Key questions for mathematics teachers - and how PISA can answer them
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Ten Questions for Mathematics Teachers… and how PISA can help answer them aims to change that. This report delves into topics such as, “How much should I encourage my students to be responsible for their own learning in mathematics?” or “As a mathematics teacher, how important is the relationship I have with my students?”. It gives teachers timely and relevant data and analyses that can help them reflect on their teaching strategies and how students learn. Contents Introduction: A teacher’s guide to mathematics teaching and learning Question 1: How much should I direct student learning in my mathematics classes? Question 2: Are some mathematics teaching methods more effective than others? Question 3: As a mathematics teacher, how important is the relationship I have with my students? Question 4: What do we know about memorisation and learning mathematics? Question 5: Can I help my students learn how to learn mathematics? Question 6: Should I encourage students to use their creativity in mathematics? Question 7: Do students’ backgrounds influence how they learn mathematics? Question 8: Should my teaching emphasise mathematical concepts or how those concepts are applied in the real world? Question 9: Should I be concerned about my students’ attitudes towards mathematics? Question 10: What can teachers learn from PISA?
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Key questions for mathematics teachers - and how PISA can answer them
- 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 background300350400450500550600650 Mexico Chile Greece Norway Sweden Iceland Israel Italy UnitedStates Spain Denmark Luxembourg Australia Ireland UnitedKingdom Hungary Canada Finland Austria Turkey Liechtenstein CzechRepublic Estonia Portugal Slovenia SlovakRepublic NewZealand Germany Netherlands France Switzerland Poland Belgium Japan Macao-China HongKong-China Korea Singapore ChineseTaipei Shanghai-China
- 3. 3 Exposure to deep math learning and social background -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 United States Shanghai-China Indexofexposuretopure mathematics Bottom quarter (disadvantaged students) Second quarter Third quarter Top quarter (advantaged students) Source: Figure 2.5b
- 4. QUESTION 1: HOW MUCH SHOULD I DIRECT STUDENT LEARNING IN MY MATHEMATICS CLASSES? 4
- 5. What knowledge, skills and character qualities do successful teachers require? 96% of teachers: My role as a teacher is to facilitate students own inquiry
- 6. What knowledge, skills and character qualities do successful teachers require? 86%: Students learn best by findings solutions on their own
- 7. What knowledge, skills and character qualities do successful teachers require? 74%: Thinking and reasoning is more important than curriculum content
- 8. Prevalence of memorisation rehearsal, routine exercises, drill and practice and/or repetition -2.00 -1.50 -1.00 -0.50 0.00 0.00 0.50 1.00 1.50 2.00 Switzerland Poland Germany Japan Korea France Sweden Shanghai-China Canada Singapore United States Norway Spain Netherlands United Kingdom Prevalence of elaboration reasoning, deep learning, intrinsic motivation, critical thinking, creativity, non-routine problems High Low Low High
- 9. 0 10 20 30 40 50 60 70 80 90 The teacher tells us what we have to learn The teacher asks questions to check whether we have understood what was taught The teacher sets clear goals for our learning The teacher asks me or my classmates to present our thinking or reasoning at some length At the beginning of a lesson, the teacher presents a short summary of the previous lesson 9 Teacher-directed strategies are used more often … OECD average of students who responded “in every lesson” or “in most lessons” Source: Figure 1.1 %
- 10. 0 10 20 30 40 50 60 70 80 90 The teacher gives different work to classmates who have difficulties and/or who can advance faster The teacher has us work in small groups to come up with joint solutions to a problem or task The teacher asks us to help plan classroom activities or topics The teacher assigns projects that require at least one week to complete 10 … than student-oriented strategies OECD average of students who responded “in every lesson” or “in most lessons” Source: Figure 1.1 %
- 11. Teaching and learning strategies in mathematics around the world 11 Source: Figure 1.2 R² = 0.10 More teacher- directed instructionTeaching More memorisation Learning OECD average More elaboration More student- oriented instruction Are East Asian education systems really so traditional? Chinese Taipei Vietnam Macao-China Korea Hong-Kong China Singapore Japan Shanghai- China Ireland Hungary France Croatia United Kingdom Australia New Zealand Uruguay Israel Memorisation most frequently used compared to elaboration strategies Teacher-directed instruction most frequently used compared to student-oriented instruction United States
- 12. R² = 0.24 0.80 1.00 1.20 300 400 500 600 700 800 Teacher-directed strategies are related with higher solution rates (OECD average) Source: Figure 1.4 Difficulty on the PISA scale 12 Greater success Less success Easy problem Difficult problem Odds ratio
- 13. -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Below Level 1 Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Index of student-oriented instruction Index of teacher-directed instruction Index of cognitive-activation instruction Students' proficiency level in PISA mathematics 13 Teaching strategies and learning outcomes Mean Index Students at Level 5 and 6 can develop and work with models for complex situations, and work strategically with advanced reasoning skills Students below Level 2 have difficulties using basic algorithms, formulae, procedures or convention
- 14. 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 What can teachers do?
