Rises in A-Level Mathematics Some Preliminary Thoughts by ACME

Rises in A-Level Mathematics Some Preliminary Thoughts by ACME Background Recent years have witnessed a sharp rise in the popularity of mathematics at A-Level. There has been widespread applauding of this positive news, partly relief given the trauma experienced by mathematics in the period immediately following the Curriculum 2000 changes. However, while there has been considerable welcoming of the upward trend, there has been no detailed analysis of the reasons why mathematics has experienced such large increases. It may be simply down to one particular factor which has led to the improved popularity of mathematics or, on the other hand, it could be due to a wide set of factors which are interrelated in a complex manner. Either way, it would appear sensible to gain a handle on the causes of the upward trend. Not only would this provide policy makers with a clearer idea as to whether explicit initiatives and government priorities are having an impact, but it may also result in the identification of best practice which might then be applicable in other subject areas. This Paper This paper represents an attempt to shed some light on the issues at play in the popularity of A-Level Mathematics. We acknowledge that there might be some technical factors at play which have contributed to the figures (and we look at the issue of double-counting later in the paper) but this paper is principally about the factors which have contributed to the real growth in numbers of learners in the classroom which has undoubtedly occurred. ACME sought views from its Outer Circle of members, and, supported by MEI, through a survey of teacher views. It does not attempt to be a scientific study, but instead be more of a flavour of what may be happening. It is anticipated that DCSF may follow up on this document with a more detailed analysis of the factors at work in A-Level Mathematics, through a survey of both practitioners and students. Recent Trends in the Popularity of Mathematics at A-Level Since 2004, there has been a rise of 20,000 in the number of A-Level Mathematics entries an increase of 45%. In the past twelve months, A-Level Mathematics entries were up 12.6% compared to twelve months previously (to 66,552) with Further Mathematics rising 15.2% to 10,073. AS-Levels demonstrated even more dramatic rises, with Mathematics surging 22.4% (to 17,466) and Further Mathematics up 47.8% (to 12,710) on twelve months ago. However, as Table 1 illustrates, in the period 2000-2004 the picture for mathematics was very different. Mathematics experienced a major trauma, with a slump in the number of entries in the aftermath of the Curriculum 2000 changes. In 2002 alone, there was an 18.5% drop in entries for A-Level Mathematics. 1

With revisions to A-Level Mathematics in 2004, targets were established for the number of entries. The original target was for 56,000 entries by 2014 which was achieved some 6 years early. A revised target has now been established 80,000 A-Level Mathematics entries for 2014, which would see mathematics vie with English for the crown of most popular A-Level, a major renaissance for the subject from its 2004 nadir. Table 1 A-Level Mathematics Entries in England, 1996-2009 Year Mathematics Entries % change on previous twelve months % of total entries across all A-Level subjects Mathematics entries (% of 17 year olds) 1996 54,125-8.7 9.2 1997 56,050 +3.6% 8.5 9.2 1998 56,589 +1.0% 8.3 9.3 1999 56,100-0.9% 8.2 9.4 2000 53,674-4.3% 8.0 9.0 2001 54,157-0.9% 7.9 8.9 2002 44,156-18.5% 6.8 7.0 2003 44,453 +0.7% 6.7 7.0 2004 46,017 +3.5% 6.8 7.1 2005 46,034 +0.0% 6.7 6.9 2006 49,805 +8.2% 7.0 7.5 2007 53,331 +7.1% 7.4 8.1 2008 59,105 +10.8% 7.8 2009 66,552 +12.6% 8.6 Source: JCQ Data, RS State of the Nation Reports Similar buoyant trends have been witnessed in Further Mathematics (FM). The number of FM A-Level entries has doubled between 2003 and 2009, surging past 10,000 during the past twelve months. Worries/Concerns A-Level Mathematics is currently in an enviable position, with strong upward movements in the number of entries. However, while many people have thoughts about what factors are driving the upward trend, or have speculated what might be having an impact, there is an absence of any detailed analysis. ACME believes that unless we gain a handle on the forces at work, there is always a fear that any rise is poorly understood, perhaps even fragile and might be susceptible to reversal with little or no notice. In addition, the other STEM subjects (and beyond) may be able to learn from the experience of mathematics if only we were able to clearly identify what is actually happening. 2

