key questions for mathematics teachers · 1. when i study for a mathematics test, i learn as much...

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



86%: Students learn best by findings solutions on their own



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


% 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


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


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


% 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


% 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


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


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


% 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


% 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


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


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

Rom

ania

Icel

and

Kaz

akhs

tan

Arg

entin

aJo

rdan

Thai

land

Uni

ted

Stat

esM

exic

oPe

ruC

zech

Rep

ublic

Mac

ao-C

hina

Uni

ted

Ara

b Em

irate

sQ

atar

Finl

and

Can

ada

Bra

zil

Bul

garia

Turk

eyTu

nisi

aPo

rtug

alU

rugu

ayM

onte

negr

oSe

rbia

Indo

nesi

aN

ethe

rland

sSp

ain

Gre

ece

Col

ombi

aSi

ngap

ore

Aus

tral

iaC

osta

Ric

aEs

toni

aSl

ovak

Rep

ublic

Irela

ndN

orw

ayR

ussi

an F

eder

atio

nO

ECD

ave

rage

New

Zea

land

Lith

uani

aC

roat

iaLu

xem

bour

gH

ong

Kon

g-C

hina

Fran

ceSw

eden

Hun

gary

Chi

leU

nite

d K

ingd

omK

orea

Aus

tria

Mal

aysi

aJa

pan

Ger

man

yLa

tvia

Den

mar

kSw

itzer

land

Chi

nese

Tai

pei

Pola

ndB

elgi

umSl

oven

iaIs

rael

Viet

Nam Ita

lySh

angh

ai-C

hina

Liec

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”


