experimental practical papers (Units 3 6). calculations Number of were steps based on 3 assumption 2 1 that 3 ory papers AS units make 1 up 8% 2 of complete a-level 19 experimental practical papers remaining 2% 2. AS unit A2 units A2 unit Theory papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 18 Level revised 4 mamatics was omitted Gcses. from findings as very few examination papers included questions of this complexity. Practical papers only SCORE Maths in science report 57

58 ExEcutivE Table 19c: Percentage summary of Level 1, 2 3 complexity type calculations in biology A-level, weighted to take account of ory component (8%) practical component (2%) mamatics enables students to underst of A-level assessments describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting A B subject s analytical nature. to explore wher re was any Number evidence of for steps this concern, 3score 2 investigated type, Theory extent papers difficulty only of mamatical 1 questions 18 within science (8%) a-levels. findings show that a large number of 1 12 C D E mamatical requirements listed in biology, chemistry Practical papers only physics specifications are not assessed. 12 those that (2%) are assessed are covered repeatedly often at a lower A-level than required. total this is likely to have 1 an 3 impact on 1 (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment in Figure addition, 24a: Percentage findings show a of disparity mamatical in way Figure aims 24c: Percentage of mamatical mamatics question parts is assessed identified across as containing different awarding question score s overall parts objective identified for this as project containing was to organisations. Level 1, Level score 2 recommends Level 3 complexity that re is type a review Level gar evidence 1, Level on 2 type, Level extent 3 complexity difficulty type of of calculations mamatical in a requirements complete A-level for each of for each sciences of calculations mamatics required in practical to access examination sciences papers in current at a-level five awarding that a framework organisations developed to regulate for a-level biology specifications A-level to establish wher this way mamatics is assessed within sciences to ensure parity across TOTAL system. was being appropriately met by assessments. work did not compare PRACTICAL mamatical requirements Level 3 Level 2 Level 1 Level 3 Level 2 Level 1 between physics, chemistry biology as it is accepted Background 4 se will 1 differ between disciplines re has been growing concern across science 8 3 findings 7 aim to provide score with evidence to community 25about mamatical dem of science inform 6 development of policy on type, extent qualifications, 2 specifically that Gcse a-level science 5 difficulty of mamatics in criteria 15 4 qualifications are not meeting needs of students in assessments 3 1 for a-levels in biology, chemistry way y assess analytical nature of science. 2 5 physics. 1 project also supports score s work on in 29 score Apublished B evidence C on DGcse Escience examination papers which Awarding reported Organisations a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics how examinations A system B should C operate D Eto ensure science qualifications Awarding are fit for Organisations purpose also its work on improving coherence between sciences mamatics. within Figure 24b: context Percentage of science was of mamatical examined in a very in project, we looked across all assessments at limited question way. parts score identified organisations as containing felt that this Level was 1, a-level for a given year, including both experimental unacceptable. Level 2 Level mamatics 3 complexity is integral type to calculations teaching practical examination papers. in ory learning examination of sciences, papers offers for biology a valuable A-level aid in understing describing scientific phenomena; as such it should be appropriately THEORY represented in biology, chemistry Level 3 physics curricula Level 1 ir assessments. 25 Percentage of question parts in a complete A level Percentage of question parts in a complete A level 2 to provide furr evidence to support se concerns, 15 score set up this project to investigate mamatics 1 found in 21 science assessments at a-level across unitary awarding organisations in 5 engl, Wales norrn irel. A B C D E Awarding Organisations Percentage of question parts in a complete A level 58 SCORE Maths in science report

59 CONTEXT methodology The question project was parts designed that contained three phases. mamatics within first was a full to establish suite of A-level nature examinations of mamatics were classified assessed within as Level 1, biology, Level chemistry 2 or Level 3, physics with Level 1 a-level most examinations familiar context. in 21. Level full 1 suite is a of context typically examinations met papers through from aqa, learning ccea, programme, edexcel, Level ocr 2 is WJec a context were that analysed contains using some four novel These groups figures comprised are calculated practising as a-level a percentage teachers, of teachers question with experience parts identified in curriculum as containing research mamatics. development Table individuals 2b shows working se for awarding percentages of organisations total number as markers, of question parts writers or examiners. Table 2c takes stardisation into account exercises weighting were employed of ory throughout papers (8%) analysis to verify practical reliability papers of (2%) judgements to calculate within average across percentage subject expert of Level groups. 1, 2 3 context aspects measures that Level follow: 3 is an unfamiliar context unlikely in a complete A-level. Figure 25a illustrates second phase aimed to measure coherence to have been met before. Appendix 5c shows an percentage of Level 1, 2 3 context calculations 1. type of mamatics. mamatical areas between teaching learning of mamatics example of levels of familiarity. in a complete A-level for each of five awarding assessed were categorised against stated sciences. re is an assumption that organisations. Figures 25b 25c illustrate se mamatical requirements for biology, chemistry mamatical concepts used to access sciences Table 2a shows percentage of mamatical percentages for ory only practical only physics respectively 1. are first taught within a mamatical context, i.e. within question parts classified as Level 1, 2 or 3 papers respectively. mamatics curriculum. project compared context 2. within extent each of A-level mamatics. unit as proportion an mamatical requirements for sciences at a-level average of for question ory only parts within practical a paper only that papers. with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics Table 3. 2a: difficulty Percentage of mamatics. of Level this 1, was 2 measured 3 context type teacher. calculations in biology A-level, calculated as a against percentage 3 criteria: of question number parts of steps identified in a as containing mamatics aim of third phase was to determine nature calculation, familiarity of context of mamatics that community would like to see complexity of question. A each category B C D E in a-level science assessments. this was achieved Context had varying levels of difficulty 3 2 each 1 was through 3 an 2 online 1 survey 3 for 2stakeholders 1 3 in 2 science 1 measured as a proportion of total number of AS units community. Depending 1 on ir expertise, 1 participants 1 question parts containing mamatics. it was not answered survey for biology, chemistry or physics AS unit measured 3 against number 66 of marks a-level assessment. participants were chosen in A2 4. units appropriateness 4 5 of mamatics We 1three groups; teaching 1 profession; 1 higher education; 1 A2 unit looked 6 at wher answer 69 required 31 scientific professional 83 bodies. 17 an 1 online survey was 66 completed 44 by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Theory papers only this was measured as a proportion of total 38 for chemistry; 1 32 for physics). 1 participants from 1 Practical number papers of question only parts 68containing 33mamatics industry 87 were also 14 consulted 94 more 6 generally 67 but as 39 most science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full at graduate level rar than directly referring to a-level. Table suite of 2b: 21 Percentage examinations of papers Level of aqa, 1, 2 ccea, 3 context type calculations in biology A-level, calculated as edexcel, a percentage ocr WJec of for total ir number respective of subjects question parts in a complete A-level at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) A B C D E experimental practical papers (Units 3 6). calculations Number of were steps based on 3 assumption 2 1 that 3 ory papers AS units make 1 up 8% 2 of complete a-level 19 experimental practical papers remaining 2% 2. AS unit A2 units A2 unit Theory papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. Practical papers only SCORE Maths in science report 59

60 ExEcutivE Table 2c: Percentage summary of Level 1, 2 3 context type calculations in biology A-level, weighted to take account of ory component (8%) practical component (2%) of A-level mamatics enables students to underst assessments describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting A B subject s analytical nature. to explore wher re was any Number evidence of for steps this concern, 3score 2 investigated C D E type, extent difficulty of mamatical questions within Theory papers only science a-levels. findings show that a large number of (8%) mamatical requirements listed in biology, chemistry Practical physics specifications papers only are 8not assessed. 4 those 4 that are (2%) assessed are covered repeatedly often at a lower A-level than required. total this is likely 8 to have 1 an 22 impact 4 on (weighted) way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. Figure 25a: Percentage of mamatical question Figure in addition, findings show a disparity in way aims 25c: Percentage of mamatical question parts identified as containing calculations set parts identified as containing calculations set mamatics is assessed across different awarding score s overall objective for this project was to in a Familiar, with Some Novel Aspects, in a Familiar, with Some Novel Aspects, organisations. score recommends that re is a review gar evidence on type, extent difficulty of Unfamiliar context in a complete A-level for Unfamiliar context in practical examination of mamatical requirements for each of sciences mamatics required to access sciences in current each of five awarding organisations papers for biology A-level at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. TOTAL PRACTICAL ensure parity across system. work did not compare mamatical requirements Unfamiliar Some Novel Familiar Unfamiliar Some Novel Familiar between physics, chemistry biology as it is accepted Background 4 1 se will differ between disciplines re has 3 been growing concern across science findings 7 aim to provide score with evidence to community 25about mamatical dem of science 6 2 inform 5 development of policy on type, extent qualifications, specifically that Gcse a-level science 15 difficulty 4 of mamatics in criteria qualifications are not meeting needs of students in 3 1 assessments 2 for a-levels in biology, chemistry way y 5 assess analytical nature of science. physics. 1 project also supports score s work on A B C D E in 29 score published evidence on Gcse science how examinations A system B should C operate D Eto ensure Awarding Organisations examination papers which reported a wide variation in science qualifications Awarding are fit for Organisations purpose also its amount of mamatics assessed across awarding Percentage of question parts in a complete A level organisations Figure 25b: Percentage confirmed of that mamatical use of mamatics question within parts identified context of as science containing was examined calculations in a very limited set in way. a Familiar, score organisations with Some Novel felt that Aspects, this was unacceptable. Unfamiliar mamatics context is calculations integral to in teaching ory examination learning of papers sciences, for biology offers A-level a valuable aid in understing describing scientific phenomena; as such it should be appropriately THEORY represented in biology, chemistry Unfamiliar physics Some curricula Novel Familiar ir assessments. Percentage of question parts in a complete A level 25 2 to provide furr evidence to support se concerns, 15 score set up this project to investigate mamatics found in 21 science assessments 1 at a-level across unitary awarding organisations in 5 engl, Wales norrn irel. A B C D E Awarding Organisations Percentage of question parts in a complete A level work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 6 SCORE Maths in science report