Views from the Chalk Face Teacher Perspectives Dovetailing ACME s desire to look in more detail at what is happening with A-Level Mathematics, MEI has conducted an online survey 1, which was widely publicised courtesy of ACME, NCETM and JMC (and its individual participating societies). Some 180 responses were received, covering 636 teachers in institutions which teach 7,738 students in 2009. This represents about 10% of A-Level Mathematics students. MEI s survey focused on what teachers considered to be the most important explanations for the increase in uptake of A-Level Mathematics out of a list of fifteen randomly ordered factors. The compilation of these fifteen factors was informed by a scoping exercise involving the ACME committee and Outer Circle.Table 2 (below) lists the fifteen factors ranked in order of the explanations seen as being most important by respondents. Table 2 Most Important Factors Explaining the Rise in A-Level Mathematics Numbers Rank Explanations Respondents 2 1. 2. 3. 4. 5. 6. 7. 8. 9= 9= More students are seeing mathematics as a subject that will give them a competitive advantage when seeking a university place or employment. Students are more conscious of the likely benefits of the subjects they choose in terms of future earnings and career prospects. Some universities are looking for more mathematics from prospective entrants. The present syllabus for Mathematics and Further Mathematics is fit for purpose and is working well. Students are coming through from GCSE with a more positive experience of mathematics. The profile of mathematics in our school or college has improved In our school or college, there has been an increase in Further Mathematics and this has improved the image of mathematics generally. Students are being encouraged by older siblings (and their friends) who have achieved success in mathematics at this level. The standard of post-16 teaching has improved in our school/college. The transition from GCSE to the start of AS Level (i.e. C1) is smoother than it used to be. 492 476 307 302 276 266 222 173 148 140 1 The survey was England, Wales and Northern Ireland. 2 The totals are weighted based on the total number of people s views which were represented in a particular school or college per individual respondent. 3

11. 12. 13. Enhancement and enrichment events and resources are influencing more students than before. We are now making more effort to recruit students into mathematics The Further Mathematics Network has been a catalyst for greater student engagement with mathematics. 14= The media are presenting mathematics more positively. 96 14= There has been a widening of participation (e.g. more 95 students with grades B and C at GCSE). Source: MEI Survey (October 2009) Major Factors at Play ACME supports MEI s interpretation of the data, which highlights four broad groupings of explanations: 116 109 109 Career Progression Establishing a good environment The mathematics curriculum In-house reputation Career Progression This group of explanations constituted the most popular (by far) as ranked by respondents. They relate to the future career and university prospects of students and include: More students are seeing mathematics as a subject that will give them a competitive advantage when seeking a university place or employment; Students are more conscious of the likely benefits of the subjects they choose in terms of future earnings and career prospects; Some universities are looking for more mathematics from prospective entrants. The first two of these received far more support than any of the other explanations. It is clear mathematics is in a strong position in terms of its perceived benefit in gaining access to and supporting study of university courses: mathematics is seen increasingly as a useful subject for supporting future HE courses e.g. medicine, psychology, the sciences the kudos and advantages of including a hard A-Level, such as maths, in a portfolio of subjects is seen as competitive advantage for university applications most able students are choosing mathematics as a way of differentiating themselves from the mass of 16-18 year olds in full-time education 4