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


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

naA

ustr

alia

Uni

ted

Kin

gdom

Sing

apor

eC

olom

bia

Icel

and

New

Zea

land

Rus

sian

Fed

erat

ion

Isra

elM

alay

sia

Uni

ted

Stat

esIre

land

Cos

ta R

ica

Lith

uani

aH

ong

Kon

g-C

hina

Latv

iaTu

rkey

Swed

enG

erm

any

Den

mar

kN

orw

ayA

ustr

iaU

nite

d A

rab

Emira

tes

Slov

enia

Mex

ico

Mac

ao-C

hina

Spai

nC

hile

OEC

D a

vera

geM

onte

negr

oFi

nlan

dIn

done

sia

Hun

gary

Bel

gium

Switz

erla

ndJo

rdan

Can

ada

Esto

nia

Japa

nPo

land

Net

herla

nds

Chi

nese

Tai

pei

Viet

Nam

Uru

guay

Kor

eaPe

ruB

razi

lR

oman

iaSl

ovak

Rep

ublic

Bul

garia

Thai

land

Gre

ece

Cro

atia

Serb

iaTu

nisi

aPo

rtug

alC

zech

Rep

ublic

Qat

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

dTu

nisi

aIn

done

sia

Kaz

akhs

tan

Chi

lePo

land

Icel

and

Esto

nia

Mex

ico

Swed

enH

ong

Kon

g-C

hina

Mon

tene

gro

Uni

ted

Kin

gdom

Den

mar

kC

olom

bia

Mac

ao-C

hina

Latv

iaSw

itzer

land

Arg

entin

aR

ussi

an F

eder

atio

nN

ew Z

eala

ndB

razi

lTh

aila

ndSl

ovak

Rep

ublic

Uru

guay

Mal

aysi

aPo

rtug

alLu

xem

bour

gC

anad

aIre

land

Peru

Aus

tria

OEC

D a

vera

geSe

rbia

Aus

tral

iaG

erm

any

Italy

Cos

ta R

ica

Viet

Nam

Lith

uani

aN

ethe

rland

sC

zech

Rep

ublic

Alb

ania

Gre

ece

Japa

nH

unga

ryIs

rael

Fran

ceC

roat

iaJo

rdan

Uni

ted

Ara

b Em

irate

sU

nite

d St

ates

Bul

garia

Shan

ghai

-Chi

naC

hine

se T

aipe

iR

oman

iaTu

rkey

Slov

enia

Sing

apor

eB

elgi

umQ

atar

Spai

nK

orea


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


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

Urug

uay

1Ita

ly 1

Luxe

mbo

urg

Gre

ece

1Is

rael

1Ch

ines

e Ta

ipei

Ja

pan

Tuni

sia

New

Zea

land

Cz

ech

Repu

blic

1Be

lgiu

m

Cana

da

Viet

Nam

1Au

stra

lia

Colo

mbi

a Se

rbia

1Ho

ng K

ong-

Chin

a M

alay

sia

Arge

ntin

a Un

ited

Stat

es

Turk

ey 1

Liec

hten

stei

n M

acao

-Chi

na

Fran

ce

Unite

d Ar

ab E

mira

tes

Chile

Bu

lgar

ia

OEC

D av

erag

e Cr

oatia

1In

done

sia

Switz

erla

nd

Icel

and

Aust

ria

Peru

La

tvia

Un

ited

King

dom

Sl

oven

ia

Esto

nia

Qat

ar

Braz

il Ro

man

ia

Mon

tene

gro

1G

erm

any

Irela

nd

Jord

an

Norw

ay

Finl

and

Russ

ian

Fede

ratio

n Sw

eden

Sl

ovak

Rep

ublic

1M

exic

o Sh

angh

ai-C

hina

Ko

rea

Hung

ary

1Li

thua

nia

Spai

n 1

Neth

erla

nds

1Si

ngap

ore

Denm

ark

Thai

land

Po

land

Ka

zakh

stan

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

Qat

ar

Luxe

mbo

urg

Tu

nisi

a

Jord

an

Aust

ralia

Sw

eden

Be

lgiu

m

Denm

ark

Un

ited

Arab

Em

irate

s

Colo

mbi

a

Arge

ntin

a

Chin

ese

Taip

ei

Chile

Cz

ech

Repu

blic

Tu

rkey

Ne

ther

land

s

Mal

aysi

a

Cana

da

Slov

ak R

epub

lic

Aust

ria

Indo

nesi

a

Rom

ania

Co

sta

Rica

Th

aila

nd

Switz

erla

nd

Urug

uay

Bu

lgar

ia

Latv

ia

Mon

tene

gro

O

ECD

aver

age

Se

rbia

Is

rael

Fr

ance

G

reec

e

Finl

and

Pe

ru

Mex

ico

G

erm

any

Un

ited

King

dom

No

rway

Es

toni

a

Unite

d St

ates

Hu

ngar

y

Irela

nd

Pola

nd

Viet

Nam

Ja

pan

Sh

angh

ai-C

hina

1Ic

elan

d

Lith

uani

a

Italy

Cr

oatia

Ka

zakh

stan

Sl

oven

ia

Hong

Kon

g-Ch

ina

Ru

ssia

n Fe

dera

tion

Sp

ain

Li

echt

enst

ein

1Si

ngap

ore

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

razi

l

8Tu

nisi

a

26Ja

pan

6

Pola

nd

22

Slov

ak R

epub

lic

24

Mex

ico

10

Uru

guay

2

2Tu

rkey

1

4M

alay

sia

8

Rom

ania

1

8Jo

rdan

1

9H

ong

Kon

g-C

hina

1

1Es

toni

a

17Sp

ain

17

Peru

Po

rtug

al

29

Mac

ao-C

hina

M

onte

negr

o

16Se

rbia

2

1Ita

ly

13

Shan

ghai

-Chi

na

12

Qat

ar

14

Lith

uani

a

16H

unga

ry

22

Slov

enia

1

4C

roat

ia

16

Cos

ta R

ica

13

Gre

ece

33

Col

ombi

a

16N

orw

ay

21

OEC

D a

vera

ge

17

Cze

ch R

epub

lic

16

Fran

ce

28

Rus

sian

Fed

erat

ion

19

Finl

and

22

New

Zea

land

1

9La

tvia

1

6Ire

land

1

4B

elgi

um

11

Luxe

mbo

urg

12

Sing

apor

e

25N

ethe

rland

s

12U

nite

d A

rab

Emira

tes

19

Kaz

akhs

tan

17

Aus

tria

1

6A

ustr

alia

1

5C

anad

a

15Ic

elan

d

18Sw

eden

1

3G

erm

any

11

Liec

hten

stei

n

31Sw

itzer

land

U

nite

d St

ates

1

5U

nite

d K

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

%


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


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

nd

-1

5Se

rbia

Col

ombi

a

-8

Fran

ce

-1

8M

onte

negr

o

C

roat

ia

-

6Is

rael

-9

Turk

ey

A

lban

ia

Sp

ain

-

10U

nite

d A

rab

Emira

tes

Qat

ar

H

ong

Kon

g-C

hina

-15

Port

ugal

-5

Irela

nd

-1

2B

ulga

ria

-

8M

acao

-Chi

na

-1

7Ja

pan

-

14B

razi

l

Chi

nese

Tai

pei

-1

2Vi

et N

am

-

9C

hile

-4

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

%


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


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

ulga

riaH

unga

ryJo

rdan

Irela

ndC

anad

aSl

oven

iaLu

xem

bour

gTu

nisi

aC

roat

iaC

zech

Rep

ublic

Pola

ndVi

et N

amG

reec

eSp

ain

Chi

leM

onte

negr

oM

exic

oR

oman

iaU

rugu

aySw

eden

Kaz

akhs

tan

Serb

iaM

acao

-Chi

naA

rgen

tina

Esto

nia

Cos

ta R

ica

Col

ombi

aIn

done

sia

Bra

zil

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


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 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


and skills



Focus on students’ abilities and skills

How:• “What is important for citizens to

know and be able to do in situations that involve mathematics?” This kind of thinking could help you decide which topics to present to your students – and how to present them

• Reading some assessment questions released by PISA might give you additional ideas for your class



points

58

Develop balanced

assessments


and skills



Be fairHow:• Teach and assess students in

ways that are fair and inclusive for everyone



points

59

Develop balanced

assessments


and skills



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



points

60

Develop balanced

assessments


and skills




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



points

61

62

62 Thank you

Findoutmoreaboutourworkatwww.oecd.org– Allpublications– Thecompletemicro-leveldatabase

Email:[email protected]:SchleicherOECD

andremember:Withoutdata,youarejustanotherpersonwithanopinion

key questions for mathematics teachers · 1. when i study for a mathematics test, i learn as much...

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