61 methodology APPROPRIATENESS mamatical groups comprised skill it was practising classified a-level as some teachers, scientific project was designed in three phases. comprehension teachers with experience question in curriculum parts where research all marks APPLICATION first was to establish nature of mamatics required development scientific individuals comprehension working were for awarding classified as Judgements were made as to wher content assessed within biology, chemistry physics scientific organisations comprehension. as markers, question Appendix writers 5d shows or examiners. an of question part reflected how mamatics is a-level examinations in 21. full suite of example stardisation of each exercises category. were employed throughout used in real world in scientific context. All of examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within question parts with mamatics were judged to Table ocr WJec were analysed using four across 21a shows subject expert percentage groups. of mamatical reflect appropriate way in which mamatics question parts classified as all marks (S), some marks could measures be used that follow: in a real scientific context. second phase aimed to measure coherence (B) or no marks (M) requiring scientific comprehension 1. type of mamatics. mamatical areas between teaching learning of mamatics within each A-level unit as an average for ory STRUCTURAL OR TAGGED ON assessed were categorised against stated sciences. re is an assumption that only practical only papers. These figures are One of measures was to ascertain wher mamatical requirements for biology, chemistry mamatical concepts used to access sciences calculated as a percentage of question parts mamatics was a structural part of question physics respectively 1. are first taught within a mamatical context, i.e. within identified as containing mamatics. Table 21b or wher mamatics was tagged on to mamatics curriculum. project compared 2. extent of mamatics. proportion shows se percentages of total number of question. All of question parts with mamatical mamatical requirements for sciences at a-level of question parts within a paper that question parts Table 21c takes into account content were judged to be a structural part of with mamatics curriculum prior to Key stage 5 included mamatics was measured as was weighting of ory papers (8%) practical question. using current national curriculum level descriptions proportion of marks within se questions papers (2%) to calculate average percentage of a 212 mamatics Gcse specification 3. this work MATHEMATICS that required mamatics. SKILLS OR SCIENTIFIC mamatical question parts where all marks, some was carried out by a researcher by a mamatics COMPREHENSION marks or no marks require scientific comprehension 3. difficulty of mamatics. this was measured teacher. Mamatical question parts within a full suite of in a complete A-level. Figure 26a illustrates against 3 criteria: number of steps in a A-level examinations were measured against percentage aim of of third mamatical phase was question to determine parts where nature all, calculation, familiarity of context extent to which scientific comprehension was some of mamatics no marks that require community scientific would comprehension like to see complexity of question. each category required to achieve full marks. If a question part in a a-level complete science A-level assessments. for each of this was five achieved awarding had varying levels of difficulty each was required no scientific comprehension to acquire organisations. through online Figures survey 26b for stakeholders 26c illustrate in se science measured as a proportion of total number of full marks it was classified as no scientific percentages community. Depending for ory only ir expertise, practical participants only papers question parts containing mamatics. it was not comprehension (mamatical skill only), if part of respectively. answered survey for biology, chemistry or physics measured against number of marks. marks required scientific comprehension in addition to a-level assessment. participants were chosen in 4. appropriateness of mamatics. We looked at wher answer required scientific three groups; teaching profession; higher education; professional bodies. an online survey was completed by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Table 21a: Percentage of mamatical question parts classified as all mark (S), some marks this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from (B) no marks (M) requiring scientific comprehension in biology A-level, calculated as a number of question parts containing mamatics. industry were also consulted more generally but as most percentage of question parts identified as containing mamatics science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group A analysed Bfull at Cgraduate level rar D than directly referring E to a-level. suite of 21 examinations papers of aqa, ccea, Scientific S B M S B M S B M S B M S B M edexcel, ocr WJec for ir respective subjects comprehension at a two-day workshop. examination papers included all AS units ory 1 papers 2 (Units 1, 42, 47 5) 54 experimental AS unit 3 practical papers 41 (Units ) calculations were based on assumption that ory A2 units papers make up 8% of complete a-level experimental A2 unit 6 practical papers 43 remaining 57 2% Theory papers only Practical papers only five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 61

62 ExEcutivE Table 21b: Percentage summary of mamatical type question parts where all marks (S), some marks (B) or no marks (M) require scientific comprehension in biology A-level, calculated as a percentage mamatics enables students to underst of total number of question parts in a complete A-level describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical nature. to explore A wher re B was any Number evidence of for steps this concern, 3score 2 investigated type, extent difficulty of mamatical questions within AS units science a-levels. findings show that a large number of mamatical AS unit 3 requirements listed in 24 biology, 35 chemistry A2 physics units 4 specifications 5 are not assessed those that 1 are assessed are covered repeatedly often at a lower A2 unit level than required. this is likely to have an impact on Theory way that papers subjects only are taught 4 1 refore 9 on 3 students Practical ability papers to have only necessary 25skills 34to progress 2 effectively to stem higher education employment C D E in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. Table 21c: Percentage score recommends of mamatical that re is type a review question gar parts evidence where on all marks type, extent (S), some difficulty marks of (B) of no mamatical marks (M) requirements require scientific for each of comprehension sciences mamatics in biology required A-level, to weighted access to sciences take account in current at of a-level ory that component a framework is (8%) developed to practical regulate component a-level specifications (2%) of A-level to establish assessments wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. A B work Cdid not compare D mamatical Erequirements Number of steps between 3 physics, 2 1 chemistry 3 2 biology 1 3 as it is 2 accepted 1 Background se will differ between disciplines. Theory papers only re has been growing concern across science findings aim to provide score with evidence to community Practical about papers only mamatical 5dem 7 of science inform development of policy on type, extent qualifications, A-level total specifically that 3Gcse 13 a-level 14 science 7 1 difficulty 7 of 8 mamatics 3 in 5 criteria qualifications (weighted) are not meeting needs of students in assessments for a-levels in biology, chemistry way y assess analytical nature of science. physics. project also supports score s work on in 29 score published evidence on Gcse science examination papers which reported a wide variation in Figure amount 26a: of Percentage mamatics assessed of mamatical across awarding organisations question parts confirmed requiring that scientific use of mamatics how examinations system should operate to ensure science qualifications are fit for purpose also its work Figure on 26b: improving Percentage coherence of mamatical between sciences question mamatics. parts requiring scientific within comprehension context of in science addition was to examined mamatical in a very comprehension in addition to mamatical in project, we looked across all assessments at limited skill to way. achieve score all organisations marks, some felt that of this was marks skill to achieve all marks, some of marks a-level for a given year, including both experimental unacceptable. or no marks mamatics in a complete is integral A-level to for teaching each of or no marks in ory examination papers for practical examination papers. learning five awarding of sciences, organisations offers a valuable aid biology A-level in understing describing scientific phenomena; as such it should be appropriately TOTAL represented in THEORY biology, chemistry Scientific physics Some curricula Scientific ir Comprehension Comprehension assessments. 4 Percentage of question parts in a complete A level 35 to provide 3 furr evidence to support se concerns, 25 score set up this project to investigate 2 mamatics found in 21 science assessments 15 at a-level across unitary awarding organisations in 1 engl, Wales norrn irel. 5 A B C D E Awarding Organisations No Scientific Comprehension Percentage of question parts in a complete A level Scientific Comprehension Some Scientific Comprehension A B C D E Awarding Organisations No Scientific Comprehension 62 SCORE Maths in science report

63 Figure methodology 26c: Percentage of mamatical groups PHASE comprised 2 BIOLOGY practising A-LEVEL a-level teachers, IN question project parts was designed requiring in three scientific phases. COMPARISON teachers with experience WITH in GCSE curriculum MATHEMATICS research comprehension first was to establish in addition nature of to mamatical mamatics AND development NATIONAL individuals CURRICULUM working for LEVEL awarding skill assessed to achieve within all biology, marks, chemistry some of physics marks DESCRIPTORS organisations as markers, question writers or examiners. or a-level no marks examinations practical in 21. examination full suite of papers stardisation exercises were employed throughout Two comparisons were used to establish for examinations biology A-level papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within coherence of biology A-levels mamatics ocr WJec were analysed using four across subject expert groups. accessed up to Key Stage 4: comparison measures that follow: PRACTICAL with second National phase Curriculum aimed to level measure descriptors coherence Scientific Some Scientific No Scientific 1. type of mamatics. mamatical areas comparison between teaching with 212 learning mamatics of mamatics GCSE Comprehension Comprehension Comprehension assessed 1 were categorised against stated specification. sciences. These re comparisons an assumption are displayed that 9 mamatical requirements for biology, chemistry in mamatical Table 22. concepts used to access sciences 8 physics 7 respectively 1. are first taught within a mamatical context, i.e. within 6 mamatics curriculum. project compared 5 2. extent of mamatics. proportion 4 mamatical requirements for sciences at a-level of 3question parts within a paper that with mamatics curriculum prior to Key stage 5 2 included mamatics was measured as was 1 using current national curriculum level descriptions proportion of marks within se questions A B C D E a 212 mamatics Gcse specification 3. this work that required mamatics. Awarding Organisations was carried out by a researcher by a mamatics 3. difficulty of mamatics. this was measured teacher. against 3 criteria: number of steps in a aim of third phase was to determine nature calculation, familiarity of context Table 22: Comparison of mamatical requirements of mamatics for biology that A-level community with mamatics would like to found see complexity of question. each category in National Curriculum Level Descriptors GCSE in a-level mamatics science assessments. specification this was achieved had varying levels of difficulty each was through an online survey for stakeholders in science measured as a proportion of total number of Mamatical community. Depending on ir expertise, participants question parts requirements containing mamatics. it Corresponding Found was not Comment as listed answered survey for biology, chemistry or physics measured in against Biology number A-level of marks. NC level(s) for Edexcel GCSE specification mamatics a-level specification assessment. participants were chosen in 4. appropriateness of mamatics. We three groups; Foundation teaching (F) profession; higher education; looked at wher answer required scientific professional Higher bodies. an (H) online survey was completed by comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; 1 Arithmetic this was measured numerical as a proportion of total 38 for chemistry; F H 32 for physics). participants from computation: number of question parts containing mamatics. industry were also consulted more generally but as most science-related industries employ at a graduate level a (a) subject recognise expert group use was expressions established in for each L4 to L8 (L4 ü ü Decimals ir comments tended to focus more on outcomes of decimal three sciences. Stard each Form; group analysed decimals full to L8 at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, stard form) edexcel, ocr WJec for ir respective subjects û ü Stard Form: this will at a two-day workshop. examination papers included be taken off new all ory papers (Units 1, 2, 4 5) 212 foundation level experimental practical papers (Units 3 6). specification calculations were based on assumption that ory papers (b) calculate make up or 8% use ratios, of complete fractions a-level L5 to L7 ü ü Percentages: reverse experimental percentages; practical papers remaining 2% 2. Percentage of question parts in a complete A level ü ü Ratios ü ü Fractions percentages are exclusive to higher level 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, (c) chemistry make estimates physics. of mamatical results requirements of are L5 available to 6 in (NB ü ü full report. 2 calculations a complete science (without a-level is using made up a of calculator); 6 units. marks students from ory will papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, always have a question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose calculator) of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 63

