KEY QUESTIONS FOR MATHEMATICS TEACHERS

Transcription

1 KEY QUESTIONS FOR MATHEMATICS TEACHERS AND HOW PISA CAN ANSWER THEM Andreas Schleicher October 7, 2016

2 2 2 PISA mathematics performance by decile of social background Mexico Chile Greece Norway Sweden Iceland Israel Italy United States Spain Denmark Luxembourg Australia Ireland United Kingdom Hungary Canada Finland Austria Turkey Liechtenstein Czech Republic Estonia Portugal Slovenia Slovak Republic New Zealand Germany Netherlands France Switzerland Poland Belgium Japan Macao-China Hong Kong-China Korea Singapore Chinese Taipei Shanghai-China

3 3 Exposure to deep math learning and social background Index of exposure to pure mathematics Bottom quarter (disadvantaged students) Second quarter Third quarter Top quarter (advantaged students) United States Shanghai-China Source: Figure 2.5b

4 QUESTION 1: HOW MUCH SHOULD I DIRECT STUDENT LEARNING IN MY MATHEMATICS CLASSES? 4

5 96% of teachers: My role as a teacher is to facilitate students own inquiry What knowledge, skills and character qualities do successful teachers require?

6 86%: Students learn best by findings solutions on their own What knowledge, skills and character qualities do successful teachers require?

7 74%: Thinking and reasoning is more important than curriculum content What knowledge, skills and character qualities do successful teachers require?

8 Prevalence of memorisation rehearsal, routine exercises, drill and practice and/or repetition United Kingdom Netherlands Norway United States Singapore Canada Shanghai-China Sweden France Germany Poland Switzerland Spain Korea Japan Prevalence of elaboration reasoning, deep learning, intrinsic motivation, critical thinking, creativity, non-routine problems High Low Low High

9 Source: Figure Teacher-directed strategies are used more often OECD average of students who responded in every lesson or in most lessons At the beginning of a lesson, the teacher presents a short summary of the previous lesson The teacher asks me or my classmates to present our thinking or reasoning at some length The teacher sets clear goals for our learning The teacher asks questions to check whether we have understood what was taught The teacher tells us what we have to learn %

10 Source: Figure than student-oriented strategies OECD average of students who responded in every lesson or in most lessons The teacher assigns projects that require at least one week to complete The teacher asks us to help plan classroom activities or topics The teacher has us work in small groups to come up with joint solutions to a problem or task The teacher gives different work to classmates who have difficulties and/or who can advance faster %

11 More memorisation Learning More elaboration Source: Figure 1.2 Teaching and learning strategies in mathematics around the world Memorisation most United frequently used compared Kingdom to elaboration strategies Uruguay New Zealand Australia United States Israel Japan Singapore More studentoriented instruction OECD average Macao-China Korea Vietnam Chinese Taipei Teaching Teacher-directed instruction most frequently used compared to student-oriented instruction France Hong-Kong China Hungary Shanghai- China Croatia Are East Asian education systems really so traditional? Ireland R² = 0.10 More teacherdirected instruction 11

12 Greater success Teacher-directed strategies are related with higher solution rates (OECD average) Odds ratio 1.20 Easy problem Difficult problem 1.00 R² = 0.24 Less success Source: Figure 1.4 Difficulty on the PISA scale 12

13 13 Teaching strategies and learning outcomes Mean Index Index of student-oriented instruction Index of teacher-directed instruction Index of cognitive-activation instruction Students below Level 2 have difficulties using basic algorithms, formulae, procedures or convention Students at Level 5 and 6 can develop and work with models for complex situations, and work strategically with advanced reasoning skills -0.4 Below Level 1 Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Students' proficiency level in PISA mathematics

14 What can teachers do? Plan mathematics lessons that strive to reach all levels of learners in a class Provide a mix of teacher-directed and student-oriented teaching strategies Let the difficulty of the mathematics problem guide the teaching strategy 14

