KEY QUESTIONS FOR MATHEMATICS TEACHERS
AND HOW PISA CAN ANSWER THEM
Andreas SchleicherOctober 7, 2016
22PISA mathematics performance by decile of social background
300
350
400
450
500
550
600
650
Mex
ico
Chi
leG
reec
eN
orw
aySw
eden
Icel
and
Isra
elIt
aly
Uni
ted
Stat
esSp
ain
Den
mar
kLu
xem
bour
gA
ustr
alia
Irel
and
Uni
ted
Kin
gdom
Hun
gary
Can
ada
Finl
and
Aus
tria
Turk
eyLi
echt
enst
ein
Cze
ch R
epub
lic
Est
onia
Por
tuga
lSl
oven
iaSl
ovak
Rep
ubli
cN
ew Z
eala
ndG
erm
any
Net
herl
ands
Fran
ceSw
itze
rlan
dP
olan
dB
elgi
umJa
pan
Mac
ao-C
hina
Hon
g K
ong-
Chi
naK
orea
Sing
apor
eC
hine
se T
aipe
iSh
angh
ai-C
hina
Source: PISA 2012
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
Inde
x of
exp
osur
e to
pur
e m
athe
mat
ics
Bottom quarter (disadvantaged students) Second quarter Third quarter Top quarter (advantaged students)
Source: Figure 2.5b
QUESTION 1: HOW MUCH SHOULD I
DIRECT STUDENT LEARNING IN MY
MATHEMATICS CLASSES?
4
Whatknowledge,skillsandcharacterqualitiesdo
successfulteachersrequire?
96% of teachers: My role as a teacher is to facilitate students own inquiry
Whatknowledge,skillsandcharacterqualitiesdo
successfulteachersrequire?
86%: Students learn best by findings solutions on their own
Whatknowledge,skillsandcharacterqualitiesdo
successfulteachersrequire?
74%: Thinking and reasoning is more important than curriculum content
Prevalence of memorisationrehearsal, 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
SwitzerlandPoland
GermanyJapanKorea
FranceSweden
Shanghai-ChinaCanada
SingaporeUnited States
NorwaySpain
NetherlandsUnited Kingdom
Prevalence of elaborationreasoning, deep learning, intrinsic motivation, critical thinking, creativity, non-routine problems
High Low Low High
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
%
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 strategiesOECD average of students who responded “in every lesson” or “in most lessons”
Source: Figure 1.1
%
Teaching and learning strategies inmathematics around the world
11Source: Figure 1.2
R² = 0.10
More teacher-directed
instructionTeaching
More memorisation
Lear
ning
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
SingaporeJapan
Shanghai- China
Ireland
Hungary
France
Croatia
United Kingdom
AustraliaNew Zealand
UruguayIsrael
Memorisation most frequently used compared to elaboration strategies
Teacher-directed instruction most
frequently used compared to student-oriented
instruction
United States
R² = 0.24
0.80
1.00
1.20
300 400 500 600 700 800
Teacher-directed strategies are related withhigher solution rates (OECD average)
Source: Figure 1.4Difficulty on the PISA scale 12
Greater success
Less success
Easy problem
Difficult problem
Odds ratio
-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
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?
QUESTION 2: WHAT DO WE KNOW ABOUT
MEMORISATION AND LEARNING MATHEMATICS?