64 ExEcutivE Table 22: continued summary mamatics enables students to underst (d) use calculators to find use L4 to EP (L4 ü ü Mean describe many scientific phenomena yet re is concern mean, stard deviations, power, mode, L5 mean, that science assessments at a-level are not reflecting exponential logarithmic functions; EP deviations. subject s analytical nature. to explore wher re was Exponential any evidence for this concern, score investigated logarithmic type, extent difficulty of mamatical questions within functions not science a-levels. findings show that a large number of found in biology) mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress û û Stard deviation: recently removed from GCSEs. Now on AS level mamatics specification effectively to stem higher education employment. û ü in addition, findings show a disparity in way aims Power functions: students are required to mamatics is assessed across different awarding score s overall objective for draw this project graphs was of to se organisations. score recommends that re is a review gar evidence on type, functions extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current û ü at a-level that a framework is developed to regulate Exponential functions: a-level specifications to establish wher this way mamatics is assessed within sciences to students are required to was being appropriately met by assessments. ensure parity across system. draw graphs of se work did not compare mamatical requirements functions between physics, chemistry biology as it is accepted Background se will û differ between û disciplines. Logarithmic functions: re has been growing concern across science On AS mamatics findings aim to provide score community about mamatical dem of science specification with evidence to inform development of policy on type, extent qualifications, (e) use calculations specifically involving that Gcse a-level L3 science to L4 ü ü difficulty of mamatics in criteria qualifications simple arithmetic are not meeting algebraic needs of students (depending assessments for a-levels in biology, chemistry transformations: way y assess analytical nature of science. on size of physics. project also supports score s work on number. in 29 score published evidence on Gcse science how examinations system should operate to ensure Algebraic examination papers which reported a wide variation in science qualifications are fit for purpose also its transformations amount of mamatics assessed across awarding work on improving coherence between sciences not found in organisations confirmed that use of mamatics mamatics. biology.) within context of science was examined in a very in project, we looked across all assessments at limited (g) +, way. -, x, score. organisations felt that this was L1 to L7 ü ü a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching (depending on practical examination papers. learning of sciences, offers a valuable aid nature of in understing describing scientific phenomena; numbers) as 2 such Hling it should data: be appropriately represented in NC levels F H Comments biology, chemistry physics curricula ir (a) use an appropriate number of L7 to L8 ü ü assessments. significant figures; to (b) provide find arithmetic furr evidence means; to support se L5 to L7 (L5 for ü ü concerns, score set up this project to investigate discrete data to mamatics found in 21 science assessments L7 for grouped at a-level across unitary awarding organisations data) in engl, Wales norrn irel. 64 SCORE Maths in science report

65 Table methodology 22: continued project was designed in three phases. groups comprised practising a-level teachers, teachers with experience in curriculum research first (c) construct was to establish or interpret nature tables, of mamatics L4 to EP (L4 for development ü üindividuals Tables, working frequency for awarding assessed frequency within tables biology, diagrams, chemistry bar physics bar charts, L4 organisations as markers, question tables, writers diagrams, or examiners. bar a-level charts examinations histograms; in 21. full suite of for frequency stardisation exercises were charts employed throughout examinations papers from aqa, ccea, edexcel, tables EP analysis for to verify reliability of judgements within ocr WJec were analysed using four histograms.) measures that follow: across subject expert groups. second û phase üaimed to measure Histograms coherence 1. type of mamatics. mamatical areas between teaching learning of mamatics (d) underst simple probability; L5 to L7 (L5 in ü ü Taken to mean only 1 assessed were categorised against stated sciences. re is an assumption that ory paper, L7 event taking place mamatical requirements for biology, chemistry mamatical concepts used to access sciences in practicals physics respectively 1. are first taught within a mamatical context, i.e. within coursework) mamatics curriculum. project compared (e) 2. underst extent of principles mamatics. of proportion EP û ü mamatical requirements for Rom sciences stratified a-level sampling of as question applied parts to scientific within a paper data; that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was (f) underst terms mean, median L5 to EP using ü current national ü curriculum Mean level descriptions proportion of marks within se questions mode stard deviation; a 212 mamatics Gcse specification 3. this work that required mamatics. was carried ü out by ü a researcher by a mamatics Median 3. difficulty of mamatics. this was measured teacher. ü ü against 3 criteria: number of steps in a Mode aim of third phase was to determine nature calculation, familiarity of context û û of mamatics that community Stard would Deviation like to see complexity of question. each category (g) use a scatter diagram to identify L6 in a-level ü science üassessments. this was achieved had varying levels of difficulty each was positive negative correlation through an online survey for stakeholders in science measured as a proportion of total number of between two variables; community. Depending on ir expertise, participants question parts containing mamatics. it was not answered survey for biology, chemistry or physics (h) select measured against use a simple number statistical of marks. EP û ü Taken to mean choosing a-level assessment. participants were chosen in test; a sampling technique 4. appropriateness of mamatics. We three groups; teaching profession; higher education; (i) make looked order at wher of magnitude answer required scientific L5 to EP professional û bodies. û an online Not survey a concept was completed taught in by calculations; comprehension in addition to mamatical (depending skill. on 97 participants across three mamatics. groups (27 for Compare biology; this was measured as a proportion of context) total 38 for chemistry; 32 for physics). with 1c) participants estimation from number of question parts containing mamatics. industry were also consulted techniques more generally but as most science-related industries employ at a graduate level a (j) subject determine expert group interpret was established population for each EP û û Appears in A-level ir comments tended to focus more on outcomes of variance, three stard sciences. deviation each group analysed full mamatics at graduate level rar than directly referring to a-level. suite stard of 21 deviation examinations (error) papers of of mean; aqa, ccea, specification edexcel, (k) underst ocr probability WJec for in ir order respective to subjects L6 to EP at underst a two-day workshop. how genetic examination ratios arise; papers included ü ü Single events all ory papers (Units 1, 2, 4 5) û ü Joint (i.e. 2 or 3) events experimental practical papers (Units 3 6). calculations (l) frame null were hyposis. based on assumption that EP û û ory Appears in A-level papers make up 8% of complete a-level mamatics experimental practical papers remaining 2% 2. specification 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 65

66 ExEcutivE Table 22: continued summary mamatics enables students to underst describe 3 Algebra: many scientific phenomena yet re is NC concern levels that (a) science change assessments subject at of a-level an equation; are not reflecting L8 subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress F ü H ü Comments In Foundation level students are required to change subject of a formula. In Higher level this includes cases where subject is on both sides of original formula or where power of a subject appears. effectively to stem higher education employment. (b) substitute numerical values into L4 to L5 (L5 for ü ü in addition, findings show a disparity in way aims algebraic equations using appropriate numbers in mamatics is assessed across different awarding units for physical quantities; thouss.) score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of (c) underst mamatical requirements use of logarithms for each of EP û û sciences mamatics required to access This appears sciences in in AS current level at in a-level relation to that quantities a framework that is range developed over to regulate a-level specifications to establish mamatics wher this several way mamatics orders of magnitude; is assessed within sciences to was being appropriately met by assessments. ensure (d) derive parity an across equation. system. L5 to L6 work did ünot compare ü mamatical requirements between physics, chemistry biology as it is accepted (e) =, <, > L4 ü ü Background se will differ between disciplines. 4 Graphs: NC level F H Comments re has been growing concern across science findings aim to provide score with evidence to community (a) translate about information mamatical between dem of L3 science to L6 (L3 for ü ü inform development of policy on type, extent qualifications, graphical, numerical specifically that algebraic Gcse a-level bar science graphs to L6 difficulty of mamatics in criteria qualifications forms; are not meeting needs of students for line graphs.) assessments for a-levels in biology, chemistry (b) way plot y two assess variables analytical from experimental nature of science. L3 to L6 (As physics. ü project ü also supports score s work on or or data; above in 4(a), in 29 score published evidence on Gcse science how examinations system should operate to ensure but will usually examination papers which reported a wide variation in science qualifications are fit for purpose also its be a line graph amount of mamatics assessed across awarding work in on improving coherence between sciences biology.) organisations confirmed that use of mamatics mamatics. within (c) calculate context rate of of science change was from examined a in a EP very ü ü Taken to mean working in project, we looked across all assessments at limited graph way. showing score a linear organisations relationship; felt that this was out a gradient a-level for a given year, including both experimental unacceptable. (d) draw mamatics use slope is integral of a tangent to teaching EP practical û examination û papers. This was previously on to a learning curve of as a measure sciences, of rate offers of a valuable aid GCSE specification in change; understing describing scientific phenomena; as such it should be appropriately represented in biology, (e) construct chemistry / or physics interpret curricula line ir L6 ü ü assessments. graphs (straight or curved). to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 66 SCORE Maths in science report

67 Table methodology 22: continued groups comprised practising a-level teachers, project was designed in three phases. teachers with experience in curriculum research first 5 Geometry: was to establish nature of mamatics NC levels development F Hindividuals Comment working for awarding assessed within biology, chemistry physics organisations as markers, question writers or examiners. (a) visualise three dimensional forms L6 ü ü a-level examinations in 21. full suite of stardisation exercises were employed throughout from two dimensional representations examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within of three dimensional objects; ocr WJec were analysed using four across subject expert groups. (b) calculate length, circumferences L4 to EP (L4 for ü ü Circles measures that follow: areas of circles, surface areas length, L6 for second phase aimed to measure coherence volumes 1. type of regular of mamatics. blocks cylinders mamatical circumference areas between to teaching learning of mamatics when assessed provided were with categorised appropriate against stated EP surface area sciences. re is an assumption that formulae mamatical requirements for biology, chemistry of cylinders.) mamatical concepts used to access sciences physics respectively 1. are first taught within a mamatical context, i.e. within ü ü mamatics curriculum. Surface project area compared for cuboids 2. extent of mamatics. proportion mamatical û requirements ü for Surface sciences area for at a-level of question parts within a paper that with mamatics curriculum cylinders prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that PHASE required 3 mamatics. SURVEY FINDINGS Figure was carried 27: out Opinions by a researcher from biology by a mamatics online difficulty of mamatics. this was measured survey teacher. respondents on spread of TYPE OF MATHEMATICS ASSESSED against 3 criteria: number of steps in a mamatical content areas within a AT A-LEVEL BIOLOGY calculation, familiarity of context biology aim of A-level third phase was to determine nature In Part A respondents were asked to consider of mamatics that community would like to see complexity of question. each category spread of mamatical content areas assessed in a-level science assessments. this was achieved had varying levels of difficulty each was within biology A-level. Figure 27 illustrates through an online survey for stakeholders in science measured as a proportion of total number of percentages of respondents that considered community. Depending on ir expertise, The Key mamatical participants question parts containing mamatics. it was not content areas were assessed spread to be good, acceptable (key mamatical answered survey for biology, chemistry or physics measured against number of marks. a-level assessment. participants A restricted were amount chosen of areas were assessed), average (limited variation in in mamatical content areas type 4. of mamatics) appropriateness of poor mamatics. (restricted We amount three groups; teaching profession; seemed higher to be education; assessed many times of mamatics looked wher assessed answer many times). required scientific professional bodies. an online survey was completed by There was a good spread of comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; different mamatical content this was measured a proportion of total 38 for chemistry; 32 for physics). areas Participants were also asked to comment on participants being assessed from areas number of mamatics of question y parts would containing like to mamatics. feature industry were also consulted more There generally was not enough but as variation most in type of mamatical highly in assessment, a little or not at all. These science-related industries employ at a graduate level content being assessed a subject expert group was established for each results are displayed in Figure 28. Participants ir comments tended to focus more on outcomes of three sciences. each group analysed full were also asked if re were any or areas of at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, mamatics not listed in requirements that edexcel, ocr WJec for ir respective subjects y felt should be included in assessments. In Part A, prior to findings of analysis, 74% of at a two-day workshop. examination papers included The only area that was mentioned more than once respondents felt that awarding organisations should all ory papers (Units 1, 2, 4 5) was converting between different units. use a framework to ensure that a broad spread of experimental practical papers (Units 3 6). mamatical requirements are assessed 52% calculations were based on assumption that ory The main concern voiced by participants was lack felt that all requirements should be assessed over papers make up 8% of complete a-level of assessment of statistics, with ors expressing a 2- year or 3- year cycle of A-levels to ensure experimental practical papers remaining 2% 2. concern that mamatics should always be taught y are taught. A third of respondents felt that if within a biology context. The lack of alignment areas are not assessed n it would mean that area with mamatics courses also worried some would not be taught at all. No respondents felt that respondents, since this would mean some students only key requirements should definitely be assessed would not have mamatical skills to access some of biology content, this was also expressed as a query about wher re should be a minimum requirement set for biology A-level in terms of grade achieved at GCSE mamatics. as opposed to all requirements. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. In Part B participants were told that some of mamatical requirements were well-covered in A-levels, for example, interpreting frequency SCORE Maths in science report 67