15 QUESTION 2: WHAT DO WE KNOW ABOUT MEMORISATION AND LEARNING MATHEMATICS? 15

16 Students use of memorisation strategies More Below the OECD average At the same level as the OECD average Above the OECD average Memorisation % of students who report they learn by heart Less Macao-China 15 Russian Federation 16 Serbia 11 Slovak Republic 11 Albania 12 Switzerland 13 Mexico 19 Poland 9 Malaysia 12 Liechtenstein 17 Viet Nam 5 Lithuania 14 Kazakhstan 22 Chinese Taipei 16 Hong Kong-China 10 Denmark 28 Italy 10 Latvia 22 Colombia 26 Iceland 23 Germany 17 Japan 12 Qatar 13 Korea 17 Slovenia 11 Tunisia 10 Romania 16 Peru 22 Croatia 9 France 19 Montenegro 13 Costa Rica 19 Argentina 21 Sweden 31 Czech Republic 25 Shanghai-China 25 Estonia 14 Bulgaria 11 OECD average 21 Turkey 13 Brazil 30 Canada 26 Singapore 22 Greece 20 Austria 13 Portugal 27 Finland 32 United States 29 Hungary 17 Luxembourg 13 Norway 28 Belgium 24 Jordan 14 Israel 14 Thailand 46 United Arab Emirates Australia 35 Chile 22 New Zealand 35 Indonesia 23 Spain 19 Netherlands 22 United Kingdom 37 Ireland 28 Uruguay 23 Source: Figure

17 Students use of memorisation strategies Memorisation More Less Below the OECD average At the same level as the OECD average Above the OECD average The index of memorisation, with values ranging from 0 to 4, reflects the number of times a student chose the following memorisation-related statements about how they learn mathematics. 1. When I study for a mathematics test, I learn as much as I can by heart. 2. When I study mathematics, I make myself check to see if I remember the work I have already done. 3. When I study mathematics, I go over some problems so often that I feel as if I could solve them in my sleep. 4. In order to remember the method for solving a mathematics problem, I go through examples again and again. Macao-China 15 Russian Federation 16 Serbia 11 Slovak Republic 11 Albania 12 Switzerland 13 Mexico 19 Poland 9 Malaysia 12 Liechtenstein 17 Viet Nam 5 Lithuania 14 Kazakhstan 22 Chinese Taipei 16 Hong Kong-China 10 Denmark 28 Italy 10 Latvia 22 Colombia 26 Iceland 23 Germany 17 Japan 12 Qatar 13 Korea 17 Slovenia 11 Tunisia 10 Romania 16 Peru 22 Croatia 9 France 19 Montenegro 13 Costa Rica 19 Argentina 21 Sweden 31 Czech Republic 25 Shanghai-China 25 Estonia 14 Bulgaria 11 OECD average 21 Turkey 13 Brazil 30 Canada 26 Singapore 22 Greece 20 Austria 13 Portugal 27 Finland 32 United States 29 Hungary 17 Luxembourg 13 Norway 28 Belgium 24 Jordan 14 Israel 14 Thailand 46 % of students who report they learn by heart United Arab Emirates Australia 35 Chile 22 New Zealand 35 Indonesia 23 Spain 19 Netherlands 22 United Kingdom 37 Ireland 28 Uruguay 23 Source: Figure

18 Memorisation is less useful as problems become more difficult (OECD average) Greater success 1.00 Odds ratio Easy problem R² = 0.81 Less 0.70 success Source: Figure 4.3 Difficult problem Difficulty of mathematics item on the PISA scale 18

19 Weaker students tend to use memorisation more (OECD average) More Correlation with the index of memorisation Memorisation Less Source: Figure 4.2 Higher selfefficacy in mathematics More openness to problem solving Higher score in mathematics More interested in mathematics Better selfconcept in mathematics More instrumental motivation for learning mathematics More perseverance Greater mathematics anxiety 19

20 What can teachers do? Encourage students to complement memorisation with other learning strategies Use memorisation strategies to build familiarity and confidence Notice how your students learn 20