15
Students’ use of memorisation strategies
Source: Figure 4.1
Mac
ao-C
hina
1
5R
ussi
an F
eder
atio
n
16
Serb
ia
11
Slov
ak R
epub
lic
11
Alb
ania
1
2Sw
itzer
land
1
3M
exic
o
19
Pola
nd
9
Mal
aysi
a
12
Liec
hten
stei
n
17
Viet
Nam
5Li
thua
nia
1
4K
azak
hsta
n
22
Chi
nese
Tai
pei
16
Hon
g K
ong-
Chi
na
10
Den
mar
k
28
Italy
1
0La
tvia
2
2C
olom
bia
2
6Ic
elan
d
23
Ger
man
y
17
Japa
n
12
Qat
ar
13
Kor
ea
17
Slov
enia
1
1Tu
nisi
a
10
Rom
ania
1
6Pe
ru
22
Cro
atia
9Fr
ance
1
9M
onte
negr
o
13
Cos
ta R
ica
1
9A
rgen
tina
2
1Sw
eden
3
1C
zech
Rep
ublic
2
5Sh
angh
ai-C
hina
2
5Es
toni
a
14
Bul
garia
1
1O
ECD
ave
rage
2
1Tu
rkey
1
3B
razi
l
30C
anad
a
26
Sing
apor
e
22
Gre
ece
2
0A
ustr
ia
13
Port
ugal
2
7Fi
nlan
d
32
Uni
ted
Stat
es
29
Hun
gary
1
7Lu
xem
bour
g
13
Nor
way
2
8B
elgi
um
24
Jord
an
14
Isra
el
14
Thai
land
4
6U
nite
d A
rab
Emira
tes
…A
ustr
alia
3
5C
hile
2
2N
ew Z
eala
nd
35
Indo
nesi
a
23
Spai
n
19
Net
herla
nds
2
2U
nite
d K
ingd
om
37
Irela
nd
28
Uru
guay
2
3
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
Mem
oris
atio
n
More
Less
Students’ use of memorisation strategies
Source: Figure 4.1
Mac
ao-C
hina
1
5R
ussi
an F
eder
atio
n
16
Serb
ia
11
Slov
ak R
epub
lic
11
Alb
ania
1
2Sw
itzer
land
1
3M
exic
o
19
Pola
nd
9
Mal
aysi
a
12
Liec
hten
stei
n
17
Viet
Nam
5Li
thua
nia
1
4K
azak
hsta
n
22
Chi
nese
Tai
pei
16
Hon
g K
ong-
Chi
na
10
Den
mar
k
28
Italy
1
0La
tvia
2
2C
olom
bia
2
6Ic
elan
d
23
Ger
man
y
17
Japa
n
12
Qat
ar
13
Kor
ea
17
Slov
enia
1
1Tu
nisi
a
10
Rom
ania
1
6Pe
ru
22
Cro
atia
9Fr
ance
1
9M
onte
negr
o
13
Cos
ta R
ica
1
9A
rgen
tina
2
1Sw
eden
3
1C
zech
Rep
ublic
2
5Sh
angh
ai-C
hina
2
5Es
toni
a
14
Bul
garia
1
1O
ECD
ave
rage
2
1Tu
rkey
1
3B
razi
l
30C
anad
a
26
Sing
apor
e
22
Gre
ece
2
0A
ustr
ia
13
Port
ugal
2
7Fi
nlan
d
32
Uni
ted
Stat
es
29
Hun
gary
1
7Lu
xem
bour
g
13
Nor
way
2
8B
elgi
um
24
Jord
an
14
Isra
el
14
Thai
land
4
6U
nite
d A
rab
Emira
tes
…A
ustr
alia
3
5C
hile
2
2N
ew Z
eala
nd
35
Indo
nesi
a
23
Spai
n
19
Net
herla
nds
2
2U
nite
d K
ingd
om
37
Irela
nd
28
Uru
guay
2
3
Below the OECD average At the same level as the OECD average Above the OECD average
% of students who report they learn by heart
17
Mem
oris
atio
n
More
Less
The index of memorisation, with values ranging from 0 to 4, reflects the number of times a student chose the following memorisation-relatedstatements 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.
Memorisation is less useful as problems become more difficult (OECD average)
R² = 0.81
0.70
1.00
300 400 500 600 700 800Difficulty of mathematics item on the PISA scale
Source: Figure 4.318
Difficult problem
Easy problem
Greater success
Less success
Odds ratio
‘Weaker’ students tend to use memorisation more (OECD average)
Higher self-efficacy in
mathematics
More openness to
problem solving
Higher score in
mathematics
More interested in mathematics
Better self-concept in
mathematics
More instrumental
motivation for learning
mathematics
More perseverance
Greater mathematics
anxiety
Correlation with the index of memorisation
Source: Figure 4.219
Mem
oris
atio
n
More
Less
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?