Similarly, changes in HE admissions policies are clearly having an impact, as is increased competition for places at university, with candidates keen to distinguish themselves from the rest of their peers. The Cambridge University and London School of Economics lists of soft subjects that the institutions would consider in a second tier may have pushed some towards more traditional subjects, including mathematics. This impact may have extended beyond simply Cambridge and LSE applicants, as there was considerable media coverage at the time: rising aspirations for university entry with so many universities able to pick from students with good A-Level grades it is no longer desirable to have A-Level Mathematics for some subjects, but essential Mathematics appears to also have benefited from a culture whereby there is more of a focus on depth, as opposed to breadth, in AS and A-Level choices. There is some suggestion that when Curriculum 2000 was first introduced, there was pressure on a science A-Level student to choose a humanity as a fourth subject, for reasons of breadth. This pressure may now have subsided, with instead the focus being on doing a STEM-related subject for reasons of depth. Moreover, mathematics seems to be seen as an increasingly important A- Level with regards to potential HE choices: I think it s probably a good thing that maths is seen as stand-alone AND a natural partner to many other A-Levels. We see many more varied combinations of other A-Levels with maths than we used to In addition, the message appears to be permeating down to students that having an A-Level in mathematics is of benefit in any future job market (as much research has demonstrated): students are more aware of the economic return with mathematics and also the increased likelihood of getting a job/career Establishing a Good Environment Underlying this group of explanations are the factors which are fostering a more positive environment for mathematics, including: Enhancement and enrichment events and resources are influencing more students than before; The Further Mathematics Network has been a catalyst for greater student engagement with mathematics; The media are presenting mathematics more positively. This group is actually the lowest scoring of the explanations but it would seem likely that they are also amongst the hardest to compare with other factors. Their effect is less tangible, longer term and at a deeper level. 5

Through government-funded STEM initiatives, the image of mathematics has clearly improved. We highlight the Further Mathematics Network (FMN), which has clearly had an effect on Further Mathematics numbers, even though the survey does not explicitly rank this as particularly significant. But this relationship is rather complex as it extends well beyond those actually taught Further Mathematics. The FMN existence and its advocacy work have caused higher education (HE) to be much more positive about FM and schools in general have also become more positive about mathematics and FM. Moreover, the work of More Maths Grads (MMG) has led to a promotion of the subject, and other STEM Enhancement and Enrichment and STEM careers activity may also be contributing to an improved image of the subject in the eyes of students. Some of it is definitely cultural, and it may be that the long-standing image problems faced by mathematics are slowly being eroded. This could, in turn, be due to the focus on mathematics in the media through television programmes such as BBC4 s The History of Mathematics but also in films and popular culture (even though the explicit factor identifying the role of the media did not score particularly highly). The Mathematics Curriculum This group of explanations relates to the mathematics experience of students within their school or college. Four explanations sit in this group: The present syllabus for Mathematics and Further Mathematics is fit for purpose and is working well; In our school or college, there has been an increase in Further Mathematics and this has improved the image of mathematics generally; Students are coming through from GCSE with a more positive experience of mathematics; The transition from GCSE to the start of AS Level (i.e. C1) is smoother than it used to be. The suitability of the syllabus was ranked fourth overall out of all fifteen factors. It is now five years since the problems caused by Curriculum 2000 were addressed, and as time passes it is likely that the system will become better at teaching courses that are more familiar, year by year. The likelihood of positive feedback loops from this must not be underestimated with improved teaching and improved results fuelling the interest of the next generation of potential students. Students appear to be having a much more positive experience at GCSE, encouraging students to continue further study of mathematics. This appears to be more of a factor than the transition between GCSE and AS-Level being any smoother, a problem which caused so many difficulties in the aftermath of Curriculum 2000. 6

students who achieve tangible success in maths at Level 2 feel confident and encouraged to continue their studies in the subject. This is increasing as the proportion achieving grades A and A* at GCSE increases Responses to the MEI survey have reinforced the growing concern with the impact of the new two-tier GCSE on progression to A-Level Mathematics. This is one area which may potentially lead to an undermining of future growth in A-Level numbers, as students perceive the gap between Level 2 and Level 3 to be too great. I am utterly shocked to see the suggestion that a possible reason for the increase is a smoother transition from GCSE to AS! I have given students the same diagnostic test for 4 years and the cohort gets worse and worse, this year almost half of our new AS students scored less than 40% in a test of basic GCSE algebra. The schools are under pressure to produce grade Cs not produce students who are ready to take on AS. The numbers of students with grade B's at GCSE has increased dramatically since the two -tier GCSE was introduced. However, in many of the feeder schools, due to the pressure of league tables etc, much of the A* material has never actually been taught to the students, so they are less likely to be familiar with the quadratic formula, factorisation, completing the square etc. This has the effect of a high percentage of students with a grade B at GCSE actually dropping the course in the early stages due to difficulty with the material.(within the first 4 weeks). In-house Reputation This group of explanations relate to the reputation of mathematics departments in schools and colleges, and the actions that staff were taking to encourage mathematics. The factors include: The profile of mathematics in our school or college has improved; Students are being encouraged by older siblings (and their friends) who have achieved success in mathematics at this level; The standard of post-16 teaching has improved in our school/college; We are now making more effort to recruit students into mathematics; There has been a widening of participation (e.g. more students with grades B and C at GCSE). While none of these factors score overly highly in the survey, it is clear that they are still having some impact on student perceptions of mathematics at A-Level. It was clear that in the immediate aftermath of Curriculum 2000, mathematics suffered through the experiences of older friends/siblings, who reported back that the subject was too difficult, deterring the next generation from choosing it. It would appear that the opposite feedback loop is now in place, with the message trickling down that this is a well-taught subject, with a very positive grade profile: 7