68 ExEcutivE Figure 28: Mamatical summary requirement areas that biology survey respondents would like to feature highly in assessment, a little in assessment or not at all mamatics enables students to underst describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting Feature Highly Feature a Little Feature Not At All subject s analytical nature. to explore wher re was 3 any evidence for this concern, score investigated type, extent 25 difficulty of mamatical questions within science a-levels. findings show that a large number of 2 mamatical requirements listed in biology, chemistry physics 15specifications are not assessed. those that are assessed are covered repeatedly often at a lower 1 level than required. this is likely to have an impact on way that subjects are taught refore on 5 students ability to have necessary skills to progress effectively to stem higher education employment. 1a 1b 1c 1d 1e 1f 1g 2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 5a 5b in addition, findings show a disparity in way aims Mamatical Requirements for Biology A-Level mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current at tables, a-level diagrams, that a histograms framework is developed bar charts. to regulate Or of requirements were relevant so majority of a-level specifications to establish wher this areas way were mamatics hardly assessed is assessed or within not assessed sciences at to all. requirements should be assessed. It was also was being appropriately met by assessments. ensure There was parity little across difference system. between those who felt thought that a range of mamatical requirements work did not compare mamatical requirements that this was appropriate those that did not. were necessary for future study or jobs. between physics, chemistry biology as it is accepted Background Some respondents thought that greater breadth se will differ between disciplines. in assessments promoted greater breadth in EXTENT OF MATHEMATICS re has been growing concern across science teaching re were concerns that if content findings aim to provide score with evidence to community about mamatical dem of science In Part A half of respondents felt that areas were not assessed y would not be taught. inform development of policy on type, extent qualifications, specifically that Gcse a-level science amount of mamatics in paper was not When comparing Figure 22 Figure 28 it is difficulty of mamatics in criteria qualifications are not meeting needs of students in enough to adequately prepare for progression to clear re is a mismatch between mamatical assessments for a-levels in biology, chemistry way y assess analytical nature of science. higher education in biology or a related subject. content areas that are assessed those that physics. However, after project viewing also supports findings score s of work analysis, on in science 29 score community published would evidence like to on be Gcse assessed science (for how 7% of examinations respondents system thought should that operate percentage to ensure examination example, plotting papers two which variables reported from a wide data variation using science of question qualifications parts containing are fit for purpose mamatics also was its logarithms amount of in mamatics relation to quantities assessed which across range awarding over work appropriate on improving (39-54% coherence of question between parts across sciences organisations several orders of confirmed magnitude). that use of mamatics awarding mamatics. organisations). Respondents were within context of science was examined in a very told that percentage of marks that required Some felt that it was not necessary to assess all in project, we looked across all assessments at limited way. score organisations felt that this was mamatics varied across awarding organisations mamatical content areas in all papers or that it a-level for a given year, including both experimental unacceptable. mamatics is integral to teaching from 13% to 25%. The most common opinion on was not necessary to assess all areas every year practical examination papers. learning of sciences, offers a valuable aid se results was that differences like this across while ors felt that if it was in specification in understing describing scientific phenomena; awarding organisations were not acceptable (77%). n it should be assessed. as such it should be appropriately represented in 48% of respondents felt that 13% was too low biology, chemistry physics curricula ir no census was reached on wher upper limit Still considering type of content areas that assessments. was too low. were assessed, respondents were told that a Number of Respondents to few provide mamatical furr evidence requirements to support were se assessed concerns, repeatedly, score rar set than up a this spread project of to skills investigate being mamatics assessed. 81% found of in respondents 21 science did assessments not think that a-level this was across appropriate. unitary awarding It was reported organisations that in engl, students Wales needed a norrn broad mamatical irel. capability refore a broad range should be assessed. It was felt that, while key requirements were most important skills to be assessed, majority In Part A, when asked wher mamatical content in ory papers in practical papers should be different, nearly two-thirds of respondents felt that it should be different. It was felt that mamatical requirements were appropriate to topic that papers lent mselves to different skills. Many cited examples 68 SCORE Maths in science report

69 of methodology how practical papers would lead to more analysis project was manipulation designed in of three data phases. rar than interpretation, first was to establish which would nature be of assessed mamatics in ory assessed papers. within They biology, felt that chemistry practical physics work was a-level an examinations opportunity for in 21. more in-depth full suite mamatics. of They examinations also reported papers that from if aqa, it was ccea, different edexcel, that it would ocr allow WJec for a were greater analysed range using of mamatical four skills measures to be that assessed follow: it would give rise to less repetition. Those who felt that mamatics should 1. be type of same mamatics. in practical mamatical papers felt areas most assessed strongly that were categorised key mamatical against skills stated should mamatical be tested in requirements both types for of biology, assessment. chemistry In Part B physics majority respectively also did 1. not think it was important 2. extent if of marks mamatics. were awarded in proportion ory of or practical question papers. parts within a paper that included mamatics was measured as was proportion DIFFICULTY of marks OF MATHEMATICS within se questions In Part that A required of survey mamatics. nearly 6% of respondents felt 3. that it difficulty did not of matter mamatics. if level this of was difficulty measured of biology against A-levels 3 criteria: was perceived number to of go steps up in due a to m calculation, containing more familiarity mamatics. of context There was a split in opinions complexity from of all three question. participant each category groups. had varying levels of difficulty each was When asked about difficulty in terms of number measured as a proportion of total number of of steps in calculations on paper, question parts containing mamatics. it was not most popular opinion (41%) was that balance measured against number of marks. on sample paper was appropriate. In Part B 4. participants appropriateness were told of mamatics. that majority We of calculations looked at wher across answer examinations required papers scientific were comprehension single step, followed in addition by to multiple mamatical step, with skill. extended this was calculations measured as a least proportion likely type of to total be found. number About of question a third parts of respondents containing mamatics. felt that re a subject should expert be group more was multiple established step for each extended calculations of three sciences. 19 in each total group 48% of analysed respondents full felt re suite of should 21 examinations be an even spread papers of aqa, three ccea, types of edexcel, calculation. ocr WJec for ir respective subjects at a two-day workshop. examination papers included In Part A when considering context as a measure all ory papers (Units 1, 2, 4 5) of difficulty, around two-thirds of teachers felt experimental practical papers (Units 3 6). that number of questions with mamatical calculations were based on assumption that ory content set in a familiar context was appropriate. papers make up 8% of complete a-level There was no agreement between higher experimental practical papers remaining 2% 2. education professional body representatives. In Part B respondents were told that in analysis of groups papers comprised it was found practising that a-level between teachers, 53% 69% teachers 2 of with experience calculations in curriculum were found research to be set in a development familiar context individuals 21. Nearly working half of for awarding respondents thought organisations that as this markers, was about question right writers amount or examiners. of stardisation mamatics exercises to be set were in a employed familiar context, throughout with analysis to or verify half agreeing reliability of that judgements re should within be across less mamatics subject expert set groups. in familiar contexts so that students had more experience of applying second phase aimed to measure coherence mamatics in unfamiliar situations. However, between teaching learning of mamatics fewer than half of respondents felt that this sciences. re is an assumption that familiarity of context was creating a problem with mamatical concepts used to access sciences progression to higher education or industry are first taught within a mamatical context, i.e. within students ability to apply mamatics in novel mamatics curriculum. project compared situations. mamatical requirements for sciences at a-level with mamatics curriculum prior to Key stage 5 Respondents were asked to make a judgement on using current national curriculum level descriptions mamatical difficulty in terms of complexity a 212 mamatics Gcse specification 3. this work in paper. In Part A just over half (59%) thought was carried out by a researcher by a mamatics that complexity was appropriate, with teacher. remainder considering complexity to be insufficient. aim of In third Part phase B, nearly was three-quarters to determine of nature participants of mamatics thought that that community recall would of common like to see mamatical in a-level science procedures assessments. should this be was assessed achieved alongside through an procedures online survey that for stakeholders involved application in science in one community. or more Depending mamatical on ir content expertise, areas; participants however, answered analysis of survey assessments for biology, chemistry showed or that physics a-level vast assessment. majority of participants mamatics were required chosen in three use groups; of only teaching recall profession; procedures higher education; relatively straightforward professional bodies. application. an online survey was completed by 97 participants across three groups (27 for biology; for chemistry; COMPARABILITY 32 for physics). ACROSS participants from AWARDING industry were also ORGANISATIONS consulted more generally but as most In science-related Part A all of industries respondents employ at agreed a graduate that level it was important ir comments that tended A-levels to focus from more all on of outcomes awarding organisations at graduate level had rar than same directly level referring of difficulty to a-level. in terms of mamatical content. When asked about awarding organisations assessing same mamatical content areas, 63% felt that only same key areas needed to be assessed, with 3% thinking that all of mamatical content areas should be assessed in same way. The vast majority (93%) thought that proportion of questions with mamatical content should be similar across awarding organisations. 74% 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report a complete Some respondents science a-level supported is made up both of 6 units. statements marks so se from percentages ory papers do (Unit not 1, represent 2, 4 5) two make different up 8% findings. of complete 2 a-level These assessment figures are average marks from of AS practical A2 papers experimental do papers not take (Unit into 3 account 6) make up weighting remaining of 2%. ory in analysis, practical question parts rar than marks were used in calculation but we maintained 8:2 weighting. papers. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in 21 There revised was mamatics no comment Gcses. on finding that almost 1% of ory papers contained mamatics set in familiar contexts. SCORE Maths in science report 69