- 15. QUESTION 2: WHAT DO WE KNOW ABOUT MEMORISATION AND LEARNING MATHEMATICS? 15
- 16. Students’ use of memorisation strategies Source: Figure 4.1 Macao-China15 RussianFederation16 Serbia11 SlovakRepublic11 Albania12 Switzerland13 Mexico19 Poland9 Malaysia12 Liechtenstein17 VietNam5 Lithuania14 Kazakhstan22 ChineseTaipei16 HongKong-China10 Denmark28 Italy10 Latvia22 Colombia26 Iceland23 Germany17 Japan12 Qatar13 Korea17 Slovenia11 Tunisia10 Romania16 Peru22 Croatia9 France19 Montenegro13 CostaRica19 Argentina21 Sweden31 CzechRepublic25 Shanghai-China25 Estonia14 Bulgaria11 OECDaverage21 Turkey13 Brazil30 Canada26 Singapore22 Greece20 Austria13 Portugal27 Finland32 UnitedStates29 Hungary17 Luxembourg13 Norway28 Belgium24 Jordan14 Israel14 Thailand46 UnitedArabEmirates13 Australia35 Chile22 NewZealand35 Indonesia23 Spain19 Netherlands22 UnitedKingdom37 Ireland28 Uruguay23 Below the OECD average At the same level as the OECD average Above the OECD average % of students who report they learn by heart 16 Memorisation More Less
- 17. Memorisation is less useful as problems become more difficult (OECD average) R² = 0.81 0.70 1.00 300 400 500 600 700 800 Difficulty of mathematics item on the PISA scale Source: Figure 4.3 18 Difficult problem Easy problem Greater success Less success Odds ratio
- 18. Encourage students to complement memorisation with other learning strategies Use memorisation strategies to build familiarity and confidence Notice how your students learn 20 What can teachers do?
- 19. QUESTION 3: CAN I HELP MY STUDENTS LEARN HOW TO LEARN MATHEMATICS? 21
- 20. There are large international differences in the use of control strategies Source: Figure 5.1 Tunisia46 Jordan43 Thailand19 Spain42 Uruguay55 Qatar53 UnitedArabEmirates55 Peru49 Indonesia39 Montenegro48 CzechRepublic35 Chile54 ChineseTaipei42 Croatia43 Turkey59 Hungary46 Romania48 Netherlands54 Slovenia32 Shanghai-China40 Ireland49 Greece46 Italy44 Brazil45 Lithuania56 Estonia48 Korea40 Argentina44 Norway48 UnitedStates40 Latvia46 SlovakRepublic49 Portugal44 Finland45 Malaysia50 Colombia40 Serbia40 UnitedKingdom43 Luxembourg55 Sweden44 Bulgaria62 OECDaverage49 NewZealand46 VietNam54 Belgium53 RussianFederation44 Poland65 Australia45 Israel61 Singapore47 CostaRica48 Austria55 Liechtenstein42 Kazakhstan49 Mexico54 Canada48 Denmark48 Albania54 Germany50 HongKong-China60 Switzerland55 France62 Japan59 Macao-China53 Iceland59 Below the OECD average At the same level as the OECD average Above the OECD average % of students who try to work out what the most important parts to learn are 22 Control More Less
- 21. Control strategies are always helpful but less so as problems become more difficult (OECD average) R² = 0.31 0.95 1.20 300 400 500 600 700 800 Difficulty of mathematics item on the PISA scale Source: Figure 5.2 24 Difficult problem Greater success Less success Easy problem Odds ratio
- 22. 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 What can teachers do?