QUESTION 3: CAN I HELP MY STUDENTS
LEARN HOW TO LEARN MATHEMATICS?
21
There are large international differences in the use of control strategies
Source: Figure 5.1
Tuni
sia
4
6Jo
rdan
4
3Th
aila
nd
19
Spai
n
42
Uru
guay
5
5Q
atar
5
3U
nite
d A
rab
Emira
tes
5
5Pe
ru
49
Indo
nesi
a
39
Mon
tene
gro
4
8C
zech
Rep
ublic
3
5C
hile
5
4C
hine
se T
aipe
i
42C
roat
ia
43
Turk
ey
59
Hun
gary
4
6R
oman
ia
48
Net
herla
nds
5
4Sl
oven
ia
32
Shan
ghai
-Chi
na
40
Irela
nd
49
Gre
ece
4
6Ita
ly
44
Bra
zil
45
Lith
uani
a
56
Esto
nia
4
8K
orea
4
0A
rgen
tina
4
4N
orw
ay
48
Uni
ted
Stat
es
40
Latv
ia
46
Slov
ak R
epub
lic
49
Port
ugal
4
4Fi
nlan
d
45
Mal
aysi
a
50
Col
ombi
a
40
Serb
ia
40
Uni
ted
Kin
gdom
4
3Lu
xem
bour
g
55
Swed
en
44
Bul
garia
6
2O
ECD
ave
rage
4
9N
ew Z
eala
nd
46
Viet
Nam
5
4B
elgi
um
53
Rus
sian
Fed
erat
ion
4
4Po
land
6
5A
ustr
alia
4
5Is
rael
6
1Si
ngap
ore
4
7C
osta
Ric
a
48
Aus
tria
5
5Li
echt
enst
ein
4
2K
azak
hsta
n
49
Mex
ico
5
4C
anad
a
48
Den
mar
k
48
Alb
ania
5
4G
erm
any
5
0H
ong
Kon
g-C
hina
6
0Sw
itzer
land
5
5Fr
ance
6
2Ja
pan
5
9M
acao
-Chi
na
53
Icel
and
5
9
Below the OECD average At the same level as the OECD average Above the OECD average
% of students whotry to work out what the most
important parts to learn are
22
Con
trol
More
Less
There are large international differences in the use of control strategies
Source: Figure 5.1
Tuni
sia
4
6Jo
rdan
4
3Th
aila
nd
19
Spai
n
42
Uru
guay
5
5Q
atar
5
3U
nite
d A
rab
Emira
tes
5
5Pe
ru
49
Indo
nesi
a
39
Mon
tene
gro
4
8C
zech
Rep
ublic
3
5C
hile
5
4C
hine
se T
aipe
i
42C
roat
ia
43
Turk
ey
59
Hun
gary
4
6R
oman
ia
48
Net
herla
nds
5
4Sl
oven
ia
32
Shan
ghai
-Chi
na
40
Irela
nd
49
Gre
ece
4
6Ita
ly
44
Bra
zil
45
Lith
uani
a
56
Esto
nia
4
8K
orea
4
0A
rgen
tina
4
4N
orw
ay
48
Uni
ted
Stat
es
40
Latv
ia
46
Slov
ak R
epub
lic
49
Port
ugal
4
4Fi
nlan
d
45
Mal
aysi
a
50
Col
ombi
a
40
Serb
ia
40
Uni
ted
Kin
gdom
4
3Lu
xem
bour
g
55
Swed
en
44
Bul
garia
6
2O
ECD
ave
rage
4
9N
ew Z
eala
nd
46
Viet
Nam
5
4B
elgi
um
53
Rus
sian
Fed
erat
ion
4
4Po
land
6
5A
ustr
alia
4
5Is
rael
6
1Si
ngap
ore
4
7C
osta
Ric
a
48
Aus
tria
5
5Li
echt
enst
ein
4
2K
azak
hsta
n
49
Mex
ico
5
4C
anad
a
48
Den
mar
k
48
Alb
ania
5
4G
erm
any
5
0H
ong
Kon
g-C
hina
6
0Sw
itzer
land
5
5Fr
ance
6
2Ja
pan
5
9M
acao
-Chi
na
53
Icel
and
5
9
Below the OECD average At the same level as the OECD average Above the OECD average
% of students whotry to work out what the most
important parts to learn are
23
Con
trol
More
Less
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.
