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?
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?
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?
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?
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
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
Notes de l'éditeur
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.