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KEY QUESTIONS FOR MATHEMATICS TEACHERS
AND HOW PISA CAN ANSWER THEM
Andreas SchleicherOctober 7, 2016
22PISA mathematics performance by decile of social background
Mex
ico
Gre
ece
Swed
en
Isra
el
Uni
ted
Stat
es
Den
mar
k
Aus
tral
ia
Uni
ted
Kin
gdom
Can
ada
Aus
tria
Liec
hten
stei
n
Esto
nia
Slov
enia
New
Zea
land
Net
herl
ands
Swit
zerl
and
Bel
gium
Mac
ao-C
hina
Kor
ea
Chi
nese
Tai
pei300
350
400
450
500
550
600
650
Source: PISA 2012
3 Exposure to deep math learning and social background
United States Shanghai-China-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30Bottom quarter (disadvantaged students) Second quarterThird quarter Top quarter (advantaged students)
Inde
x of
exp
osur
e to
pur
e m
athe
mat
ics
Source: Figure 2.5b
4
QUESTION 1: HOW MUCH SHOULD I
DIRECT STUDENT LEARNING IN MY
MATHEMATICS CLASSES?
What knowledge, skills
and character qualities do successful teachers require?
96% of teachers: My role as a teacher is to facilitate students
own inquiry
What knowledge, skills
and character qualities do successful teachers require?
86%: Students learn best by findings solutions on their
own
What knowledge, skills
and character qualities do successful teachers require?
74%: Thinking and reasoning is more important than curriculum content
Prevalence of memorisation
rehearsal, routine exercises, drill and practice and/or repetition
-1.60 -1.40 -1.20 -1.00 -0.80 -0.60 -0.40 -0.20 0.00Switzerland
PolandGermany
JapanKorea
FranceSweden
Shanghai-ChinaCanada
SingaporeUnited States
NorwaySpain
NetherlandsUnited Kingdom
0.000.200.400.600.801.001.201.401.601.802.00
Prevalence of elaborationreasoning, deep learning, intrinsic motivation, critical thinking, creativity, non-routine problems
High Low Low High
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 previ-
ous lesson
0 10 20 30 40 50 60 70 80 90
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
%
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 com-
plete
0 10 20 30 40 50 60 70 80 90
10
… than student-oriented strategiesOECD 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
Source: Figure 1.2
R² = 0.102181859010917
More teacher-
directed in-structionTeaching
More memorisa-
tion
Lear
ning
OECD average
More elaboration
More student-ori-
ented instruc-tion
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
Australia
New ZealandUrugua
yIsrael
Memorisation most frequently used
compared to elaboration strategies
Teacher-directed instruction most frequently used
compared to student-oriented instruction
United States
12
300 400 500 600 700 8000.80
1.00
1.20
R² = 0.240573379865677
Teacher-directed strategies are related with higher solution rates (OECD average)
Source: Figure 1.4Difficulty on the PISA scale
Greater success
Less success
Easy problem
Difficult problem
Odds ratio
Below Level 1
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6Index of student-oriented instructionIndex of teacher-directed instructionIndex 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
What can teachers do?
15
QUESTION 2: WHAT DO WE KNOW ABOUT
MEMORISATION AND LEARNING MATHEMATICS?
16
Students’ use of memorisation strategies
Source: Figure 4.1
Below the OECD average At the same level as the OECD averageAbove the OECD average
% of students who report
they learn by heart
Mem
oris
atio
n
More
Less
18
Memorisation is less useful as problems become more difficult (OECD average)
300 400 500 600 700 8000.70
1.00
R² = 0.811771493557881
Difficulty of mathematics item on the PISA scale
Memorisation is associated
with a lower chance of success
as problems become more
difficult
Source: Figure 4.3
Difficult problem
Easy problem
Greater success
Less success
Odds ratio
20
Encourage students to complement memorisation with other learning strategies
Use memorisation strategies to build familiarity and confidence
Notice how your students learn
What can teachers do?
21
QUESTION 3: CAN I HELP MY STUDENTS
LEARN HOW TO LEARN MATHEMATICS?