- 23. QUESTION 4: SHOULD I ENCOURAGE MY STUDENTS TO USE THEIR CREATIVITY IN MATHEMATICS? 26
- 24. Students’ use of elaboration strategies Source: Figure 6.1 UnitedKingdom20 Iceland18 Australia20 Ireland23 France19 NewZealand19 Israel26 Canada26 Austria32 Japan29 Belgium22 Singapore31 Uruguay22 Germany33 Netherlands24 HK-China30 Luxembourg33 CostaRica33 Norway23 Finland23 UnitedStates30 Portugal29 OECDaverage30 Denmark23 Indonesia38 Switzerland32 Bulgaria27 Macao-China32 Chile24 Albania33 Sweden24 Kazakhstan29 Greece35 UAE32 Hungary37 Brazil25 Argentina35 Liechtenstein41 Estonia38 Mexico27 Spain39 Turkey28 Shanghai-China35 Poland27 Colombia33 Korea43 Latvia32 CzechRepublic40 VietNam41 Croatia48 Slovenia56 Romania36 RussianFed.41 Montenegro39 Malaysia38 Peru30 Italy46 Serbia50 SlovakRepublic40 Lithuania30 Thailand34 Qatar34 ChineseTaipei42 Jordan44 Tunisia44 Below the OECD average At the same level as the OECD average Above the OECD average % of students who understand new concepts by relating them to things they already know 27 Elaboration More Less
- 25. Elaboration strategies are more useful as problems become more difficult (OECD average) R² = 0.82 0.80 1.50 300 400 500 600 700 800 Difficulty of mathematics item on the PISA scaleSource: Figure 6.2 29 Difficult problem Greater success Less success Easy problem Odds ratio
- 26. Combining elaboration and control strategies leads to success on difficult items Elaboration strategies Control strategies Combining memorisation and elaboration strategies Combining memorisation and control strategies Combining elaboration and control strategies Easy item Difficult item Students who combine elaboration and control strategies are about twice as successful on difficult items as students who mainly use memorisation strategies Students using these strategies are more likely to answer items correctly than students using mainly memorisation Students using these strategies are less likely to answer items correctly than students using mainly memorisation Source: Figure 6.3 30 More successLess success
- 27. 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 What can teachers do?
- 28. QUESTION 5: ARE SOME MATHEMATICS TEACHING METHODS MORE EFFECTIVE THAN OTHERS? 32
- 29. Students perform better when teachers use cognitive-activation instruction more often -15 -10 -5 0 5 10 15 20 25 30 35 40 Albania Romania Iceland Kazakhstan Argentina Jordan Thailand UnitedStates Mexico Peru CzechRepublic Macao-China UnitedArabEmirates Qatar Finland Canada Brazil Bulgaria Turkey Tunisia Portugal Uruguay Montenegro Serbia Indonesia Netherlands Spain Greece Colombia Singapore Australia CostaRica Estonia SlovakRepublic Ireland Norway RussianFederation OECDaverage NewZealand Lithuania Croatia Luxembourg HongKong-China France Sweden Hungary Chile UnitedKingdom Korea Austria Malaysia Japan Germany Latvia Denmark Switzerland ChineseTaipei Poland Belgium Slovenia Israel VietNam Italy Shanghai-China Liechtenstein After accounting for other teaching strategies Source: Figure 2.2 Score-point difference Cognitive-activation instruction is associated with a 19-point increase in mathematics score across OECD countries, after accounting for other teaching strategies 33 Lower scores Higher scores
- 30. Cognitive-activation strategies are related to performance, particularly for advantaged students -15 -10 -5 0 5 10 15 20 helps students learn from mistakes gives problems that require thinking for an extended time 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 Disadvantaged students Advantaged studentsScore-point difference The teacher … 35 Lower scores Higher scores Source: OECD, PISA 2012 Database
- 31. 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 What can teachers do?