Enjoyment of the subject and the way it is taught can have very positive effects. Individual teachers who are respected and who teach in an interesting way seem to have higher numbers of students continuing maths to Level 3 a bright 16 year old might well think maths is hard, but I m quite good at it, and if 40%+ get a grade A then I too have a good chance reputationally their older friends/siblings will be telling them that it isn t that hard so this will give them confidence to choose it where before they might have been put off by tales of it being difficult to pass Future Trends The MEI survey also asked respondents about actual numbers of students in 2008 and 2009, and those projected for 2010. Comparing the percentage increase between 2008 and 2009 with what actually occurred allows a judgment to be made as to whether the respondents were representative, and it would appear that the answer is yes. The 2010 figure provides a broad indication of whether the upward trend is continuing. However, we counsel caution as the sample was self-selecting so any conclusion must be at best speculative. Nevertheless, based on these findings, Table 3 indicates another sharp rise in those studying A-Level Mathematics and Further Mathematics (both in double figure percentage rises) is to be expected in 2010. Table 3 Number of Students Certificating for A-Level Mathematics Year Maths Change Real FM Change Real 2008 6,895 - - 1,189 - - 2009 7,738 +12.23% +12.2% 1,364 +14.7% +15.2% 2010 (Estimate) 8,512 +10% - 1,613 +18.3% - Double-Counting Since the figures on A-Level Mathematics entries were announced in August, there has been considerable debate as to whether some element of double counting is inflating figures. We understand that DCSF have asked QCDA and the awarding bodies to investigate the data in more detail to assess the extent of this potential problem. There are a number of rather complex methods by which double-counting may occur. The most likely occurrence would typically be if a student completes and certificates A-Level Mathematics at the end of Year 12, and then takes FM in Year 13, and asks for both to be 8

certificated at the end of Year 13, with more combinations of units now available to Mathematics. However, this is not a common pattern of delivery in most centres. Instead, Maths and FM AS-Levels are taught in parallel in Year 12, followed by A2 units in Year 13. This model ought to leave no option for double-counting occurring. The MEI survey has captured just 73 students in 20 institutions as being in this category. This would suggest that double-counting may account for only about 1% of the reported 12.2% increase of the figures reported in August. It is not so easy to be as confident at AS-Level, where the situation is considerably more complicated. The survey did not attempt to gain a handle on the extent of the problem at AS- Level but it would seem reasonable to assume that the very large rises seen in August 2009 can be partially explained by double-counting. However, to gain a real handle on the situation, we await the interrogation of the data by DCSF and QCDA. Conclusion We are sure there has been substantial real growth in the popularity of A-Level Mathematics but discussion and evaluation would be much better founded with data which showed the numbers of new candidates not the numbers of entries (getting rid of duplications from people switching awarding bodies would be difficult for the awarding bodies, but it would be easy for the DCSF). This would seem particularly important at AS-Level, where there is genuine confusion surrounding the large rises reported in the 2009 entries. That being said, being able to gain a genuine understanding of what is driving student choice of A-Level Mathematics would be of real benefit to policy makers and the community alike. By having more knowledge on what is working well, what is not functioning as it should be, and what might actually be outside of the control of policy makers altogether, will help equip us with intelligence on what to focus more attention, and also inform what could be applied in other subject areas. Therefore, more detailed research by DCSF is required. This research would be enhanced considerably if there was a particular focus on the student voice, to gain a real understanding on what is driving their decision making. ACME October 2009 9