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.
Control strategies are always helpful but less so as problems become more difficult (OECD average)
R² = 0.310.95
1.20
300 400 500 600 700 800Difficulty of mathematics item on the PISA scale
Source: Figure 5.224
Difficult problem
Greater success
Less success
Easy problem
Odds ratio
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?
QUESTION 4: SHOULD I ENCOURAGE MY STUDENTS TO USE THEIR
CREATIVITY IN MATHEMATICS?
26
Students’ use of elaboration strategies
Source: Figure 6.1
Uni
ted
Kin
gdom
2
0Ic
elan
d
18
Aus
tral
ia
20
Irela
nd
23
Fran
ce
19
New
Zea
land
1
9Is
rael
2
6C
anad
a
26
Aus
tria
3
2Ja
pan
2
9B
elgi
um
22
Sing
apor
e
31
Uru
guay
2
2G
erm
any
3
3N
ethe
rland
s
24
HK
-Chi
na
30
Luxe
mbo
urg
3
3C
osta
Ric
a
33
Nor
way
2
3Fi
nlan
d
23
Uni
ted
Stat
es
30
Port
ugal
2
9O
ECD
ave
rage
3
0D
enm
ark
2
3In
done
sia
3
8Sw
itzer
land
3
2B
ulga
ria
27
Mac
ao-C
hina
3
2C
hile
2
4A
lban
ia
33
Swed
en
24
Kaz
akhs
tan
2
9G
reec
e
35
UA
E
32
Hun
gary
3
7B
razi
l
25A
rgen
tina
3
5Li
echt
enst
ein
4
1Es
toni
a
38
Mex
ico
2
7Sp
ain
3
9Tu
rkey
2
8Sh
angh
ai-C
hina
3
5Po
land
2
7C
olom
bia
3
3K
orea
4
3La
tvia
3
2C
zech
Rep
ublic
4
0Vi
et N
am
41
Cro
atia
4
8Sl
oven
ia
56
Rom
ania
3
6R
ussi
an F
ed.
41
Mon
tene
gro
3
9M
alay
sia
3
8Pe
ru
30
Italy
4
6Se
rbia
5
0Sl
ovak
Rep
ublic
4
0Li
thua
nia
3
0Th
aila
nd
34
Qat
ar
34
Chi
nese
Tai
pei
42
Jord
an
44
Tuni
sia
4
4
Below the OECD average At the same level as the OECD average Above the OECD average
% of students whounderstand new
concepts by relating them to things they
already know
27
Ela
bora
tion
More
Less
Students’ use of elaboration strategies
Source: Figure 6.1
Uni
ted
Kin
gdom
2
0Ic
elan
d
18
Aus
tral
ia
20
Irela
nd
23
Fran
ce
19
New
Zea
land
1
9Is
rael
2
6C
anad
a
26
Aus
tria
3
2Ja
pan
2
9B
elgi
um
22
Sing
apor
e
31
Uru
guay
2
2G
erm
any
3
3N
ethe
rland
s
24
HK
-Chi
na
30
Luxe
mbo
urg
3
3C
osta
Ric
a
33
Nor
way
2
3Fi
nlan
d
23
Uni
ted
Stat
es
30
Port
ugal
2
9O
ECD
ave
rage
3
0D
enm
ark
2
3In
done
sia
3
8Sw
itzer
land
3
2B
ulga
ria
27
Mac
ao-C
hina
3
2C
hile
2
4A
lban
ia
33
Swed
en
24
Kaz
akhs
tan
2
9G
reec
e
35
UA
E
32
Hun
gary
3
7B
razi
l
25A
rgen
tina
3
5Li
echt
enst
ein
4
1Es
toni
a
38
Mex
ico
2
7Sp
ain
3
9Tu
rkey
2
8Sh
angh
ai-C
hina
3
5Po
land
2
7C
olom
bia
3
3K
orea
4
3La
tvia
3
2C
zech
Rep
ublic
4
0Vi
et N
am
41
Cro
atia
4
8Sl
oven
ia
56
Rom
ania
3
6R
ussi
an F
ed.