- 32. QUESTION 6: AS A MATHEMATICS TEACHER, HOW IMPORTANT IS THE RELATIONSHIP I HAVE WITH MY STUDENTS? 37
- 33. Better teacher-students relations are associated with greater students’ sense of belonging to school 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 Kazakhstan Shanghai-China Australia UnitedKingdom Singapore Colombia Iceland NewZealand RussianFederation Israel Malaysia UnitedStates Ireland CostaRica Lithuania HongKong-China Latvia Turkey Sweden Germany Denmark Norway Austria UnitedArabEmirates Slovenia Mexico Macao-China Spain Chile OECDaverage Montenegro Finland Indonesia Hungary Belgium Switzerland Jordan Canada Estonia Japan Poland Netherlands ChineseTaipei VietNam Uruguay Korea Peru Brazil Romania SlovakRepublic Bulgaria Thailand Greece Croatia Serbia Tunisia Portugal CzechRepublic Qatar Luxembourg Italy Argentina France Liechtenstein After accounting for differences in mathematics performance Source: Table III.5.19; OECD, PISA 2012 Database Mean index difference 38 Change in the index of sense of belonging that is associated with a one-unit increase in the index of teacher-student relations
- 34. A better disciplinary climate is associated with greater mathematics familiarity Liechtenstein Finland Tunisia Indonesia Kazakhstan Chile Poland Iceland Estonia Mexico Sweden HongKong-China Montenegro UnitedKingdom Denmark Colombia Macao-China Latvia Switzerland Argentina RussianFederation NewZealand Brazil Thailand SlovakRepublic Uruguay Malaysia Portugal Luxembourg Canada Ireland Peru Austria OECDaverage Serbia Australia Germany Italy CostaRica VietNam Lithuania Netherlands CzechRepublic Albania Greece Japan Hungary Israel France Croatia Jordan UnitedArabEmirates UnitedStates Bulgaria Shanghai-China ChineseTaipei Romania Turkey Slovenia Singapore Belgium Qatar Spain Korea Source: Figure 3.1 39 Familiaritywith mathematics Greater Less
- 35. Teachers report higher job satisfaction when fewer students have behavioural problems None 1% to 10% 11% to 30% 31% or more Percentage of students with behavioural problems 40 Teacherjob satisfaction More satisfied Less satisfied Source: Figure 3.2; OECD, Talis 2013 Database
- 36. Focus time and energy on creating a positive classroom climate Invest time in building strong relationships with your students 41 What can teachers do?
- 37. QUESTION 7: DO STUDENTS’ BACKGROUNDS INFLUENCE HOW THEY LEARN MATHEMATICS? 42
- 38. Disadvantaged students have less exposure to both applied math….Portugal CostaRica Uruguay1 Italy1 Luxembourg Greece1 Israel1 ChineseTaipei Japan Tunisia NewZealand CzechRepublic1 Belgium Canada VietNam1 Australia Colombia Serbia1 HongKong-China Malaysia Argentina UnitedStates Turkey1 Liechtenstein Macao-China France UnitedArabEmirates Chile Bulgaria OECDaverage Croatia1 Indonesia Switzerland Iceland Austria Peru Latvia UnitedKingdom Slovenia Estonia Qatar Brazil Romania Montenegro1 Germany Ireland Jordan Norway Finland RussianFederation Sweden SlovakRepublic1 Mexico Shanghai-China Korea Hungary1 Lithuania Spain1 Netherlands1 Singapore Denmark Thailand Poland Kazakhstan Bottom quarter (disadvantaged students) Top quarter (advantaged students) 43 Source: Figure 7.1a Exposuretoapplied mathematics More exposure Less exposure
- 39. … and deep mathematics NewZealand Portugal Brazil Qatar Luxembourg Tunisia Jordan Australia Sweden Belgium Denmark UnitedArabEmirates Colombia Argentina ChineseTaipei Chile CzechRepublic Turkey Netherlands Malaysia Canada SlovakRepublic Austria Indonesia Romania CostaRica Thailand Switzerland Uruguay Bulgaria Latvia Montenegro OECDaverage Serbia Israel France Greece Finland Peru Mexico Germany UnitedKingdom Norway Estonia UnitedStates Hungary Ireland Poland VietNam Japan Shanghai-China1 Iceland Lithuania Italy Croatia Kazakhstan Slovenia HongKong-China RussianFederation Spain Liechtenstein1 Singapore Macao-China1 Korea Bottom quarter (disadvantaged students) Top quarter (advantaged students) 44 Source: Figure 7.1a Exposuretopure mathematics More exposure Less exposure
- 40. 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 What can teachers do?