21 QUESTION 3: CAN I HELP MY STUDENTS LEARN HOW TO LEARN MATHEMATICS? 21

22 There are large international differences in the use of control strategies More Below the OECD average At the same level as the OECD average Above the OECD average Control % of students who try to work out what the most important parts to learn are Less Tunisia 46 Jordan 43 Thailand 19 Spain 42 Uruguay 55 Qatar 53 United Arab Emirates 55 Peru 49 Indonesia 39 Montenegro 48 Czech Republic 35 Chile 54 Chinese Taipei 42 Croatia 43 Turkey 59 Hungary 46 Romania 48 Netherlands 54 Slovenia 32 Shanghai-China 40 Ireland 49 Greece 46 Italy 44 Brazil 45 Lithuania 56 Estonia 48 Korea 40 Argentina 44 Norway 48 United States 40 Latvia 46 Slovak Republic 49 Portugal 44 Finland 45 Malaysia 50 Colombia 40 Serbia 40 United Kingdom 43 Luxembourg 55 Sweden 44 Bulgaria 62 OECD average 49 New Zealand 46 Viet Nam 54 Belgium 53 Russian Federation 44 Poland 65 Australia 45 Israel 61 Singapore 47 Costa Rica 48 Austria 55 Liechtenstein 42 Kazakhstan 49 Mexico 54 Canada 48 Denmark 48 Albania 54 Germany 50 Hong Kong-China 60 Switzerland 55 France 62 Japan 59 Macao-China 53 Iceland 59 Source: Figure

23 There are large international differences in the use of control strategies More Below the OECD average At the same level as the OECD average Above the OECD average The index of control strategies, with values ranging from 0 to 4, reflects the number of times a student chose the following control-related statements about how they learn mathematics. Control Less 1. When I study for a mathematics test, I try to work out what the most important parts to learn are. 2. When I study mathematics, I try to figure out which concepts I still have not understood properly. 3. When I study mathematics, I start by working out exactly what I need to learn. 4. When I cannot understand something in mathematics, I always search for more information to clarify the problem. % of students who try to work out what the most important parts to learn are Tunisia 46 Jordan 43 Thailand 19 Spain 42 Uruguay 55 Qatar 53 United Arab Emirates 55 Peru 49 Indonesia 39 Montenegro 48 Czech Republic 35 Chile 54 Chinese Taipei 42 Croatia 43 Turkey 59 Hungary 46 Romania 48 Netherlands 54 Slovenia 32 Shanghai-China 40 Ireland 49 Greece 46 Italy 44 Brazil 45 Lithuania 56 Estonia 48 Korea 40 Argentina 44 Norway 48 United States 40 Latvia 46 Slovak Republic 49 Portugal 44 Finland 45 Malaysia 50 Colombia 40 Serbia 40 United Kingdom 43 Luxembourg 55 Sweden 44 Bulgaria 62 OECD average 49 New Zealand 46 Viet Nam 54 Belgium 53 Russian Federation 44 Poland 65 Australia 45 Israel 61 Singapore 47 Costa Rica 48 Austria 55 Liechtenstein 42 Kazakhstan 49 Mexico 54 Canada 48 Denmark 48 Albania 54 Germany 50 Hong Kong-China 60 Switzerland 55 France 62 Japan 59 Macao-China 53 Iceland 59 Source: Figure

24 Greater Odds ratio 1.20 success Control strategies are always helpful but less so as problems become more difficult (OECD average) Easy problem Difficult problem Less 0.95 success Source: Figure 5.2 R² = Difficulty of mathematics item on the PISA scale 24

25 What can teachers do? Make sure that your own teaching doesn t prevent students from adopting control strategies Familiarise yourself with the specific activities to use of control strategies Encourage students to reflect on how they learn 25

26 QUESTION 4: SHOULD I ENCOURAGE MY STUDENTS TO USE THEIR CREATIVITY IN MATHEMATICS? 26

27 Students use of elaboration strategies More Below the OECD average At the same level as the OECD average Above the OECD average Elaboration % of students who understand new concepts by relating them to things they already know Less Source: Figure 6.1 United Kingdom 20 Iceland 18 Australia 20 Ireland 23 France 19 New Zealand 19 Israel 26 Canada 26 Austria 32 Japan 29 Belgium 22 Singapore 31 Uruguay 22 Germany 33 Netherlands 24 HK-China 30 Luxembourg 33 Costa Rica 33 Norway 23 Finland 23 United States 30 Portugal 29 OECD average 30 Denmark 23 Indonesia 38 Switzerland 32 Bulgaria 27 Macao-China 32 Chile 24 Albania 33 Sweden 24 Kazakhstan 29 Greece 35 UAE 32 Hungary 37 Brazil 25 Argentina 35 Liechtenstein 41 Estonia 38 Mexico 27 Spain 39 Turkey 28 Shanghai-China 35 Poland 27 Colombia 33 Korea 43 Latvia 32 Czech Republic 40 Viet Nam 41 Croatia 48 Slovenia 56 Romania 36 Russian Fed. 41 Montenegro 39 Malaysia 38 Peru 30 Italy 46 Serbia 50 Slovak Republic 40 Lithuania 30 Thailand 34 Qatar 34 Chinese Taipei 42 Jordan 44 Tunisia 44 27