41
Mon
tene
gro
3
9M
alay
sia
3
8Pe
ru
30
Italy
4
6Se
rbia
5
0Sl
ovak
Rep
ublic
4
0Li
thua
nia
3
0Th
aila
nd
34
Qat
ar
34
Chi
nese
Tai
pei
42
Jord
an
44
Tuni
sia
4
4
Below the OECD average At the same level as the OECD average Above the OECD average
% of students whounderstand new
concepts by relating them to things they
already know
28
Ela
bora
tion
More
Less
The index of elaboration strategies, with values ranging from 0 to 4, reflects the number of times a student chose the following elaboration-related 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.
2. When I study mathematics, I think of new ways to get the answer.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.
Elaboration strategies are more useful as problems become more difficult (OECD average)
R² = 0.82003
0.80
1.50
300 400 500 600 700 800
Difficulty of mathematics item on the PISA scaleSource: Figure 6.229
Difficultproblem
Greater success
Less success
Easy problem
Odds ratio
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 andcontrol 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 likelyto answer items correctly
than students using mainly memorisation
Source: Figure 6.330
More successLess success
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?
QUESTION 5: ARE SOME MATHEMATICS
TEACHING METHODS MORE EFFECTIVE THAN
OTHERS?
32
Students perform better when teachers use cognitive-activation instruction more often
-15-10
-505
10152025303540
Alb
ania
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ain
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ong
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man
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iaIs
rael
Viet
Nam Ita
lySh
angh
ai-C
hina
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hten
stei
n
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
Students are exposed to a variety of cognitive-activation strategies
0 10 20 30 40 50 60 70 80
The teacher asks us to explain how we have solved a problem
The teacher presents problems that require us to apply what we have learned to new contexts
The teacher helps us to learn from mistakes we have made
The teacher gives problems that can be solved in several different ways
The teacher asks questions that make us reflect on the problem
The teacher presents problems in different contexts so that we know whether we have understood the concepts
The teacher gives problems that require us to think for an extended time
The teacher presents problems for which there is no immediately obvious method of solution
The teacher asks us to decide on our own procedures for solving complex problems
%
OECD average of students who responded “in every lesson” or “in most lessons”
Source: Figure 2.134
Cognitive-activation strategies are related toperformance, 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
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?
QUESTION 6: AS A MATHEMATICS
TEACHER, HOW IMPORTANT IS THE
RELATIONSHIP I HAVE WITH MY STUDENTS?
37
Better teacher-students relations are associated withgreater students’ sense of belonging to school
0.200.250.300.350.400.450.500.550.60
Kaz
akhs
tan
Shan
ghai
-Chi
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ustr
alia
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ted
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gdom
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apor
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and
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land
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Fed
erat
ion
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Uni
ted
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esIre
land
Cos
ta R
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ong
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erm
any
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mar
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rab
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tes
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enia
Mex
ico
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ao-C
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Spai
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D a
vera
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onte
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oFi
nlan
dIn
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Hun
gary
Bel
gium
Switz
erla
ndJo
rdan
Can
ada
Esto
nia
Japa
nPo
land
Net
herla
nds
Chi
nese
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pei
Viet
Nam
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guay
Kor
eaPe
ruB
razi
lR
oman
iaSl
ovak
Rep
ublic
Bul
garia
Thai
land
Gre
ece
Cro
atia
Serb
iaTu
nisi
aPo
rtug
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zech
Rep
ublic
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arLu
xem
bour
gIta
lyA
rgen
tina
Fran
ceLi
echt
enst
ein
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
A better disciplinary climate is associated with greater mathematics familiarity
Liec
hten
stei
nFi
nlan
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nisi
aIn
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Kaz
akhs
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ong
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iaSw
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eder
atio
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ew Z
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Cos
ta R
ica
Viet
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Lith
uani
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zech
Rep
ublic
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ania
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ece
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nH
unga
ryIs
rael
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ceC
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ates
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garia
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se T
aipe
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oman
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apor
eB
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umQ
atar
Spai
nK
orea
Source: Figure 3.139
Fam
ilia
rity
wit
h m
athe
mat
ics
Greater
Less
Teachers report higher job satisfaction when fewer students have behavioural problems
None 1% to 10% 11% to 30% 31% or morePercentage of students with behavioural problems
40
Teac
her
job
sati
sfac
tion
More satisfied
Less satisfied
Source: Figure 3.2; OECD, Talis 2013 Database
Focus time and energy on creating a positive classroom climate
Invest time in building strong relationships with your students
41
What can teachers do?