- 41. QUESTION 8: SHOULD I BE CONCERNED ABOUT MY STUDENTS’ ATTITUDES TOWARDS MATHEMATICS? 47
- 43. 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 What can teachers do?
- 44. WHAT HAS PISA TAUGHT US? 56
- 45. Develop balanced assessments Focus on students’ abilities and skills Be fair Collaborate with others Innovate, innovate, innovate 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 What has PISA taught us? A policy programme in 5 points 57
- 46. Develop balanced assessments Focus on students’ abilities and skills Be fair Collaborate with others Innovate, innovate, innovate 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 What has PISA taught us? A policy programme in 5 points 58
- 47. Develop balanced assessments Focus on students’ abilities and skills Be fair Collaborate with others Innovate, innovate, innovate Be fair How: • Teach and assess students in ways that are fair and inclusive for everyone What has PISA taught us? A policy programme in 5 points 59
- 48. Develop balanced assessments Focus on students’ abilities and skills Be fair Collaborate with others Innovate, innovate, innovate Collaborate with others How: • Listen to your students • Collaborate with other teachers • Participate in school decision- making • Communicate with parents and learn from experts in your field What has PISA taught us? A policy programme in 5 points 60
- 49. Develop balanced assessments Focus on students’ abilities and skills Be fair Collaborate with others Innovate, innovate, innovate 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 What has PISA taught us? A policy programme in 5 points 61
- 50. 62 62 Thank you Find out more about our work at www.oecd.org – All publications – The complete micro-level database Email: Andreas.Schleicher@OECD.org Twitter: SchleicherOECD and remember: Without data, you are just another person with an opinion
Editor's Notes
- Largest differences: New Zealand, Netherlands, Portugal, Belgium
- The quality of education can never exceed the quality of teaching and teachers. But what exactly are the knowledge, skills and character qualities that will make teachers successful? How and to what extent are these related to teachers’ education? Some people explain poor learning outcomes in their country by claiming that their teachers come from the bottom third of their college graduates, while high-performing countries recruit their teachers from the top third. Surely, top school systems pay a great deal of attention to how they select their staff. They work hard to improve the performance of teachers who are struggling, they provide an environment in which teachers work together to frame good practice, and they establish intelligent pathways for teachers to grow in their careers. But does all that mean that in those countries the top third of graduates chose to become teachers rather than lawyers, doctors or engineers?
- The quality of education can never exceed the quality of teaching and teachers. But what exactly are the knowledge, skills and character qualities that will make teachers successful? How and to what extent are these related to teachers’ education? Some people explain poor learning outcomes in their country by claiming that their teachers come from the bottom third of their college graduates, while high-performing countries recruit their teachers from the top third. Surely, top school systems pay a great deal of attention to how they select their staff. They work hard to improve the performance of teachers who are struggling, they provide an environment in which teachers work together to frame good practice, and they establish intelligent pathways for teachers to grow in their careers. But does all that mean that in those countries the top third of graduates chose to become teachers rather than lawyers, doctors or engineers?
- The quality of education can never exceed the quality of teaching and teachers. But what exactly are the knowledge, skills and character qualities that will make teachers successful? How and to what extent are these related to teachers’ education? Some people explain poor learning outcomes in their country by claiming that their teachers come from the bottom third of their college graduates, while high-performing countries recruit their teachers from the top third. Surely, top school systems pay a great deal of attention to how they select their staff. They work hard to improve the performance of teachers who are struggling, they provide an environment in which teachers work together to frame good practice, and they establish intelligent pathways for teachers to grow in their careers. But does all that mean that in those countries the top third of graduates chose to become teachers rather than lawyers, doctors or engineers?