28 Students use of elaboration strategies More Below the OECD average At the same level as the OECD average Above the OECD average Elaboration Less Source: Figure 6.1 The index of elaboration strategies, with values ranging from 0 to 4, reflects the number of times a student chose the following elaborationrelated statements about how they learn mathematics. 1. When I study for a mathematics test, I try to understand new concepts by relating them to things I already know. % of students who understand new 2. When I study mathematics, I think of new ways to get the answer. concepts by relating them to things they already know 3. When I study mathematics, I try to relate the work to things I have learned in other subjects. 4. I think about how the mathematics I have learned can be used in everyday life. United Kingdom 20 Iceland 18 Australia 20 Ireland 23 France 19 New Zealand 19 Israel 26 Canada 26 Austria 32 Japan 29 Belgium 22 Singapore 31 Uruguay 22 Germany 33 Netherlands 24 HK-China 30 Luxembourg 33 Costa Rica 33 Norway 23 Finland 23 United States 30 Portugal 29 OECD average 30 Denmark 23 Indonesia 38 Switzerland 32 Bulgaria 27 Macao-China 32 Chile 24 Albania 33 Sweden 24 Kazakhstan 29 Greece 35 UAE 32 Hungary 37 Brazil 25 Argentina 35 Liechtenstein 41 Estonia 38 Mexico 27 Spain 39 Turkey 28 Shanghai-China 35 Poland 27 Colombia 33 Korea 43 Latvia 32 Czech Republic 40 Viet Nam 41 Croatia 48 Slovenia 56 Romania 36 Russian Fed. 41 Montenegro 39 Malaysia 38 Peru 30 Italy 46 Serbia 50 Slovak Republic 40 Lithuania 30 Thailand 34 Qatar 34 Chinese Taipei 42 Jordan 44 Tunisia 44 28

29 Elaboration strategies are more useful as problems become more difficult (OECD average) Greater success1.50 Odds ratio R² = Difficult problem Less 0.80 success Easy problem Difficulty of mathematics item on the PISA scale Source: Figure

30 Combining elaboration and control strategies leads to success on difficult items Easy item Difficult item Elaboration strategies Control strategies Combining memorisation and elaboration strategies Combining memorisation and control strategies Combining elaboration and control strategies Students using these strategies are less likely to answer items correctly than students using mainly memorisation Students using these strategies are more likely to answer items correctly than students using mainly memorisation Students who combine elaboration and control strategies are about twice as successful on difficult items as students who mainly use memorisation strategies Less success More success Source: Figure

31 What can teachers do? Emphasise the use of elaboration strategies on challenging tasks Challenge all of your students, without raising mathematics anxiety Develop versatile learners Create assessments that challenge students to prepare them for deeper learning 31

32 QUESTION 5: ARE SOME MATHEMATICS TEACHING METHODS MORE EFFECTIVE THAN OTHERS? 32

33 Students perform better when teachers use cognitive-activation instruction more often Higher scores Lower scores Score-point difference Source: Figure 2.2 After accounting for other teaching strategies Cognitive-activation instruction is associated with a 19-point increase in mathematics score across OECD countries, after accounting for other teaching strategies Albania Romania Iceland Kazakhstan Argentina Jordan Thailand United States Mexico Peru Czech Republic Macao-China United Arab Emirates Qatar Finland Canada Brazil Bulgaria Turkey Tunisia Portugal Uruguay Montenegro Serbia Indonesia Netherlands Spain Greece Colombia Singapore Australia Costa Rica Estonia Slovak Republic Ireland Norway Russian Federation OECD average New Zealand Lithuania Croatia Luxembourg Hong Kong-China France Sweden Hungary Chile United Kingdom Korea Austria Malaysia Japan Germany Latvia Denmark Switzerland Chinese Taipei Poland Belgium Slovenia Israel Viet Nam Italy Shanghai-China Liechtenstein 33