QUESTION 7: DO STUDENTS’ BACKGROUNDS
INFLUENCE HOW THEY LEARN MATHEMATICS?
42
Disadvantaged students have less exposure to both applied math….
Portu
gal
Cost
a Ri
ca
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ech
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ong-
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ited
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es
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ab E
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e Cr
oatia
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ria
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ited
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ar
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ark
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land
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land
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Bottom quarter (disadvantaged students) Top quarter (advantaged students)
43Source: Figure 7.1a
Exp
osur
eto
appl
ied
mat
hem
atic
s
More exposure
Less exposure
… and deep mathematicsNe
w Z
eala
nd
Portu
gal
Braz
il
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ar
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nisi
a
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ralia
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m
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ark
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ited
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Em
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ech
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ther
land
s
Mal
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a
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da
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epub
lic
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ria
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a
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ania
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sta
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Th
aila
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ia
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ia
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age
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rael
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ance
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ru
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ico
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erm
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ited
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rway
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ates
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ssia
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Sp
ain
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echt
enst
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1Si
ngap
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M
acao
-Chi
na 1
Kore
a
Bottom quarter (disadvantaged students) Top quarter (advantaged students)
44Source: Figure 7.1a
Exp
osur
eto
pure
mat
hem
atic
s
More exposure
Less exposure
20
30
40
50
60
70
80
90
Thai
land
5A
rgen
tina
17
Indo
nesi
a
Chi
nese
Tai
pei
23
Chi
le
20
Kor
ea
22
Bul
garia
2
8B
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pan
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ak R
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lic
24
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ico
10
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2
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ong
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29
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M
onte
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ar
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unga
ry
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16
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ta R
ica
13
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ece
33
Col
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orw
ay
21
OEC
D a
vera
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17
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ch R
epub
lic
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ce
28
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Fed
erat
ion
19
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and
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Zea
land
1
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land
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um
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Sing
apor
e
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ethe
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rab
Emira
tes
19
Kaz
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17
Aus
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ustr
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erm
any
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Liec
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n
31Sw
itzer
land
U
nite
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ates
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5U
nite
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ingd
om
15
Den
mar
k
23Is
rael
1
0Vi
et N
am
14
Disadvantaged students Advantaged students
Disadvantaged students more likely to have negative view of their own capabilities in mathematics
%
45Source: Figure 7.3
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?
QUESTION 8: SHOULD I BE CONCERNED
ABOUT MY STUDENTS’ ATTITUDES TOWARDS
MATHEMATICS?