- Note: The OECD average includes all member countries of the OECD except Latvia.
- Note: The OECD average includes all member countries of the OECD except Latvia.
- Notes: Odds ratio, after accounting for other teaching strategies, OECD average. Statistically significant odds ratios are marked in a darker tone. Chile and Mexico are not included in the OECD average.
- OECD average Results from PISA show that, on average across OECD countries, students who scored at the lower levels of mathematics proficiency, particularly at or below Level 1, most frequently reported that they are exposed to student-oriented, formative-assessment and teacher-directed instruction. Conversely, students who reported greater exposure to cognitive activation instruction scored, on average, at higher levels of proficiency in mathematics, notably at Level 5 or 6. Before accounting for other teaching strategies, cognitive-activation instruction is associated with an increase of about five score points on the PISA mathematics assessment. After accounting for the other three teaching strategies, the average improvement in mathematics performance associated with cognitive-activation instruction is as large as 19 score points. Remarkably, after accounting for the other teaching strategies, there is a positive association between cognitive-activation instruction and mean mathematics performance in every country and economy that participated in PISA 2012, except Albania. Results from PISA also show that these teaching strategies are associated with the learning environment and organisation of schools. For example, schools in which these teaching strategies are used more frequently tend to be those with more supportive teachers, where there are good teacher-student relations, where teachers are skilled in managing their classrooms and maintain discipline, and are those whose students reported feeling a greater sense of belonging at school. The strength of the relationship between the learning environment and instructional strategies is greater with teacher directed and cognitive-activation strategies, and is weaker with student-oriented strategies. Student-oriented instruction is something of an exception in that its relationship with classroom discipline is weak and often negative, most likely because small-group discussions or other methods that aim to give students a more active role in the learning process can generate or require a more dynamic – and, to some, louder – classroom environment.
- Note: The technique of memorisation strategies to learn something completely so that it can later be recalled or repeated. In mathematics classes, teachers often encourage students to use their memories through activities such as rehearsal, routine exercises and drills.
- Note: The technique of memorisation strategies to learn something completely so that it can later be recalled or repeated. In mathematics classes, teachers often encourage students to use their memories through activities such as rehearsal, routine exercises and drills.
- Notes: Statistically significant odds ratios are marked in a darker tone. Chile and Mexico are not included in the OECD average. Odds ratio are calculated across 48 education systems.
- Note: Control strategies from the teacher’s perspective: they are allowing students to set their own goals and track their own learning progress, helping learners control their own learning (e.g. organising material, creating a study plan). It is is related to concepts such as efficiency, strategic learning, self-regulation and metacognition.
- Note: Control strategies from the teacher’s perspective: they are allowing students to set their own goals and track their own learning progress, helping learners control their own learning (e.g. organising material, creating a study plan). It is is related to concepts such as efficiency, strategic learning, self-regulation and metacognition.
- Notes: Statistically significant odds ratios are marked in a darker tone. Chile and Mexico are not included in the OECD average. Odds ration are calculated across 48 education systems.
- Note: Elaboration strategies from the teacher perspective: they encourage students to make connections among mathematics tasks, link students’ learning to their own prior knowledge and real-life situations, and find different ways of solving a problem (e.g. strategies include developing analogies and examples, brainstorming, using concept maps). They are helping students understand new information in mathematics and retain this information over the long term The index of elaboration strategies is based on the four questions about learning strategies in the student questionnaire. In each question, students were asked to choose among three mutually exclusive statements corresponding to the following approaches to learning mathematics: memorisation, elaboration and control.
- Note: Elaboration strategies from the teacher perspective: they encourage students to make connections among mathematics tasks, link students’ learning to their own prior knowledge and real-life situations, and find different ways of solving a problem (e.g. strategies include developing analogies and examples, brainstorming, using concept maps). They are helping students understand new information in mathematics and retain this information over the long term The index of elaboration strategies is based on the four questions about learning strategies in the student questionnaire. In each question, students were asked to choose among three mutually exclusive statements corresponding to the following approaches to learning mathematics: memorisation, elaboration and control.