34 Students are exposed to a variety of cognitive-activation strategies OECD average of students who responded in every lesson or in most lessons The teacher asks us to decide on our own procedures for solving complex problems The teacher presents problems for which there is no immediately obvious method of solution The teacher gives problems that require us to think for an extended time The teacher presents problems in different contexts so that we know whether we have understood the concepts The teacher asks questions that make us reflect on the problem The teacher gives problems that can be solved in several different ways The teacher helps us to learn from mistakes we have made The teacher presents problems that require us to apply what we have learned to new contexts The teacher asks us to explain how we have solved a problem % Source: Figure

35 Cognitive-activation strategies are related to performance, particularly for advantaged students Higher scores Score-point difference 20 Disadvantaged students Advantaged students Lower scores The teacher helps students learn from mistakes gives problems that require thinking for an extended time Source: OECD, PISA 2012 Database lets students decide on their own procedures makes students reflect on the problem gives problems that can be solved in different ways presents problems in different contexts asks students to explain how they solved a problem gives problems with no immediate solution asks students to apply what they have learned to new contexts 35

36 What can teachers do? Find ways to use cognitive-activation strategies in all of your classes Look at what the research says about how students best learn mathematics Collaborate with other teachers 36

37 QUESTION 6: AS A MATHEMATICS TEACHER, HOW IMPORTANT IS THE RELATIONSHIP I HAVE WITH MY STUDENTS? 37

38 Better teacher-students relations are associated with greater students sense of belonging to school Mean index difference Change in the index of sense of belonging that is associated with a one-unit increase in the index of teacher-student relations After accounting for differences in mathematics performance Kazakhstan Shanghai-China Australia United Kingdom Singapore Colombia Iceland New Zealand Russian Federation Israel Malaysia United States Ireland Costa Rica Lithuania Hong Kong-China Latvia Turkey Sweden Germany Denmark Norway Austria United Arab Emirates Slovenia Mexico Macao-China Spain Chile OECD average Montenegro Finland Indonesia Hungary Belgium Switzerland Jordan Canada Estonia Japan Poland Netherlands Chinese Taipei Viet Nam Uruguay Korea Peru Brazil Romania Slovak Republic Bulgaria Thailand Greece Croatia Serbia Tunisia Portugal Czech Republic Qatar Luxembourg Italy Argentina France Liechtenstein Source: Table III.5.19; OECD, PISA 2012 Database 38

39 Greater A better disciplinary climate is associated with greater mathematics familiarity Familiarity with mathematics Less Source: Figure 3.1 Liechtenstein Finland Tunisia Indonesia Kazakhstan Chile Poland Iceland Estonia Mexico Sweden Hong Kong-China Montenegro United Kingdom Denmark Colombia Macao-China Latvia Switzerland Argentina Russian Federation New Zealand Brazil Thailand Slovak Republic Uruguay Malaysia Portugal Luxembourg Canada Ireland Peru Austria OECD average Serbia Australia Germany Italy Costa Rica Viet Nam Lithuania Netherlands Czech Republic Albania Greece Japan Hungary Israel France Croatia Jordan United Arab Emirates United States Bulgaria Shanghai-China Chinese Taipei Romania Turkey Slovenia Singapore Belgium Qatar Spain Korea 39

40 Teacher job satisfaction More satisfied Teachers report higher job satisfaction when fewer students have behavioural problems Less satisfied None 1% to 10% 11% to 30% 31% or more Percentage of students with behavioural problems Source: Figure 3.2; OECD, Talis 2013 Database 40

41 What can teachers do? Focus time and energy on creating a positive classroom climate Invest time in building strong relationships with your students 41