70 ExEcutivE of respondents summary felt that awarding organisations should use a framework to ensure a broad spread mamatics enables students to underst of mamatical requirements are assessed. describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting In Part B, 78% of respondents felt that subject s analytical nature. to explore wher re was difference across awarding organisations in any evidence for this concern, score investigated proportion of marks at A-level for mamatical type, extent difficulty of mamatical questions within content was not acceptable. science a-levels. findings show that a large number of mamatical COHERENCE requirements BETWEEN listed in biology, chemistry MATHEMATICS physics specifications AND THE are not SCIENCES assessed. those that are assessed are covered repeatedly often at a lower level Respondents than required. were this asked is likely which to have was an impact most on important way that feature subjects of are mamatics taught refore in biology on students A-levels: ability proportion to have of necessary paper skills that to progress contained effectively mamatical to stem content, higher education appropriateness employment. of in mamatical addition, findings content show covered a disparity in in assessments way mamatics or difficulty is assessed of mamatics across different in awarding organisations. assessments. score Out of recommends se choices, that 89% re agreed is a review of that mamatical appropriateness requirements of for mamatical each of sciences at content a-level covered that a in framework assessments is developed was to regulate most important. way mamatics is assessed within sciences to ensure parity across system. Two-thirds of participants agreed that mamatics Background GCSE should be adequate preparation for mamatics in a science A-level rar than re students has needing been growing support concern of across a separate science community mamatics about qualification. mamatical It was dem felt that of science qualifications, mamatics specifically GCSE that should Gcse be adequate a-level science qualifications preparation to are build not meeting on, although needs of mamatics students in in way biology y assess A-level would analytical go nature beyond of it science. in terms of application of mamatics in novel in 29 score published evidence on Gcse science situations. examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within 3.4 VIEWS context FROM of science INDUSTRY was examined in a very limited way. score organisations felt that this was TYPE OF MATHEMATICS ASSESSED unacceptable. mamatics is integral to teaching WITHIN SCIENCE A-LEVEL learning of sciences, offers a valuable aid in There understing were concerns describing that scientific mamatical phenomena; as elements such it should did not be properly appropriately prepare represented students in for biology, higher education, chemistry including physics curricula fact that ir assessments. mamatics needed for engineering was only found within furr mamatics A-level. There to was provide also a furr feeling evidence that re to support was grade se inflation concerns, in current score science set up A-levels, this project that to re investigate was mamatics low quality in found mamatical in 21 science content assessments that at re a-level was across a problem unitary distinguishing awarding organisations between in engl, (mamatical) Wales ability norrn of an irel. A an A* graded science student. The industry representatives were asked which mamatical content areas from a given list y felt were important in A-level science assessments. All areas listed ( shown below) were felt to be important, with subsequent comments clarifying ir opinions: Arithmetic computation an important foundation skill Hling data a vital skill for extracting information from data Algebra a crucial area, in particular rearranging equations using generic formulae Geometry less important only necessary at a basic level aims Trigonometry a lot of scientific work cannot be completed without trigonometry score s overall objective for this project was to Graphs important to communicate data gar evidence on type, extent difficulty of trends mamatics required to access sciences in current a-level Application specifications of mamatics to establish very wher important, this was if not being vital, appropriately needs lots met of by practice. assessments. work did not compare mamatical requirements Calculus was mentioned repeatedly as an between physics, chemistry biology as it is accepted important aspect of mamatics, as it was needed se will differ between disciplines. in so many careers. It was felt to be important for students findings aim to be to provide able to score complete with calculations evidence to inform without a development calculator so of that policy y on developed type, extent a feel for numbers difficulty of could mamatics spot mistakes. in criteria Complex assessments numbers, vectors, for a-levels risk assessment in biology, chemistry probability physics. were or aspects project also of mamatics supports score s not mentioned work how above that examinations industry system representatives should operate felt to were ensure science important qualifications to A-level are science fit for purpose students. Statistics also its work was mentioned improving by half coherence of representatives between sciences because mamatics. it is commonly used in biology, in process, design manufacturing engineering in in optimisation project, of we experiments. looked across all assessments at a-level for a given year, including both experimental practical There was examination general agreement papers. that mamatics in science A-levels needed to go beyond that found in mamatics GCSE that this was not a problem. It was felt that mamatics only needed to be re when science demed it, but that it was necessary to go beyond mamatics GCSE if it was to prepare students for higher education. 7 SCORE Maths in science report

71 3.4.2 methodology EXTENT OF MATHEMATICS All of project industry was designed representatives in three phases. agreed that it would first was not to matter establish if nature amount of or difficulty mamatics of mamatics assessed within in biology, science chemistry A-levels increased, physics even a-level if this examinations resulted in 21. A-levels full being suite of perceived to examinations be more difficult. papers from Reasons aqa, given ccea, included edexcel, that ocr A-levels WJec needed were analysed to be more using competitive four internationally, measures that follow: that if difficulty was not re that 1. assessments type of mamatics. were of less mamatical use to higher areas education assessed were industry categorised that against if it deterred stated a student, mamatical n perhaps requirements y should for biology, not have chemistry been taking physics A-level respectively anyway. It 1. was recognised that, if changes were made, that more mamatics specialist 2. extent support of may mamatics. be needed. proportion of question parts within a paper that included DEMAND mamatics OF MATHEMATICS was measured as was proportion of marks within se questions Industry representatives main concern regarding that required mamatics. mamatical element of science A-levels was 3. perceived difficulty of lack mamatics. of fluency this was lack measured of ability against of 3 A-level criteria: students number to use of steps in apply a ir mamatical calculation, knowledge familiarity in a of new context situation; this was problematic complexity as of this was question. a skill each y category would be expected had varying to use levels in work. of difficulty each was measured as a proportion of total number of There question were concerns parts containing that mamatics. mamatical it was not elements measured did not against properly number prepare of students marks. for higher education, including fact that 4. appropriateness of mamatics. We mamatics needed for engineering sat only within looked at wher answer required scientific furr mamatics A-level. Lastly, re was a comprehension in addition to mamatical skill. feeling that re was grade inflation in current this was measured as a proportion of total science A-levels, that re was low quality in number of question parts containing mamatics. mamatical content that re was a problem distinguishing a subject expert between group was established (mamatical) for each ability of an of A three an sciences. A* graded each science group analysed student. Industry full representatives suite of 21 examinations were asked papers to comment of aqa, ccea, on aspects edexcel, of ocr mamatical WJec for difficulty ir respective used in subjects Phase 1 at analysis a two-day of workshop. A-level examination papers. Most papers felt included that students all ory should papers be (Units tackling 1, 2, mamatics 4 5) in familiar experimental unfamiliar contexts; practical work papers contexts (Units 3 would 6). be unfamiliar calculations were unfamiliar based on contexts assumption differentiated that ory difficulty papers make in up assessments. 8% of complete In terms a-level of complexity, most experimental of industry practical representatives papers remaining reported 2% that 2. y groups would comprised like to see practising a mixture a-level of calculations teachers, that involved teachers with straightforward experience in recall curriculum of routine research classroom procedures, development those individuals that required working application for awarding of mamatics organisations as within markers, one question area of mamatics writers or examiners. those stardisation that required exercises application were employed in more throughout than one area analysis of mamatics. to verify reliability While of calculations judgements involving within straightforward across subject recall expert were groups. felt to underpin some science, re was a perceived need to differentiate second phase aimed to measure coherence by including more complex calculations to between teaching learning of mamatics give a greater challenge to keep students engaged. sciences. re is an assumption that It was reiterated that mamatics should be mamatical concepts used to access sciences what was necessary to support science, but are first taught within a mamatical context, i.e. within that science should not be dumbed down mamatics curriculum. project compared in order to avoid inclusion of more complex mamatical requirements for sciences at a-level mamatics. All of industry representatives with mamatics curriculum prior to Key stage 5 wanted to see more multiple step extended using current national curriculum level descriptions calculations than single step calculations. a 212 mamatics Gcse specification 3. this work was carried out by a researcher by a mamatics PARITY ACROSS AWARDING teacher. ORGANISATIONS aim of third phase was to determine nature Most of industry representatives felt that re of mamatics that community would like to see should not be differences across awarding in a-level science assessments. this was achieved organisations in terms of difficulty of through an online survey for stakeholders in science mamatics assessed, assessed content community. Depending on ir expertise, participants or amount of mamatics assessed in answered survey for biology, chemistry or physics science A-levels. It was felt that variety in a-level assessment. participants were chosen in lscape of qualifications was not understood three groups; teaching profession; higher education; by industry that employers did not want to professional bodies. an online survey was completed by ask which awarding organisations awarded 97 participants across three groups (27 for biology; qualification when assessing cidates. They 38 for chemistry; 32 for physics). participants from felt that aligning mamatics element would industry were also consulted more generally but as most remove temptation for awarding organisations science-related industries employ at a graduate level to lower stards to attract more cidates ir comments tended to focus more on outcomes for schools to opt for an easier examination. at graduate level rar than directly referring to a-level. One respondent felt that admissions tutors were aware of differences across awarding organisations anor that, if re were transparent differences across awarding organisations in terms of mamatical content, that it may lead to more diversity when it came to recruitment. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 71

72 APPENDICES ExEcutivE APPENDIX summary 1: SUMMER 21 A-LEVEL PAPERS ANALYSED mamatics enables students to underst Subject Awarding Organisation describe many scientific phenomena yet re is concern that Physics science assessments at a-level are not AQA reflecting subject s analytical nature. to explore wher re was any evidence for this concern, score investigated CCEA type, extent difficulty of mamatical Edexcel questions within A level Physics A Physics Physics science a-levels. findings show that a large number of OCR Physics B mamatical requirements listed in biology, chemistry physics specifications are not assessed. WJEC those that Physics are Chemistry assessed are covered repeatedly often AQAat a lower level than required. this is likely to have an impact on CCEA way that subjects are taught refore on students ability to have necessary skills Edexcel to progress Chemistry Chemistry Chemistry effectively to stem higher education employment. OCR Chemistry A in addition, findings show a disparity in way aims WJEC Chemistry mamatics is assessed across different awarding score s overall objective for this project was to organisations. Biology score recommends that AQA re is a review of mamatical requirements for each CCEA of sciences gar evidence on Biology type, extent difficulty of mamatics required Biology to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this Edexcel Biology way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. OCR work did not compare Biology mamatical (H421) requirements Background WJEC between physics, chemistry Biology biology as it is accepted se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 72 SCORE Maths in science report