22
There are large international differences in the use of control strategies
Source: Figure 5.1
Tunis
ia
46
Thail
and
19
Urugua
y 5
5
United
Arab Emira
tes
55
Indon
esia
39
Czech
Repub
lic
35
Chines
e Taip
ei
42
Turke
y 5
9
Roman
ia
48
Sloven
ia
32
Irelan
d 4
9
Italy
44
Lithu
ania
56
Korea
40
Norway
48
Latvi
a 4
6
Portug
al
44
Malays
ia
50
Serbia
40
Luxe
mbourg
55
Bulgari
a 6
2
New Ze
aland
46
Belgium
53
Poland
65
Israe
l 6
1
Costa
Rica
48
Liech
tenste
in
42
Mexico
54
Denmark
48
German
y 5
0
Switzerl
and
55
Japa
n 5
9
Icelan
d 5
9
Below the OECD average At the same level as the OECD averageAbove the OECD average
% of students who try to work
out what the most important parts to learn
are
Con
trol
More
Less
Control strategies are always helpful but less so as problems become more difficult (OECD average)
300 400 500 600 700 8000.95
1.20
R² = 0.309815623974217
Difficulty of mathematics item on the PISA scale
Using control strategies is associated with a lower chance of success as problems become more difficult
Source: Figure 5.224
Difficult problem
Greater success
Less success
Easy problem
Odds ratio
25
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
What can teachers do?
26
QUESTION 4: SHOULD I ENCOURAGE MY STUDENTS TO USE THEIR
CREATIVITY IN MATHEMATICS?
27
Students’ use of elaboration strategies
Source: Figure 6.1
Below the OECD average At the same level as the OECD averageAbove the OECD average
% of students who understand new
concepts by relating them to
things they already know
Elab
orat
ion
More
Less
29
Elaboration strategies are more useful as problems become more difficult (OECD average)
300 400 500 600 700 8000.80
1.50
R² = 0.820032961220149
Difficulty of mathematics item on the PISA scale
Using elaboration
strategies is
associated with a
greater chance of
success as problems
become more
difficult
Source: Figure 6.2
Difficult problem
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
Difficult item Easy 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 6.330
More successLess success
31
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
What can teachers do?
32
QUESTION 5: ARE SOME MATHEMATICS
TEACHING METHODS MORE EFFECTIVE THAN OTHERS?
33
Students perform better when teachers use cognitive-activation instruction more often
Alb
ania
Icel
and
Arg
entin
a
Thai
land
Mex
ico
Cze
ch R
epub
lic
Uni
ted
Ara
b Em
irate
s
Finl
and
Bra
zil
Turk
ey
Port
ugal
Mon
tene
gro
Indo
nesi
a
Spai
n
Col
ombi
a
Aus
tral
ia
Esto
nia
Irela
nd
Rus
sian
Fed
erat
ion
New
Zea
land
Cro
atia
Hon
g K
ong-
Chi
na
Swed
en
Chi
le
Kor
ea
Mal
aysi
a
Ger
man
y
Den
mar
k
Chi
nese
Tai
pei
Bel
gium
Isra
el
Italy
Liec
hten
stei
n
-20
-10
0
10
20
30
40After 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
Lower scores
Higher
scores
Cognitive-activation strategies are related to performance, particularly for advantaged students
-15
-10
-5
0
5
10
15
20Disadvantaged students Advantaged studentsScore-point difference
The teacher …
35
Lower scores
Higher
scores
Source: OECD, PISA 2012 Database
36
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
What can teachers do?
37
QUESTION 6: AS A MATHEMATICS
TEACHER, HOW IMPORTANT IS THE
RELATIONSHIP I HAVE WITH MY STUDENTS?
38
Better teacher-students relations are associated with greater students’ sense of belonging to school
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
0.200.250.300.350.400.450.500.550.60
After accounting for differences in mathematics performance
Source: Table III.5.19; OECD, PISA 2012 Database
Mean index difference
Change in the index of sense of belonging that is associated with a one-unit increase in the index of teacher-student relations
39
A better disciplinary climate is associated with greater mathematics familiarity
Source: Figure 3.1
Fam
iliar
ity
wit
h m
athe
mat
ics
Greater
Less
40
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
Having fewer students with behavioural problems
is associated with greater job satisfaction among teachers
Teac
her
job
sati
sfac
tion
More satisfied
Less satisfied
Source: Figure 3.2; OECD, Talis 2013 Database
41
Focus time and energy on creating a positive classroom climate
Invest time in building strong relationships with your students
What can teachers do?
42
QUESTION 7: DO STUDENTS’ BACKGROUNDS
INFLUENCE HOW THEY LEARN MATHEMATICS?
43
Disadvantaged students have less exposure to both applied math….