42 QUESTION 7: DO STUDENTS BACKGROUNDS INFLUENCE HOW THEY LEARN MATHEMATICS? 42

43 Exposure to applied mathematics Disadvantaged students have less exposure to both applied math. More exposure Bottom quarter (disadvantaged students) Top quarter (advantaged students) Less exposure Source: Figure 7.1a Portugal Costa Rica Uruguay 1 Italy 1 Luxembourg Greece 1 Israel 1 Chinese Taipei Japan Tunisia New Zealand Czech Republic 1 Belgium Canada Viet Nam 1 Australia Colombia Serbia 1 Hong Kong-China Malaysia Argentina United States Turkey 1 Liechtenstein Macao-China France United Arab Emirates Chile Bulgaria OECD average Croatia 1 Indonesia Switzerland Iceland Austria Peru Latvia United Kingdom Slovenia Estonia Qatar Brazil Romania Montenegro 1 Germany Ireland Jordan Norway Finland Russian Federation Sweden Slovak Republic 1 Mexico Shanghai-China Korea Hungary 1 Lithuania Spain 1 Netherlands 1 Singapore Denmark Thailand Poland Kazakhstan 43

44 and deep mathematics Exposure to pure mathematics More exposure Bottom quarter (disadvantaged students) Top quarter (advantaged students) Less exposure Source: Figure 7.1a New Zealand Portugal Brazil Qatar Luxembourg Tunisia Jordan Australia Sweden Belgium Denmark United Arab Emirates Colombia Argentina Chinese Taipei Chile Czech Republic Turkey Netherlands Malaysia Canada Slovak Republic Austria Indonesia Romania Costa Rica Thailand Switzerland Uruguay Bulgaria Latvia Montenegro OECD average Serbia Israel France Greece Finland Peru Mexico Germany United Kingdom Norway Estonia United States Hungary Ireland Poland Viet Nam Japan Shanghai-China 1 Iceland Lithuania Italy Croatia Kazakhstan Slovenia Hong Kong-China Russian Federation Spain Liechtenstein 1 Singapore Macao-China 1 Korea 44

45 Disadvantaged students more likely to have negative view of their own capabilities in mathematics % Disadvantaged students Advantaged students 20 Thailand 5 Argentina 17 Indonesia Chinese Taipei 23 Chile 20 Korea 22 Bulgaria 28 Brazil 8 Tunisia 26 Japan 6 Poland 22 Slovak Republic 24 Mexico 10 Uruguay 22 Turkey 14 Malaysia 8 Romania 18 Jordan 19 Hong Kong-China 11 Estonia 17 Spain 17 Peru Portugal 29 Macao-China Montenegro 16 Serbia 21 Italy 13 Shanghai-China 12 Qatar 14 Lithuania 16 Hungary 22 Slovenia 14 Croatia 16 Costa Rica 13 Greece 33 Colombia 16 Norway 21 OECD average 17 Czech Republic 16 France 28 Russian Federation 19 Finland 22 New Zealand 19 Latvia 16 Ireland 14 Belgium 11 Luxembourg 12 Singapore 25 Netherlands 12 United Arab Emirates 19 Kazakhstan 17 Austria 16 Australia 15 Canada 15 Iceland 18 Sweden 13 Germany 11 Liechtenstein 31 Switzerland United States 15 United Kingdom 15 Denmark 23 Israel 10 Viet Nam 14 Source: Figure

46 What can teachers do? Review the curriculum you are covering for the year Don t shy away from challenging mathematics topics Make your students aware of the importance of mathematics for their future careers, particularly students from disadvantaged backgrounds 46

47 QUESTION 8: SHOULD I BE CONCERNED ABOUT MY STUDENTS ATTITUDES TOWARDS MATHEMATICS? 47

48 Girls are more anxious about mathematics than boys % Boys All students Girls Netherlands -13 Denmark -20 Sweden -13 Iceland -10 United Kingdom -17 Switzerland -17 Liechtenstein -23 Finland -22 Germany -15 Shanghai-China -20 Norway -14 Estonia -7 Kazakhstan Czech Republic -8 Austria -10 Luxembourg -15 Latvia -5 United States -10 Poland -7 Lithuania -8 Slovak Republic -11 Russian Federation -5 Belgium -14 OECD average -12 Canada -15 Australia -15 Singapore -4 Slovenia -7 Hungary -9 New Zealand -15 Serbia Colombia -8 France -18 Montenegro Croatia -6 Israel -9 Turkey Albania Spain -10 United Arab Emirates Qatar Hong Kong-China -15 Portugal -5 Ireland -12 Bulgaria -8 Macao-China -17 Japan -14 Brazil Chinese Taipei -12 Viet Nam -9 Chile -4 Costa Rica -11 Greece -10 Peru -6 Thailand -4 Italy -7 Malaysia Uruguay -6 Indonesia -5 Romania Korea -10 Mexico -7 Jordan Tunisia -3 Argentina Source: Figure