73 APPENDIX methodology 2: MATHEMATICAL REQUIREMENTS FOR PHYSICS groups comprised A-LEVEL practising 22 a-level teachers, project was designed in three phases. teachers with experience in curriculum research 1. Arithmetic Computation 4. Geometry Trigonometry first was to establish nature of mamatics development individuals working for awarding Cidates should be able to: (a) calculate areas of triangles, circumferences areas of assessed within biology, chemistry physics organisations as markers, question writers or examiners. (a) use a calculator for addition, subtraction, multiplication circles, surface areas volumes of rectangular blocks, a-level division; examinations in 21. full suite of stardisation cylinders spheres; exercises were employed throughout (b) examinations recognise papers use expressions from aqa, in ccea, decimal edexcel, form; ( stard (b) analysis use Pythagoras to verify orem, reliability similarity of judgements of triangles within ocr from deleted WJec from were this analysed requirement using recorded four separately across angle sum subject of a triangle; expert groups. as 1(h) to illustrate how commonly each occurred.) (c) use sines, cosines tangents in physical problems; measures that follow: (c) use ratios, fractions percentages; (d) use second sinѳ phase tanѳ aimed Ѳ to cos measure Ѳ 1 for small coherence Ѳ; (d) 1. use calculators type of to mamatics. find use x n, 1/x, mamatical x 2, x, log l x, areas (e) between underst teaching relationship learning between of degrees mamatics radians e x, log assessed e x; were categorised against stated translate sciences. from re one to is an assumption or. that (e) use calculators to hle sinѳ, cosѳ, tanѳ, sin -1 Ѳ, cos -1 Ѳ, mamatical requirements for biology, chemistry 5. mamatical Graphs concepts used to access sciences tan -1 Ѳ when Ѳ is expressed in degrees or radians. physics respectively 1. (a) are translate first taught information within a between mamatical graphical, context, numerical i.e. within (f) recognise use SI prefixes 1-12, 1-9, 1-6, 1-3, 1 3, algebraic mamatics forms; 1 curriculum. project compared extent 9 of mamatics. proportion (b) plot two variables from experimental or or data using (g) hle calculations so that significant figures are neir lost mamatical requirements for sciences at a-level of question parts within a paper that appropriate scales for graph plotting; or carried beyond what is justified; with mamatics curriculum prior to Key stage 5 included mamatics was measured as was (c) plot data on a log-linear graph determine wher y (h) stard form. using change current exponentially national curriculum determine level exponent; descriptions proportion of marks within se questions 2. Hling data (d) plot a 212 data on mamatics a log-log graph Gcse specification decide wher 3. this data work obey (a) show that an required awareness mamatics. of order of magnitude of physical was a carried power law out by determine a researcher exponent; by a mamatics quantities make order of magnitude calculations; (e) 3. difficulty of mamatics. this was measured teacher. select appropriate variables for graph plotting; (b) use an appropriate number of significant figures; (f) underst that y = mx + c represents a linear relationship against 3 criteria: number of steps in a (c) find arithmetic means medians; aim rearrange of third relationships phase was into to this determine form where appropriate; nature (d) express calculation, changes as familiarity percentages of context vice versa; (g) of mamatics determine that slope / gradient community intercept would like of a to linear see (e) underst complexity use of logarithmic question. scales each in relation category to in a-level graph in science appropriate assessments. physical this units; was achieved quantities had varying which levels range of over difficulty several orders each of magnitude. was (h) determine gradient of a tangent to a non-linear graph by through an online survey for stakeholders in science measured as a proportion of total number of drawing use slope of tangent as a measure of 3. Algebra community. rate of change; Depending on ir expertise, participants (a) change question subject parts containing of an equation mamatics. by manipulation it was of not (i) answered choose by inspection survey for a biology, straight line chemistry or curved or line physics which will terms, measured including against positive number negative, of integer marks. fractional a-level serve assessment. best straight participants line through were a set of chosen data points indices square roots 4. appropriateness of mamatics. We three presented groups; graphically; (b) substitute numerical values into algebraic equations using teaching profession; higher education; (j) underst possible physical significance of area appropriate looked at units wher for physical answer quantities required scientific professional bodies. an online survey was completed by between a curve x axis be able to calculate it or (c) check comprehension dimensional in consistency addition to of mamatical physical equations skill. 97 participants across three groups (27 for biology; measure it by counting squares as appropriate; substitute numerical values into such equations using this was measured as a proportion of total (k) 38 for underst chemistry; use 32 for slope physics). of a tangent participants to a curve from as appropriate units for physical quantities; number of question parts containing mamatics. industry a means were to also obtain consulted gradient. more Underst generally but use as most (d) solve simple algebraic equations including y=k/x, y=k/x 2 science-related notation d/dt for industries a rate of employ change; (e) at a graduate level a subject formulate expert use group simple was algebraic established equations for each as (l) ir underst comments tended use multiplicative to focus more scales on (1, 1, outcomes 1...); mamatical models of physical situations, identify of three sciences. each group analysed full (m) use logarithmic plots to test exponential power law inadequacy of such models at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, variations; (f) underst use symbols: <, <<, >>, >, ~,,, x, edexcel, ocr WJec for ir respective subjects (n) sketch simple functions including y = k/x, y = kx 2 y = k/x 2, y x, dx/dt = sinѳ, y = cosѳ, y = e at a two-day workshop. examination papers included -kx. (o) underst or recognise physical significance of a all ory papers (Units 1, 2, 4 5) straight line passing or not passing through origin. experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete 22 During course of research it was established that awarding organisations adapted mamatical requirements a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question set by parts Ofqual. rar This than list marks represent were used an amalgamation in calculation of but we mamatical maintained requirements 8:2 weighting. used by awarding organisations, linked 3 closely edexcel to 212 that a set specification by Ofqual. was The used text for in red purpose represents of additions analysis as it was changes considered made representative to list of during typical content analysis found process in in order revised to mamatics more accurately Gcses. capture mamatical content. SCORE Maths in science report 73

74 ExEcutivE APPENDIX summary 3: MATHEMATICAL REQUIREMENTS FOR CHEMISTRY A-LEVEL 22 mamatics 1 Arithmetic enables numerical students computation: to underst describe (a) recognise many scientific use expressions phenomena in decimal yet re is concern that stard science form; assessments at a-level are not reflecting subject s (b) use ratios, analytical fractions nature. percentages; to explore wher re was (c) make estimates of results of calculations any evidence for this concern, score investigated (without using a calculator); type, extent difficulty of mamatical questions within (d) use calculators to find use power, exponential science logarithmic a-levels. functions findings (x n, show 1/x, x, that loga large number of l x, e x, log e x); mamatical (e) +, -, x,. requirements listed in biology, chemistry physics specifications are not assessed. those that are 2 Hling assessed data: are covered repeatedly often at a lower (a) use an appropriate number of significant figures; level than required. this is likely to have an impact on (b) find arithmetic means; (c) way construct that subjects interpret frequency are taught tables refore diagrams, on students bar charts ability to histograms; have necessary skills to progress effectively (d) use an to appropriate stem higher number education of decimal places. employment. in addition, findings show a disparity in way 3 Algebra: mamatics is assessed across different awarding (a) underst use symbols: =, <, <<, >>, >,, organisations. score recommends that re is a review ~, μ; of (b) change mamatical subject requirements of an equation; for each of sciences at (c) a-level substitute numerical that a framework values into is algebraic developed equations to regulate way using mamatics appropriate units is assessed for physical within quantities; sciences to ensure (d) solve parity simple across algebraic equations; system. (e) use logarithms in relation to quantities which range over several orders of magnitude. Background re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. 4 Graphs: (a) translate interpret information between graphical, numerical algebraic forms; (b) plot two variables from experimental or or data; (c) underst that y = mx + c represents a linear relationship; (d) determine slope intercept of a linear graph; (e) calculate rate of change from a graph showing a linear relationship; (f) draw use slope of a tangent to a curve as a measure of rate of change; (g) interpret a spectrum. 5 Geometry trigonometry: a) appreciate angles shapes in regular 2-D 3-D structures; b) visualise represent 2-D 3-D forms including aims two-dimensional representations of 3-D objects; c) underst symmetry of 2-D 3-D shapes. score s overall objective for this project was to gar evidence on type, extent difficulty of mamatics required to access sciences in current a-level specifications to establish wher this was being appropriately met by assessments. work did not compare mamatical requirements between physics, chemistry biology as it is accepted se will differ between disciplines. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 74 SCORE Maths in science report

75 APPENDIX methodology 4: MATHEMATICAL REQUIREMENTS FOR BIOLOGY groups comprised A-LEVEL practising 22 a-level teachers, project was designed in three phases. teachers with experience in curriculum research 1 Arithmetic numerical computation: 3 Algebra: first was to establish nature of mamatics development individuals working for awarding (a recognise use expressions in decimal (a) change subject of an equation; assessed within biology, chemistry physics organisations as markers, question writers or examiners. stard form; (b) substitute numerical values into algebraic equations (b) a-level calculate examinations or use ratios, in 21. fractions full percentages; suite of stardisation using appropriate exercises units for were physical employed quantities; throughout (c) examinations make estimates papers of from results aqa, of calculations ccea, edexcel, (c) analysis underst to verify use reliability of logarithms of judgements in relation to quantities within ocr (without WJec using a were calculator); analysed using four across that range subject over several expert orders groups. of magnitude; (d) use calculators to find use mean, stard (d) derive an equation; measures that follow: deviations, power, exponential logarithmic functions; (e) =, second <, >. phase aimed to measure coherence (e) 1. use calculations type of mamatics. involving simple arithmetic mamatical areas between teaching learning of mamatics algebraic transformations: 4 assessed were categorised against stated Graphs: sciences. re is an assumption that (f) underst use correlations; (a) mamatical requirements for biology, chemistry mamatical translate information concepts between used to graphical, access numerical sciences (g) +, -, x,. algebraic forms; physics respectively 1. are first taught within a mamatical context, i.e. within (b) plot two variables from experimental or or data; 2 Hling data: (c) calculate mamatics rate of curriculum. change from a graph project showing compared a linear 2. extent of mamatics. proportion (a) use an appropriate number of significant figures; mamatical relationship; requirements for sciences at a-level (b) find of arithmetic question means; parts within a paper that (d) with draw mamatics use slope curriculum of a tangent prior to to a curve Key stage as a 5 (c) construct included or mamatics interpret tables, was frequency measured tables as was using measure current of rate national of change; curriculum level descriptions diagrams, proportion bar charts of marks histograms; within se questions (e) construct / or interpret line graphs. a 212 mamatics Gcse specification 3. this work (d) underst that required simple mamatics. probability; was carried out by a researcher by a mamatics (e) underst principles of sampling as applied 5 Geometry: 3. to scientific difficulty data; of mamatics. this was measured (a) teacher. visualise three dimensional forms from two dimensional (f) underst against 3 criteria: terms mean, number median of steps mode in a representations of three dimensional objects; aim of third phase was to determine nature stard calculation, deviation; familiarity of context (b) calculate circumferences areas of circles, surface (g) use a scatter diagram to identify positive negative of mamatics areas volumes that of regular community blocks would cylinders like to when see complexity of question. each category correlation between two variables; in a-level provided science with appropriate assessments. formulae. this was achieved had varying levels of difficulty each was (h) select use a simple statistical test; (i) make measured order of as magnitude a proportion calculations; of total number of (j) determine question parts interpret containing population mamatics. variance, stard it was not deviation measured stard against deviation number (error) of of marks. mean; (k) underst probability in order to underst how 4. genetic appropriateness ratios arise; of mamatics. We (l) frame looked null hyposis. at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 75

