Developing Critical Thinking Through Singapore Math

Keys Grade School, Manila, The Philippines
raising
critical thinkers
through
singapore math
May 2010
Dr Yeap Ban Har
National Institute of Education
Nanyang Technological University
Singapore
Slides are available for download.

TanjongPagar PCF Kindergarten Singapore
international
perspectives
mathematics
on
teaching

What counts as mathematical proficiency?

procedural fluency
conceptual reasoning

strategic competence
K E Y S
1 2 3 4
5 6 7 8
9 10 11 12
3948 ?

17
7
10
17 – 3
adaptive reasoning

productive disposition

What counts as mathematical proficiency?

mathz4kidz Learning Centre, Penang, Malaysia
Trends in
Mathematics
This whole shape stands for 1.
& Science Studies
What does this stand for?
apply
their understanding
and knowledge
in a variety of
complex situations

Trends in
Mathematics
& ScienceStudy
explain
their reasoning

Math for Developing Intellectual Competence

Mathematics as a vehicle to develop and improve a person’s intellectual competence.
Princess Elizabeth Primary School, Singapore

mathematics
education
“
an excellent vehicle for the development and improvement of a person’s intellectual competence
”
Bina Bangsa School, Bandung, Indonesia
Ministry of Education Singapore 2006

mathematics
using to develop
children’s
intelligence

4
7
47
11
Edgewood Elementary School, New York, USA
47 – 11

Edgewood Elementary School, New York

Edgewood Elementary School, New York, USA

What is Singapore Math?
Challenging Materials

Meiling and Raja started on a 36-km cycling trip at the same time. They cycled at the same speed for the first 12 km. For the remaining 24 km, Meiling cycled at a faster speed. She arrived at the finishing point 10 minutes before Raja who was 4 km behind her. Raja did not change his speed throughout the trip and he completed the trip at 11 10.
(a) At what time did the trip start?
(b) What was Meiling’s average speed for the remaining 24 km of the trip in m/min?
(PSLE Grade 6)
Meiling’s average speed was 480 m/min for the last part of the trip.
Meiling
Raja
Raja: 10 min  4 km
Raja: First 12 km  30 min
Raja: Last 24 km  60 min
??? min  36 km
Meiling: Last 24 km  50 min
Meiling: 24000 m  50 min
11 10 hrs 10 10 hrs  09 40 hrs
Raja, and hence Meiling, started the trip at 09 40.

The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?
(TeckWhye Primary School, Grade 6)
Album A
Album B
Album C

The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?
(TeckWhye Primary School, Grade 6)
7 units  ?
7 units  36 x 7 = 210 + 42 = 252
There were 252 more stamps in Album C than Album A in the end.
Album A
Album B
Album C
468
13 units  444 + 24 = 468
1 unit  468 ÷ 13 = 36
390
78

High Student Achievement

TIMSS
Trends in International Maths and Science Studies
1995
2003
2007
Grade 4
Advanced
38
41
38
High
70
74
73
Intermediate
89
92
91
Low
96
98
97
Catholic High School (Primary), Singapore

TIMSS
Sweden
Median
U S A
Japan
Singapore
Grade 4
Advanced
3
10
5
41
23
High
24
40
26
74
61
Intermediate
69
77
67
92
89
Low
93
95
90
98
98
Elementary School in Japan

TIMSS
Average
Hong Kong
Singapore
Korea
Taiwan
Grade 8
Advanced
2
40
31
45
40
High
15
70
64
71
71
Intermediate
46
88
85
86
90
Low
75
97
94
95
98
TelokKurau Primary School

TIMSS 2007
AVERAGE
MALAYSIA
SINGAPORE
Grade 8
Advanced
2
40
2
High
15
70
18
Intermediate
46
88
50
Low
75
97
82
Northlight School, Singapore

TIMSS
Grade 4
Grade 8
Singapore
Advanced
41
40
High
74
70
Intermediate
92
88
Low
98
97
Catholic High School (Primary)

TIMSS
Grade 4
Grade 8
U S A
Advanced
10
6
High
40
31
Intermediate
77
67
Low
95
92

TIMSS
Grade 4
Grade 8
England
Advanced
16
8
High
48
35
Intermediate
79
69
Low
94
90

TIMSS
Grade 4
Grade 8
International
Advanced
5
2
High
26
15
Intermediate
67
46
Low
90
75

Using Mathematics to Develop Intelligent Behaviors

what are
intelligent
behaviors?

1000
- 124
mathematics
& intelligent
behaviors

9
9
1
1000
999
- 124
- 124
875
for
1000
looking connections
- 124
876
BinaBangsa School, Bandung, Indonesia

to
ability explain
A Grade 6 US textbook written using the Singapore Pedagogy

mathematics
& intelligent
behaviours

3
4
÷
3
=
3
x
4
3
4
=

How to make sure the butterfly cannot flyHow do you get a butterfly?First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.If the butterfly is not left to struggle to come out of the cocoon, it will never fly.We can learn an important lesson from the butterfly.If we do not have struggles and challenges in our work, we will never grow strong and capable. If life has no difficulties, we will become weak and helpless.Lim Siong GuanHead, Civil Service

11 cm
4 cm
5 cm
5 cm
to use
5 cm
ability knowledge
Area = (11 + 5) ÷ 2 x 4

Key Success Factors

Some of us come from English-speaking homes. Some of us don’t. I speak Malay at home.
This is what help me learn mathematics well.…
Princess Elizabeth Primary School, Singapore
Factors That Contribute to High Achievement Level in Mathematics

We like our teacher.
Once, she was absent for two days. We missed her. She told she had to learn new things to teach us better.
teacher
quality
North Vista Primary School, Singapore
National Institute of Education, Singapore

x

Keys Grade School. Manila, The Philippines
professional development
in-service
HougangPrimary School, Singapore

parental
expectations
Last Saturday, Mum and Dad went to school – to learn the model method so they can help me with schoolwork. But Mum said she did not get it.
In the end I had to teach her.
Seminar for Parents on Problem Solving

Teaching Every Child

singapore
math
Bruner’s
theory
We use concrete materials to learn mathematics.
Photos: Princess Elizabeth Primary School, Singapore

singapore
math
emphasis on
concrete to
pictorial to abstract
representations
Catholic High School (Primary) Singapore

singapore
math
especially on
the model method
mathz4kidz Learning Center, Malaysia

A lion weighs 135 kg. A cow weigh 87 kg more than the lion. An elephant weighs 139 more than the cow. How heavy is the elephant? (Primary 2)
TelokKurau Primary School, Singapore

bruner’s theory
concrete

concrete
experiences

from
concrete
to
pictorial

from
pictorial
to
abstract
All Kids Are Intelligent Series

symbols

using
concrete
materials
Ateneo Grade School, Manila, The Philippines
A Public School in Chile

Fuchun Primary School, Singapore
interaction
Vygotsky’s Theory
Children Learn in Social Situations

skemp’s
theory
conceptual
understanding
BinaBangsa School, Semarang, Indonesia

singapore
math
banhar.yeap@nie.edu.sg
yeapbanhar@gmail.com
www.askyeapbanhar.blogspot.com
www.math.nie.edu.sg/T3
www.mathz4kidz.com
thank you

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Developing Critical Thinking Through Singapore Math

by Jimmy Keng on May 20, 2010

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