49 More exposure to pure mathematics problems in tests than in lessons is associated with greater anxiety More anxiety Students who are more exposed to pure mathematics in tests than in lessons are more anxious than students who are similarly exposed in tests and in lessons Less anxiety Algebraic word problems Contextualised mathematics problems Procedural tasks Pure mathematics problems Source: Figure

50 Higher selfconcept Students frequently exposed to applied mathematics have better opinions about their own capabilities Lower selfconcept Algebraic word problems Contextualised mathematics problems Procedural tasks Pure mathematics problems Source: Figure

51 What can teachers do? In addition to what you teach, think about whom you teach and how you teach Prepare students for what to expect on math tests Explore innovative teaching tools for mathematics 51

52 QUESTION 9: SHOULD MY TEACHING EMPHASISE CONCEPTS OR HOW THOSE CONCEPTS ARE APPLIED? 52

53 Weak relationship between exposure to applied and pure mathematics Greater exposure to applied mathematics OECD average R² = 0.05 OECD average Source: Figure 8.1 Greater exposure to pure mathematics 53

54 Score-point difference Frequent exposure to pure mathematics concepts is associated with better mathematics performance Exposure to applied mathematics Exposure to pure mathematics Korea Chinese Taipei Netherlands Singapore New Zealand Malaysia Hong Kong-China Belgium Qatar Australia Switzerland United Arab Emirates Germany Japan Liechtenstein France Peru Lithuania United Kingdom Iceland United States Finland Austria Italy OECD average Slovak Republic Norway Thailand Russian Federation Portugal Turkey Israel Latvia Bulgaria Hungary Jordan Ireland Canada Slovenia Luxembourg Tunisia Croatia Czech Republic Poland Viet Nam Greece Spain Chile Montenegro Mexico Romania Uruguay Sweden Kazakhstan Serbia Macao-China Argentina Estonia Costa Rica Colombia Indonesia Brazil Denmark Shanghai-China Albania Source: Figure

55 What can teachers do? Cover core mathematics ideas in sufficient depth and show how they are related Don t just cover the fundamentals of the curriculum Provide students with a variety of applied problems to solve 55

56 WHAT HAS PISA TAUGHT US? 56

57 What has PISA taught us? Innovate, innovate, innovate Collaborate with others Develop balanced assessments A policy programme in 5 points Be fair Focus on students abilities and skills Develop balanced assesments How: Make sure your teaching and assessments are balanced Use multiple types of assessments, including oral tests, collaborative problem-solving and long-term projects Take advantage of questions from PISA that have been made public by the OECD or from PISA for Schools exams to serve this purpose 57

58 What has PISA taught us? Innovate, innovate, innovate Collaborate with others Develop balanced assessments A policy programme in 5 points Be fair Focus on students abilities and skills Focus on students abilities and skills How: What is important for citizens to know and be able to do in situations that involve mathematics? This kind of thinking could help you decide which topics to present to your students and how to present them Reading some assessment questions released by PISA might give you additional ideas for your class 58

59 What has PISA taught us? Be fair Innovate, innovate, innovate Develop balanced assessments A policy programme in 5 points Focus on students abilities and skills How: Teach and assess students in ways that are fair and inclusive for everyone Collaborate with others Be fair 59

60 What has PISA taught us? Innovate, innovate, innovate Collaborate with others Develop balanced assessments A policy programme in 5 points Be fair Focus on students abilities and skills How: Collaborate with others Listen to your students Collaborate with other teachers Participate in school decisionmaking Communicate with parents and learn from experts in your field 60

61 What has PISA taught us? Innovate, innovate, innovate Collaborate with others Develop balanced assessments A policy programme in 5 points Be fair Focus on students abilities and skills Innovate, innovate, innovate How: New approaches to teaching are tried and tested all the time, with varying degrees of success Read up on strategies that have been successful for other teachers Participate in innovation networks Once you re more confident with the risks and rewards associated : you ll be the one developing new strategies and resources for your colleagues to try 61

62 62 Thank you Find out more about our work at All publications The complete micro-level database Twitter: SchleicherOECD and remember: Without data, you are just another person with an opinion 62