76 ExEcutivE APPENDIX summary 5a: EXAMPLES OF MATHEMATICAL QUESTIONS WITHIN A SCIENCE A-LEVEL OF A SINGLE STEP CALCULATION, A MULTIPLE STEP CALCULATION AND AN EXTENDED STEP mamatics enables students to underst CALCULATION 23 describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical nature. to explore wher re was SINGLE STEP CALCULATION any evidence for this concern, score investigated type, Taken extent from: CCEA difficulty AY111 of mamatical (AS/1) 21 questions Jun 11 within 7(b)(iii) science Straightforward a-levels. one-line findings calculation show that a using large definition number of of e.m.f. mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements between physics, chemistry biology as it is accepted Background se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 23 These examples are for physics only; chemistry biology will be added at a later date 76 SCORE Maths in science report

77 MULTIPLE methodology STEP CALCULATION groups comprised practising a-level teachers, project was designed in three phases. teachers with experience in curriculum research Taken from: CCEA AY111 (AS/1) 21 Jun 11 5(b) first was to establish nature of mamatics development individuals working for awarding Multi-step because (i) Equation must be constructed; (ii) solved algebraically for square root to give speed assessed within biology, chemistry physics organisations as markers, question writers or examiners. a-level examinations in 21. full suite of stardisation exercises were employed throughout examinations papers from aqa, ccea, edexcel, analysis to verify reliability of judgements within ocr WJec were analysed using four across subject expert groups. measures that follow: second phase aimed to measure coherence 1. type of mamatics. mamatical areas between teaching learning of mamatics assessed were categorised against stated sciences. re is an assumption that mamatical requirements for biology, chemistry mamatical concepts used to access sciences physics respectively 1. are first taught within a mamatical context, i.e. within mamatics curriculum. project compared 2. extent of mamatics. proportion mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics teacher. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 77

78 ExEcutivE EXTENDED summary STEP CALCULATION mamatics Taken from: enables CCEA students AY111 to (AS/1) underst 21 Jun 11 9(b)(iii) describe Extended many calculation scientific because phenomena yet value re of is concern cross-sectional area found in an earlier part of question that has science to be combined assessments with at a-level value of are gradient not reflecting from graph to give a value of resistivity subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements between physics, chemistry biology as it is accepted Background se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 78 SCORE Maths in science report

79 EXTENDED methodology STEP CALCULATION continued project was designed in three phases. first was to establish nature of mamatics assessed within biology, chemistry physics a-level examinations in 21. full suite of examinations papers from aqa, ccea, edexcel, ocr WJec were analysed using four measures that follow: 1. type of mamatics. mamatical areas assessed were categorised against stated mamatical requirements for biology, chemistry physics respectively extent of mamatics. proportion of question parts within a paper that included mamatics was measured as was proportion of marks within se questions that required mamatics. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. groups comprised practising a-level teachers, teachers with experience in curriculum research development individuals working for awarding organisations as markers, question writers or examiners. stardisation exercises were employed throughout analysis to verify reliability of judgements within across subject expert groups. second phase aimed to measure coherence between teaching learning of mamatics sciences. re is an assumption that mamatical concepts used to access sciences are first taught within a mamatical context, i.e. within mamatics curriculum. project compared mamatical requirements for sciences at a-level with mamatics curriculum prior to Key stage 5 using current national curriculum level descriptions a 212 mamatics Gcse specification 3. this work was carried out by a researcher by a mamatics teacher. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 79

80 ExEcutivE EXTENDED summary STEP CALCULATION continued mamatics enables students to underst describe many scientific phenomena yet re is concern that science assessments at a-level are not reflecting subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. in addition, findings show a disparity in way mamatics is assessed across different awarding organisations. score recommends that re is a review of mamatical requirements for each of sciences at a-level that a framework is developed to regulate way mamatics is assessed within sciences to ensure parity across system. Background re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. aims score s overall objective for this project was to gar evidence on type, extent difficulty of mamatics required to access sciences in current a-level specifications to establish wher this was being appropriately met by assessments. work did not compare mamatical requirements between physics, chemistry biology as it is accepted se will differ between disciplines. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 8 SCORE Maths in science report

81 APPENDIX methodology 5b: EXAMPLES OF MATHEMATICAL QUESTIONS groups comprised WITHIN A practising SCIENCE a-level A-LEVEL teachers, OF A LEVEL project 1, LEVEL was designed 2 AND in LEVEL three phases. 3 teachers with experience in curriculum research first was to establish nature of mamatics development individuals working for awarding assessed within biology, chemistry physics organisations as markers, question writers or examiners. LEVEL 1 a-level examinations in 21. full suite of stardisation exercises were employed throughout Taken examinations from: papers CCEA from AY121 aqa, (AS/1) ccea, 27 edexcel, Jun 11 2(a) analysis to verify reliability of judgements within This ocr is a straightforward WJec were analysed application using of four a stard formulacross subject expert groups. measures that follow: second phase aimed to measure coherence 1. type of mamatics. mamatical areas between teaching learning of mamatics assessed were categorised against stated sciences. re is an assumption that mamatical requirements for biology, chemistry mamatical concepts used to access sciences physics respectively 1. are first taught within a mamatical context, i.e. within mamatics curriculum. project compared 2. extent of mamatics. proportion mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics teacher. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 81

82 ExEcutivE LEVEL 2 summary mamatics Taken from: enables CCEA students AY211 to (A2/1) underst 24 May 211 6(b) describe This requires many understing scientific phenomena of algebra yet re is concern careful application to follow through calculation correctly that science assessments at a-level are not reflecting subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements between physics, chemistry biology as it is accepted Background se will differ between disciplines. LEVEL 3 re has been growing concern across science community Taken from: about CCEA findings aim to provide score with evidence to mamatical AY221 (A2/2) dem 6 Jun of 211 science 6(b) inform development of policy on type, extent qualifications, This requires specifically understing that Gcse of algebra a-level trigonometry science decision on how to proceed with solution qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 82 SCORE Maths in science report

83 APPENDIX methodology 5c: EXAMPLES OF MATHEMATICAL QUESTIONS groups comprised WITHIN A practising SCIENCE a-level A-LEVEL teachers, OF A project LEVEL was 1, designed LEVEL in 2 three AND phases. LEVEL 3 CONTEXT teachers with experience in curriculum research first was to establish nature of mamatics development individuals working for awarding assessed within biology, chemistry physics organisations as markers, question writers or examiners. LEVEL 1 a-level examinations in 21. full suite of stardisation exercises were employed throughout Taken examinations from: papers CCEA from AY221 aqa, (A2/2) ccea, 6 edexcel, Jun 211 6(a)(i) analysis to verify reliability of judgements within On ocr this specification, WJec were analysed cidates using should four have calculated across V/d as part subject of expert learning groups. programme measures that follow: second phase aimed to measure coherence 1. type of mamatics. mamatical areas between teaching learning of mamatics assessed were categorised against stated sciences. re is an assumption that mamatical requirements for biology, chemistry mamatical concepts used to access sciences physics respectively 1. are first taught within a mamatical context, i.e. within mamatics curriculum. project compared 2. extent of mamatics. proportion mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics teacher. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 83

84 ExEcutivE LEVEL 2 summary mamatics Taken from: enables CCEA students AY111 to (AS/1) underst 21 Jun 11 5(a)(i) describe Efficiency many calculations scientific phenomena ratios yet are re not that is concern routine in context (of bouncing balls) that science assessments at a-level are not reflecting subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current at a-level that a framework is developed to regulate LEVEL 3 a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure Taken parity from: across WJEC 1324/1 system. (PH4) 21 Jun 11 5(b)(ii)(I) work did not compare mamatical requirements It is highly unlikely that graph specific analysis between will have physics, been chemistry met before biology as it is accepted Background se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 84 SCORE Maths in science report

85 APPENDIX methodology 5d: EXAMPLES OF MATHEMATICAL QUESTIONS groups comprised WITHIN A practising SCIENCE a-level A-LEVEL teachers, WHERE project ALL was MARKS, designed SOME in three phases. OF THE MARKS, NONE teachers OF MARKS with experience REQUIRE in curriculum SCIENTIFIC research COMPREHENSION first was to establish IN nature ADDITION of mamatics TO MATHEMATICAL development SKILL individuals working for awarding assessed within biology, chemistry physics organisations as markers, question writers or examiners. ALL MARKS REQUIRE SCIENTIFIC COMPREHENSION a-level examinations in 21. full suite of stardisation exercises were employed throughout Taken examinations from: papers 21 OCR from aqa, Physics ccea, B edexcel, (G491) Unit 1 2a analysis to verify reliability of judgements within This ocr requires WJec both were recall analysed of using scientific four definition of stress across calculation subject expert of groups. quotient measures that follow: second phase aimed to measure coherence 1. type of mamatics. mamatical areas between teaching learning of mamatics assessed were categorised against stated sciences. re is an assumption that mamatical requirements for biology, chemistry mamatical concepts used to access sciences physics respectively 1. are first taught within a mamatical context, i.e. within mamatics curriculum. project compared 2. extent of mamatics. proportion mamatical requirements for sciences at a-level of question parts within a paper that with mamatics curriculum prior to Key stage 5 included mamatics was measured as was using current national curriculum level descriptions proportion of marks within se questions a 212 mamatics Gcse specification 3. this work that required mamatics. was carried out by a researcher by a mamatics teacher. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. 4. appropriateness of mamatics. We looked at wher answer required scientific comprehension in addition to mamatical skill. this was measured as a proportion of total number of question parts containing mamatics. a subject expert group was established for each of three sciences. each group analysed full suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; 38 for chemistry; 32 for physics). participants from industry were also consulted more generally but as most science-related industries employ at a graduate level ir comments tended to focus more on outcomes at graduate level rar than directly referring to a-level. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 85