Port
ugal
Co
sta
Rica
U
rugu
ay 1
Italy
1Lu
xem
bour
g G
reec
e 1
Isra
el 1
Chin
ese
Taip
ei
Japa
n Tu
nisi
a N
ew Z
eala
nd
Cze
ch R
epub
lic 1
Bel
gium
C
anad
a Vi
et N
am 1
Aus
tral
ia
Col
ombi
a Se
rbia
1H
ong
Kon
g-C
hina
M
alay
sia
Arge
ntin
a U
nite
d St
ates
Tu
rkey
1Li
echt
enst
ein
Mac
ao-C
hina
Fr
ance
U
nite
d Ar
ab E
mira
tes
Chi
le
Bul
garia
O
ECD
aver
age
Cro
atia
1In
done
sia
Switz
erla
nd
Icel
and
Aus
tria
Pe
ru
Latv
ia
Unite
d K
ingd
om
Slov
enia
Es
toni
a Q
atar
Br
azil
Rom
ania
M
onte
negr
o 1
Ger
man
y Ire
land
Jo
rdan
N
orw
ay
Finl
and
Rus
sian
Fed
erat
ion
Swed
en
Slov
ak R
epub
lic 1
Mex
ico
Shan
ghai
-Chi
na
Kor
ea
Hun
gary
1Li
thua
nia
Spai
n 1
Net
herla
nds
1Si
ngap
ore
Den
mar
k Th
aila
nd
Pola
nd
Kaz
akhs
tan
Bottom quarter (disadvantaged students) Top quarter (advantaged students)
Source: Figure 7.1a
Expo
sure
to
appl
ied
mat
hem
atic
s
More exposur
e
Less exposure
44
… and deep mathematicsN
ew Z
eala
nd
Port
ugal
Br
azil
Q
atar
Lu
xem
bour
g
Tuni
sia
Jo
rdan
Au
stra
lia
Swed
en
Bel
gium
De
nmar
k
Uni
ted
Ara
b Em
irate
s
Col
ombi
a
Arge
ntin
a
Chin
ese
Taip
ei
Chi
le
Cze
ch R
epub
lic
Turk
ey
Net
herla
nds
M
alay
sia
C
anad
a
Slov
ak R
epub
lic
Aus
tria
In
done
sia
Ro
man
ia
Cos
ta R
ica
Th
aila
nd
Switz
erla
nd
Urug
uay
B
ulga
ria
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
U
nite
d Ki
ngdo
m
Nor
way
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
C
roat
ia
Kaz
akhs
tan
Sl
oven
ia
Hong
Kon
g-Ch
ina
R
ussi
an F
eder
atio
n
Spai
n
Liec
hten
stei
n 1
Sing
apor
e
Mac
ao-C
hina
1K
orea
Bottom quarter (disadvantaged students) Top quarter (advantaged students)
Source: Figure 7.1a
Expo
sure
to
pure
m
athe
mat
ics
More exposur
e
Less exposure
46
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
What can teachers do?
47
QUESTION 8: SHOULD I BE CONCERNED
ABOUT MY STUDENTS’ ATTITUDES TOWARDS
MATHEMATICS?
48
Net
herla
nds
-
13
Swed
en
-1
3
Uni
ted
Kin
gdom
.
..
Liec
hten
stei
n
-23
Ger
man
y
-15
Nor
way
-14
Kaz
akhs
tan
Aus
tria
-10
Latv
ia
-5
Pola
nd
-
7
Slov
ak R
epub
lic
...
Bel
gium
-14
Can
ada
-
15
Sing
apor
e
-4
Hun
gary
-9
Serb
ia
Fran
ce
-1
8
Cro
atia
-6
Turk
ey
Spai
n
-10
Qat
ar
Port
ugal
-5
Bul
garia
-8
Japa
n
-14
Chi
nese
Tai
pei
-1
2
Chi
le
-
4
Gre
ece
-
10
Thai
land
-4
Mal
aysi
a
Indo
nesi
a
-5
Kor
ea
-1
0
Jord
an
Arg
entin
a
20
30
40
50
60
70
80
90 Boys All students Girls
Girls are more anxious about mathematics than boys
%
Source: Figure 9.1
51
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
What can teachers do?
56
WHAT HAS PISA TAUGHT US?
57
Develop balanced assessme
nts
Focus on students’ abilities
and skills
Be fairCollabora
te with others
Innovate, innovate, innovate
Develop balanced assesmentsHow: • 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
58
Develop balanced assessme
nts
Focus on students’ abilities
and skills
Be fairCollabora
te 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
59
Develop balanced assessme
nts
Focus on students’ abilities
and skills
Be fairCollabora
te 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
60
Develop balanced assessme
nts
Focus on students’ abilities
and skills
Be fairCollabora
te 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
61
Develop balanced assessme
nts
Focus on students’ abilities
and skills
Be fairCollabora
te with others
Innovate, innovate, innovate
Innovate, innovate, innovateHow: • 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
62
62 Thank you
Find out more about our work at www.oecd.org– All publications– The complete micro-level database
Email: [email protected]: SchleicherOECD
and remember:Without data, you are just another person with an opinion