- Notes: Statistically significant odds ratios are marked in a darker tone. Chile and Mexico are not included in the OECD average. Odds ration are calculated across 48 education systems.
- Note: Odds ratios for the easy and intermediate items are not statistically significant. Statistically significant odds ratios for difficult items are marked in a darker tone. Odds ratio of succeeding on PISA mathematics items compared to using mainly memorisation strategies, across 48 education systems.
- Notes: Statistically significant values before accounting for other teaching strategies are marked in a darker tone. All values after accounting for other teaching strategies are statistically significant. Other teaching strategies refer to the PISA indices of teacher-directed, student-oriented and formative-assessment instruction. The index of cognitive-activation instruction measures the extent to which teachers encourage students to acquire deep knowledge through instructional practices such as giving students problems that require them to think for an extended time, presenting problems for which there is no immediately obvious way of arriving at a solution, and helping students to learn from the mistakes they have made.
- Notes: Statistically significant values for disadvantaged students are marked in a darker tone. All values for advantaged students are statistically significant. Disadvantaged (advantaged) students are those schools in the bottom (top) quarter of the PISA index of economic, social and cultural status.
- Note: All changes in the index of sense of belonging that are associated with a one-unit increase in the index of teacher-student relations are statistically significant. Countries and economies are ranked in descending order of the 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.
- Notes: Statistically significant values are marked in a darker tone. The index of disciplinary climate is based on students' reports of the frequency with which interruptions occur in mathematics class. Higher values on the index indicate a better disciplinary climate. The index of familiarity with mathematics is based on students’ responses to 13 items measuring students’ self-reported familiarity with mathematics concepts, such as exponential function, divisor and quadratic function. Countries and economies are ranked in ascending order of the change in the index of familiarity with mathematics associated with a one-unit increase in the index of disciplinary climate.
- Notes: Lower secondary teachers' job satisfaction by the percentage of students with behavioural problems. Data on students with behavioural problems are reported by teachers and refer to a randomly chosen class they currently teach in their weekly timetable. To assess teachers’ job satisfaction, TALIS asked teachers to indicate how satisfied they feel about their job (on a four-point scale ranging from “strongly disagree” to “strongly agree”) by responding to a number of statements about their work environment (“I would like to change to another school if that were possible”; “I enjoy working at this school”; “I would recommend my school as a good place to work”; and “All in all, I am satisfied with my job”) and the teaching profession (“The advantages of being a teacher clearly outweigh the disadvantages”; “If I could decide again, I would still choose to work as a teacher”; “I regret that I decided to become a teacher”; and “I wonder whether it would have been better to choose another profession”). The analysis is based on the average of the countries participating in the TALIS Survey.
- The difference between the top and the bottom quarters of the PISA index of economic, social and cultural status is not statistically significant. Note: The index of exposure to applied mathematics measures student-reported experience with applied mathematics tasks at school, such as working out from a train timetable how long it would take to get from one place to another or calculating how much more expensive a computer would be after adding tax.
- The difference between the top and the bottom quarters of the PISA index of economic, social and cultural status is not statistically significant. Note: The index of exposure to applied mathematics measures student-reported experience with applied mathematics tasks at school, such as working out from a train timetable how long it would take to get from one place to another or calculating how much more expensive a computer would be after adding tax.
- Note: Statistically significant percentage-point differences between boys and girls are shown next to the country/economy name.
- Judit: shorter title
- Notes: The index of exposure to pure mathematics measures student-reported experience with mathematics tasks requiring knowledge of algebra (linear and quadratic equations). The index of exposure to applied mathematics measures student-reported experience with applied mathematical tasks at school, such as working out from a train timetable how long it would take to get from one place to another or calculating how much more expensive a computer would be after adding tax.
- Notes: Statistically significant values are marked in a darker tone. The index of exposure to pure mathematics measures student-reported experience with mathematics tasks at school requiring knowledge of algebra (linear and quadratic equations). The index of exposure to applied mathematics measures student-reported experience with applied mathematical tasks at school, such as working out from a train timetable how long it would take to get from one place to another or calculating how much more expensive a computer would be after adding tax.