47
20
30
40
50
60
70
80
90
Net
herla
nds
-
13D
enm
ark
-
20Sw
eden
-13
Icel
and
-
10U
nite
d K
ingd
om
-1
7Sw
itzer
land
-17
Liec
hten
stei
n
-23
Finl
and
-
22G
erm
any
-
15Sh
angh
ai-C
hina
-20
Nor
way
-14
Esto
nia
-7K
azak
hsta
n
C
zech
Rep
ublic
-8
Aus
tria
-10
Luxe
mbo
urg
-
15La
tvia
-5
Uni
ted
Stat
es
-1
0Po
land
-7
Lith
uani
a
-8
Slov
ak R
epub
lic
-1
1R
ussi
an F
eder
atio
n
-5
Bel
gium
-14
OEC
D a
vera
ge
-1
2C
anad
a
-15
Aus
tral
ia
-1
5Si
ngap
ore
-4Sl
oven
ia
-
7H
unga
ry
-
9N
ew Z
eala
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-1
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rbia
Col
ombi
a
-8
Fran
ce
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onte
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C
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-9
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ey
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ain
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tes
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H
ong
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-15
Port
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nd
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ulga
ria
-
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-Chi
na
-1
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Tai
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9C
hile
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Cos
ta R
ica
-
11G
reec
e
-10
Peru
-6
Thai
land
-4
Italy
-7
Mal
aysi
a
U
rugu
ay
-
6In
done
sia
-5R
oman
ia
K
orea
-10
Mex
ico
-7Jo
rdan
Tuni
sia
-3A
rgen
tina
Boys All students Girls
Girls are more anxious about mathematics than boys
%
48Source: Figure 9.1
Algebraic word problems
Contextualised mathematics
problems
Procedural tasks Pure mathematics problems
49
More exposure to pure mathematics problems in tests than in lessons is associated with greater anxiety
Source: Figure 9.2
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
More anxiety
Algebraic word problems
Contextualised mathematics
problems
Procedural tasks Pure mathematics problems
50
Students frequently exposed to applied mathematics have better opinions about their own capabilities
Source: Figure 9.3
Higher self-
concept
Lower self-
concept
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?
QUESTION 9: SHOULD MY TEACHING
EMPHASISE CONCEPTS OR HOW THOSE CONCEPTS
ARE APPLIED?
52
R² = 0.05
Weak relationship between exposure to applied and pure mathematics
OE
CD
ave
rage
Source: Figure 8.1
OECD average
53Greater exposure to pure mathematics
Gre
ater
expo
sure
to a
ppli
ed
mat
hem
atic
s
-20-10
010203040506070
Kor
eaC
hine
se T
aipe
iN
ethe
rland
sSi
ngap
ore
New
Zea
land
Mal
aysi
aH
ong
Kon
g-C
hina
Bel
gium
Qat
arA
ustr
alia
Switz
erla
ndU
nite
d A
rab
Emira
tes
Ger
man
yJa
pan
Liec
hten
stei
nFr
ance
Peru
Lith
uani
aU
nite
d K
ingd
omIc
elan
dU
nite
d St
ates
Finl
and
Aus
tria
Italy
OEC
D a
vera
geSl
ovak
Rep
ublic
Nor
way
Thai
land
Rus
sian
Fed
erat
ion
Port
ugal
Turk
eyIs
rael
Latv
iaB
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unga
ryJo
rdan
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Bra
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Den
mar
kSh
angh
ai-C
hina
Alb
ania
Exposure to applied mathematics Exposure to pure mathematics
Frequent exposure to pure mathematics concepts is associated with better mathematics performance
Score-point difference
54Source: Figure 8.2
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
What can teachers do?
WHAT HAS PISA TAUGHT US?
56
Develop balanced
assessments
Focus on students’ abilities
and skills
Be fairCollaborate 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
Develop balanced
assessments
Focus on students’ abilities
and skills
Be fairCollaborate 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
Develop balanced
assessments
Focus on students’ abilities
and skills
Be fairCollaborate with others
Innovate, innovate, innovate
Be fairHow:• 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
Develop balanced
assessments
Focus on students’ abilities
and skills
Be fairCollaborate with others
Innovate, innovate, innovate
Collaborate with othersHow:• 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
Develop balanced
assessments
Focus on students’ abilities
and skills
Be fairCollaborate 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
62
62 Thank you
Findoutmoreaboutourworkatwww.oecd.org– Allpublications– Thecompletemicro-leveldatabase
Email:[email protected]:SchleicherOECD
andremember:Withoutdata,youarejustanotherpersonwithanopinion