86 ExEcutivE SOME OF THE summary MARKS REQUIRE SCIENTIFIC COMPREHENSION mamatics Taken from: enables CCEA students AY211 to (A2/1) underst 24 May 211 9(a)(i) describe Some of many this part scientific just required phenomena pressing yet re is lg concern button, but third (first blank) column requires some that understing science assessments of physics, at a-level derived are not from reflecting question stem, unit has got to be checked as correct subject s analytical nature. to explore wher re was any evidence for this concern, score investigated type, extent difficulty of mamatical questions within science a-levels. findings show that a large number of mamatical requirements listed in biology, chemistry physics specifications are not assessed. those that are assessed are covered repeatedly often at a lower level than required. this is likely to have an impact on way that subjects are taught refore on students ability to have necessary skills to progress effectively to stem higher education employment. in addition, findings show a disparity in way aims mamatics is assessed across different awarding score s overall objective for this project was to organisations. score recommends that re is a review gar evidence on type, extent difficulty of of mamatical requirements for each of sciences mamatics required to access sciences in current at a-level that a framework is developed to regulate a-level specifications to establish wher this way mamatics is assessed within sciences to was being appropriately met by assessments. ensure parity across system. work did not compare mamatical requirements between physics, chemistry biology as it is accepted Background se will differ between disciplines. re has been growing concern across science community about mamatical dem of science qualifications, specifically that Gcse a-level science qualifications are not meeting needs of students in way y assess analytical nature of science. in 29 score published evidence on Gcse science examination papers which reported a wide variation in amount of mamatics assessed across awarding organisations confirmed that use of mamatics within context of science was examined in a very limited way. score organisations felt that this was unacceptable. mamatics is integral to teaching learning of sciences, offers a valuable aid in understing describing scientific phenomena; as such it should be appropriately represented in biology, chemistry physics curricula ir assessments. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. findings aim to provide score with evidence to inform development of policy on type, extent difficulty of mamatics in criteria assessments for a-levels in biology, chemistry physics. project also supports score s work on how examinations system should operate to ensure science qualifications are fit for purpose also its work on improving coherence between sciences mamatics. in project, we looked across all assessments at a-level for a given year, including both experimental practical examination papers. 86 SCORE Maths in science report

87 SOME methodology OF THE MARKS REQUIRE SCIENTIFIC COMPREHENSION continued project was designed in three phases. first was to establish nature of mamatics assessed within biology, chemistry physics a-level examinations in 21. full suite of examinations papers from aqa, ccea, edexcel, ocr WJec were analysed using four measures that follow: 1. type of mamatics. mamatical areas assessed were categorised against stated mamatical requirements for biology, chemistry physics respectively extent of mamatics. proportion of question parts within a paper that included mamatics was measured as was proportion of marks within se questions that required mamatics. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. groups comprised practising a-level teachers, teachers with experience in curriculum research development individuals working for awarding organisations as markers, question writers or examiners. stardisation exercises were employed throughout analysis to verify reliability of judgements within across subject expert groups. second phase aimed to measure coherence between teaching learning of mamatics sciences. re is an assumption that mamatical concepts used to access sciences are first taught within a mamatical context, i.e. within mamatics curriculum. project compared mamatical requirements for sciences at a-level with mamatics curriculum prior to Key stage 5 using current national curriculum level descriptions a 212 mamatics Gcse specification 3. this work was carried out by a researcher by a mamatics teacher. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in NONE 4. OF appropriateness THE MARKS of REQUIRE mamatics. SCIENTIFIC We COMPREHENSION three groups; teaching profession; higher education; looked at wher answer required scientific professional bodies. an online survey was completed by Taken from: WJEC 1321/1 (PH1) 24 May 211 5(b)(i) comprehension in addition to mamatical skill. 97 participants across three groups (27 for biology; Calculation of area of a circle - no physics required this was measured as proportion of total 38 for chemistry; 32 for physics). participants from number of question parts containing mamatics. industry were also consulted more generally but as most science-related industries employ at a graduate level a subject expert group was established for each ir comments tended to focus more on outcomes of three sciences. each group analysed full at graduate level rar than directly referring to a-level. suite of 21 examinations papers of aqa, ccea, edexcel, ocr WJec for ir respective subjects at a two-day workshop. examination papers included all ory papers (Units 1, 2, 4 5) experimental practical papers (Units 3 6). calculations were based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. SCORE Maths in science report 87

88 ExEcutivE APPENDIX summary 6: FRAMEWORK FOR ANALYSING A-LEVEL THEORY AND PRACTICAL PAPERS methodology groups comprised practising a-level teachers, mamatics enables students to underst project was designed in three phases. teachers with experience in curriculum research describe many scientific phenomena yet re is concern first was to establish nature of mamatics development individuals working for awarding THEORY PAPERS FRAMEWORK that science assessments at a-level are not reflecting assessed within biology, chemistry physics organisations as markers, question writers or examiners. subject s analytical nature. to explore wher re was a-level examinations in 21. full suite of stardisation exercises were employed throughout any Awarding evidence for Body: this concern, score investigated Unit: Specification: examinations papers from aqa, ccea, Date: edexcel, analysis to verify reliability AS or of judgements A2: within type, extent difficulty of mamatical questions within ocr WJec were analysed using four across subject expert groups. science Question a-levels. Appropriateness: findings show that does a large it number Relationship of of Number Type of measures Complexity that follow: Number Are associated marks purely second for phase aimed Familiarity to measure coherence mamatical number requirements reflect how listed mamatics in biology, in chemistry mamatics to question part physics specifications science are is used not assessed. in real those that of steps mamatics of 1. task type of mamatics. of marks mamatical mamatics areas skills or do between y require teaching of learning contextof mamatics assessed were that categorised require against scientific stated comprehension sciences. re is an assumption that are assessed are covered world? repeatedly often at a lower level than required. this is likely to have an impact on mamatical mamatics requirements for biology, chemistry physics respectively 1. mamatical concepts used to access sciences are first taught within a mamatical context, i.e. within way that subjects are taught refore on mamatics curriculum. project compared Yes No Structural part Tagged on single multi Extended 1 students ability to have necessary skills to progress 2. to 4 extent of mamatics. Mamatics proportion Scientific both mamatical requirements for sciences at a-level calculation effectively to stem higher education employment. of question parts within a paper skillsthat comp with mamatics curriculum prior to Key stage 5 in addition, findings show a disparity in way aims included mamatics was measured as was using current national curriculum level descriptions mamatics is assessed across different awarding proportion of marks within se questions score s overall objective for this project was to a 212 mamatics Gcse specification 3. this work organisations. score recommends that re is a review that required mamatics. gar evidence on type, extent difficulty of was carried out by a researcher by a mamatics of mamatical requirements for each of sciences at a-level that a framework is developed to regulate way mamatics is assessed within sciences to ensure parity across system. mamatics required to access sciences in current a-level specifications to establish wher this was being appropriately met by assessments. work did not compare mamatical requirements between physics, chemistry biology as it is accepted teacher. Background se will differ between disciplines. 3. difficulty of mamatics. this was measured against 3 criteria: number of steps in a calculation, familiarity of context complexity of question. each category had varying levels of difficulty each was measured as a proportion of total number of question parts containing mamatics. it was not measured against number of marks. aim of third phase was to determine nature of mamatics that community would like to see in a-level science assessments. this was achieved through an online survey for stakeholders in science community. Depending on ir expertise, participants answered survey for biology, chemistry or physics a-level assessment. participants were chosen in three groups; teaching profession; higher education; professional bodies. an online survey was completed by 97 participants across three groups (27 for biology; re has been growing concern across science findings aim to provide score with evidence to community about mamatical dem of science inform development of policy on type, extent qualifications, specifically that Gcse a-level science difficulty of mamatics in criteria 4. appropriateness of mamatics. We qualifications PRACTICAL are PAPERS not meeting FRAMEWORK needs of students in assessments for a-levels in biology, chemistry looked at wher answer required scientific way y assess analytical nature of science. physics. project also supports score s work on comprehension in addition to mamatical skill. in 29 score published evidence on Gcse science how examinations system should operate to ensure this was measured as a proportion of total 38 for chemistry; 32 for physics). participants from Awarding Body: Unit: Specification: Date: examination papers which reported a wide variation in science qualifications are fit for purpose also its number of question parts containing mamatics. industry were also consulted AS more or A2: generally but as most amount of mamatics assessed across awarding work on improving coherence between sciences science-related industries employ at a graduate level Question Number Type of Complexity Number Familiarity Associated a subject expert marks group purely was for established mamatics for each Comments organisations confirmed that use of mamatics mamatics. ir comments tended to focus more on outcomes number of steps mamatics of task of marks of context or of do y three require sciences. scientific each group comprehension analysed full at graduate level rar than directly referring to a-level. within part / section context of science was examined in a very suite of 21 examinations papers of aqa, ccea, in project, we looked across that all assessments require at limited way. score organisations felt that this was edexcel, ocr WJec for ir respective subjects a-level for a given year, including mamatics both experimental unacceptable. mamatics is integral to teaching at a two-day workshop. examination papers included practical examination papers. learning of sciences, offers a valuable aid all ory papers (Units 1, 2, 4 5) in understing single describing multi scientific phenomena; Extended as such it should be appropriately represented calculation in biology, chemistry physics curricula ir assessments. 1 to Mamatics experimental Scientific practical papers both (Units 3 6). skills calculations were comp based on assumption that ory papers make up 8% of complete a-level experimental practical papers remaining 2% 2. to provide furr evidence to support se concerns, score set up this project to investigate mamatics found in 21 science assessments at a-level across unitary awarding organisations in engl, Wales norrn irel. 1 five awarding organisations use mamatical requirements defined by ofqual in developing ir specifications for biology, chemistry physics. mamatical requirements are available in full report. 2 a complete science a-level is made up of 6 units. marks from ory papers (Unit 1, 2, 4 5) make up 8% of complete a-level assessment marks from practical experimental papers (Unit 3 6) make up remaining 2%. in analysis, question parts rar than marks were used in calculation but we maintained 8:2 weighting. 3 edexcel 212 a specification was used for purpose of analysis as it was considered representative of typical content found in revised mamatics Gcses. 88 SCORE Maths in science report SCORE Maths in science report 89

89 APPENDIX 7: ACKNOWLEDGEMENTS WORKING GROUP Charles Tracy Clare Thomson Rachel Lambert-Forsyth John Bentham Mary Ratcliff Martin Smith Alice Rogers Michael Reiss Erica Tyson David Swinscoe Kay Stephenson Rosalind Mist Mario Moustras Ellen Weavers Niall MacKay OTHER ACKNOWLEDGEMENTS AND THANKS Geoffrey Wake Jerry McCarthy Ti Clausen May Peter Hall Stu Lloyd All those involved in analysing A-level papers, with particular thanks to: David Peet Laurie Mansfield Tony Tooth Ginny Hales David James Stu Billington All those involved in completing survey or questionnaire from teachers, HE representatives, representatives from Professional Bodies industry representatives PROJECT TEAM Clare Green Fiona Miller Tamsin Barton 9 SCORE Maths in science report

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