raising critical thinkers through singapore math keys grade school manila january 2010

raisingcritical thinkersthrough

singapore mathDr Yeap Ban Har

National Institute of EducationNanyang Technological University

Singapore

internationalperspectives

on mathematicsteaching

Tanjong Pagar PCF Kindergarten Singapore

What counts as mathematical proficiency?

procedural fluency

conceptual reasoningKeys Grade School, Manila, The Philippines

strategic competence

K E Y S1 2 3 45 6 7 89 10 11 12

3948 ?Keys Grade School, Manila, The Philippines

adaptive reasoning

17

710

17 – 3

Keys Grade School, Manila, The Philippines

productive disposition

Keys Grade School, Manila, The Philippines

What counts as mathematical proficiency?

their understandingin a variety of

complex situations

mathz4kidz Learning Centre, Penang, Malaysia

This whole shape

stands for 1.

Trends inMathematics& Science Studies

applyand knowledge

What does this stand

for?

Trends inMathematics& Science Study

explaintheir reasoningmathz4kidz Learning Centre, Penang, Malaysia

What is Singapore Math?

“an excellent vehicle to develop and improve a person’s intellectual competence”

Princess Elizabeth Primary School, Singapore

education

Bina Bangsa School, Bandung, Indonesia

mathematics

Ministry of Education Singapore 2006

an excellent vehicle for the development and improvement of

a person’s intellectual competence

“

”

using to develop

mathematicschildren’s

intelligence

4 7

47

11

47 – 11 Edgewood Elementary School, New York, USA

Edge

woo

d El

emen

tary

Sch

ool,

New

Yor

k

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)

MeilingRaja

Raja: 1o min 4 km

Raja: 1o min 4 km

??? min 36 km

Raja: 90 min 36 km

11 10 hrs 10 10 hours 09 40 hrsRaja, and hence Meiling, started the trip at 09 40.

Raja: First 12 km 30 min Raja: Last 24 km 60 min

Meiling: Last 24 km 50 min

Meiling: 24000 m 50 min

Meiling: 2400 m 5 minMeiling: 480 m 1 min

Meiling’s average speed was 480 m/min for the last part of the trip.

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?

(Teck Whye 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?

(Teck Whye Primary School, Grade 6)

Album A

Album B

Album C

13 units 444 + 24 = 4681 unit 468 ÷ 13 = 36

468

390 78

7 units ?7 units 36 x 7 = 210 + 42 = 252There were 252 more stamps in Album C than Album A in the end.

What is Singapore Math?Challenging Materials for Every Child

Advanced

Intermediate

Low

High

1995

2003

2007

38 4138

70 7473

89 9291

96 9897

Grade 4

Catholic High School (Primary)

TIMSSTrends in International Maths and Science Studies

Advanced

Intermediate

Low

High

Swed

en

Med

ian

U S

A

3 105

24 4026

69 7767

93 9590

Grade 4

Elementary School in Japan

TIMSSTrends in International Maths and Science Studies

Japa

n

Sing

apor

e

4123

7461

9289

9898

Advanced

Intermediate

Low

High

Aver

age

Hon

g Ko

ng

Sing

apor

e

2 4031

15 7064

46 8885

75 9794

Grade 8

Telok Kurau Primary School

TIMSSTrends in International Maths and Science Studies

Kore

a

Taiw

an

4540

7171

8690

9598

Northlight School, Singapore

Advanced

Intermediate

Low

High

AVER

AGE

MAL

AYSI

A

SIN

GAP

ORE

TIMSS 2007

2 402

15 7018

46 8850

75 9782

Grade 8

Advanced

Intermediate

Low

High

Gra

de 4

41

74

92

98

Singapore

Catholic High School (Primary)

TIMSSTrends in International Maths and Science Studies

Gra

de 8

40

70

88

97

Advanced

Intermediate

Low

High

Gra

de 4

10

40

77

95

U S A

Catholic High School (Primary)

TIMSSTrends in International Maths and Science Studies

Gra

de 8

6

31

67

92

Advanced

Intermediate

Low

High

Gra

de 4

16

48

79

94

England

Catholic High School (Primary)

TIMSSTrends in International Maths and Science Studies

Gra

de 8

8

35

69

90

Advanced

Intermediate

Low

High

Gra

de 4

5

26

67

90

International

Catholic High School (Primary)

TIMSSTrends in International Maths and Science Studies

Gra

de 8

2

15

46

75

Using Mathematics to Develop Intelligent Behaviors

intelligent

what arebehaviors?

1000- 124

mathematics& intelligent

behaviors

1000- 124

199

1000- 124

999- 124 875

876

forlooking

connections

Bina Bangsa School, Bandung, Indonesia

ability

explainto

A Grade 6 US textbook written using the Singapore Pedagogy

mathematics& intelligent

behaviours

34

÷3 = 3 x 43

= 4

How to make sure the butterfly cannot fly

How 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 Guan Head, Civil Service

5 cm

5 cm5 cm

11 cm

4 cm

Area = (11 + 5) ÷ 2 x 4

ability knowledge

to use

Teaching Every Child

Princess Elizabeth Primary School, Singapore

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.…

Factors That Contribute to High Achievement Level in Mathematics

These are my friends in Primary 1.

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.

Princess Elizabeth Primary School, Singapore

teacherquality

National Institute of Education, Singapore

Keys Grade School, Manila, The Philippines

x

singaporemath

professional developmentin-service

Photo: Keys Grade School. Manila, The Philippines

Photo: Hougang Primary School, Singapore

singaporemath

parentalexpectations

Photos: Seminar for Parents on Problem Solving

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.

singaporemath

Bruner’stheory

Photos: Princess Elizabeth Primary School, Singapore

We use concrete materials to learn mathematics.

Photos: Keys Grade School, Manila, The Philippines

singaporemath

emphasis onconcrete topictorial to abstract

representations

Photo: Catholic High School (Primary) Singapore

singaporemath

especially onthe model method

Photo: mathz4kidz Learning Center, Malaysia

Photo: Telok Kurau Primary School, Singapore

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)

bruner’s theoryconcrete

mathz4kidz Learning Centre, Penang, Malaysia

concreteexperiences

mathz4kidz Learning Centre, Penang, Malaysia

pictorialconcreteto

from

mathz4kidz Learning Centre, Penang, Malaysia

abstractpictorialto

from

All Kids Are Intelligent Series

symbols

mathz4kidz Learning Centre, Penang, Malaysia

concrete

A Public School in Chile

usingmaterials

Ateneo Grade School, Manila, The Philippines

Vygotsky’s Theory

Children Learn in Social

Situations

Fuch

un P

rimar

y Sc

hool

, Sin

gapo

re

interaction

conceptual

Bina Bangsa School, Semarang, Indonesia

skemp’s

understandingtheory

Keys Grade School, Manila, The Philippines

Keys Grade School, Manila, The Philippines

variationtheoryof

diene’s

A Singapore Textbook for Kindergarten

variationtheoryof

diene’s

variationtheoryof

diene’s

big ideas

Princess Elizabeth Primary School, Singapore

mathematical

number sensevisualization

connections

Princess Elizabeth Primary School, Singapore

Princess Elizabeth Primary School, Singapore

singaporemath

thank you

banhar.yeap@nie.edu.sg

www.askyeapbanhar.blogspot.com

www.math.nie.edu.sg