teaching mathematics eff ti leffectively for the 21st century€¦ · mathematics curriculum...

APEC-Tsukuba International Conference IV

2010/2/20

1

Teaching Mathematics Eff ti lEffectively for the 21stCentury

Yeap Ban-Har, Ph.D.National Institute of Education

Nanyang Technological University Singapore

[email protected]

Catholic High School (Primary)

The MPK Lecture

Teaching Mathematics Effectively to

Engage Students for the 21st

Century


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introduction

Wellington Primary School

Task

• Move 3 sticks to make 2 squares.


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Task


Task



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Task


Task



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Task


• 88 children took part in a swimmingtiti 1/3 f th b d 3/7 f th

A Problem from Singapore Classroom

competition. 1/3 of the boys and 3/7 of thegirls wore swimming goggles. Altogether 34children wore swimming goggles.

How many girls wore swimming goggles onthat day?y

Fairfield Methodist Primary School

88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuanmemakai kacamata renang. Total ada 34 anak yang memakai kacamata renang.Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu?


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• 88 anak mengikuti perlombaan berenang. 1/3k l ki l ki d 3/7 k

A Problem from Singapore Classroom

anak laki-laki dan 3/7 anak perempuanmemakai kacamata renang.Total ada 34 anak yang memakai kacamatarenang.Berapa jumlah anak perempuan yangBerapa jumlah anak perempuan yangmemakai kacamata renang pada hari itu?

Fairfield Methodist Primary School


• 88 children took part in a swimming competition. 1/3 of the boys and 3/7of the girls wore swimming goggles Altogether 34 children woreof the girls wore swimming goggles. Altogether 34 children woreswimming goggles.

How many girls wore swimming goggles on that day?


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88


34 54

• 88 children took part in a swimming competition. 1/3 of the boys and 3/7of the girls wore swimming goggles. Altogether 34 children woreswimming goggles.

How many girls wore swimming goggles on that day?

34

54 – 34 = 2034 – 20 = 14

54


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3 x 7 = 21

21 girls wear goggles.

21 anak perempuan memakai kacamata renang

A Curriculum That Helps Average Students Reach High Achievement

21 anak perempuan memakai kacamata renangKurikulum yang membantu murid‐murid

dengan kemampuan

biasa / rata‐ratamencapai prestasi

yang tinggi.


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Mathematics Curriculum Framework

Monitoring of one’s own thinkingS lf l ti f l i

BeliefsInterest

Appreciation

Mathematical Problem Solving

Reasoning, communication & connectionsThinking skills &

Numerical calculationAlgebraic manipulation

Spatial visualizationData analysisMeasurement

Self‐regulation of learningppConfidencePerseverance

ConceptsNumericalAlgebraic

GeometricalStatistical

ProbabilisticAnalytical

heuristicsApplication & modelling

Use of mathematical toolsEstimation

1995

2003

2007Grade 4

TIMSSTrends in International Maths and Science Studies

Advanced

Intermediate

High

38 4138

70 7473

89 9291

Low 96 9897



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Swed

en

Med

ian

U S A

Grade 4


Japa

n

ingapo

re

Advanced

Intermediate

High

S

3 105

24 4026

69 7767

S

4123

7461

9289

Low 93 9590

Elementary School in Japan

9898

Average

ong Ko

ng

ingapo

re

Grade 8


Korea

Taiwan

Advanced

Intermediate

High

A Ho S

2 4031

15 7064

46 8885

4540

7171

8690

Low 75 9794

Telok Kurau Primary School

9598


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Average

ndon

esia

Thailand

Grade 8


Malaysia

ingapo

re

Advanced

Intermediate

High

A In T

2 30

15 124

46 4414

M S

402

7018

8850

Low 75 6648

Effective Methods in Teaching Mathematics

9782

mathematicsteaching

effective

Bina Bangsa School, Indonesia


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Primary Mathematics 1A

Pedagogical Principle:Bruner

Prinsip Pedagogi: Bruner

Number Bonds

PCF Kindergarten Telok BlangahPCF Kindergarten Telok Blangah


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Number Bonds

PCF Kindergarten Telok Blangah

Bruner

The concrete

DivisionPembagian

pictorial abstract approach is used to help the majority of learners to develop strong foundation in mathematics.

National Institute of Education

Pendekatan kongkret gambar abstrak, dipergunakan untuk menolong sebagian besar pelajar untuk membangun dasar matematika yang kuat.


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My Pals Are Here! Mathematics 1B

DivisionPembagian

Photo: Princess Elizabeth Primary School

DivisionPembagian


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My Pals Are Here! Mathematics 1B

DivisionPembagian

summary

Elementary School in Chile


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Skemp

Understanding in mathematics

• relational(conceptual)

• instrumental (procedural)

• conventional Pedagogical i i l

Teaching for conceptual understanding is given emphasis in Singapore Math.

Principle:SkempPrinsip

Pedagogi: Skemp

Primary Mathematics Standards Edition Grade 6

Skemp

Pedagogical i i l

Matematika Singapura menitik‐beratkan pengajaran pada pemahaman konsep.

Principle:SkempPrinsip

Pedagogi: Skemp



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Fraction DivisionPembagian Pecahan


3 kue dibagi secara rata kepada beberapa anak. Setiap anak mendapatkan ¾bagian kue. Berapa anak yang mendapatkan ¾ bagian kue?


Jika Anda memotong 1 bagian penuh menjadi ¾ bagian, Anda mendapatkan 1 dan 1/3 tiga seperempat. Jadi, di dalam 3 bagian penuh ada 3 x 1 1/3 atau 3 x 4/3.


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summary

Scarsdale Middle School New York

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 b fl l h h h h l Thi k f hbutterfly 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


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Dienes

Dienes encouraged the use ofvariation in mathematics education –perceptual variation andmathematical variation.

Dienes menganjurkan penggunaan

Pedagogical

Dienes menganjurkan penggunaanvariasi dalam pengajaranmatematika - variasi persepsi danvariasi matematika.

Primary Mathematics Standards Edition

Principle:Dienes

Prinsip Pedagogi: Dienes

Pedagogical Principle:Dienes



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Pedagogical Principle:DienesDienes


Jane berlatih piano selama ¾ jam per hari. Berapa menit dia berlatih setiap harinya?

1 jam = 60 menit

60 ÷ 4 = 15

15 x 3 = 45

¾ x 60 = 45


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Mathematical Variation

Variasi dari segi Matematika

Di sebuah kelas, 2/5 muridnya memakai kacamata.a) Berapa bagiankah murid yang tidak memakai kacamata?b) Jika 16 murid memakai kacamata, berapa jumlah murid seluruhnya?

16

Di sebuah kelas, 2/5 muridnya memakai kacamata.a) Berapa bagiankah murid yang tidak memakai kacamata?b) Jika 16 murid memakai kacamata, berapa jumlah murid seluruhnya?

Nicole membeli 30 butir telur. Dia memakai 2/3 telur yang dibeli untuk memanggang kue.Berapa telur yang tersisa?

16

Berapa telur yang tersisa?

30


Variasi dari segi Matematika


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effectiveteaching

Keys Grade School , Manila

Pictorial Before Abstract

Gambar sebelum abstrak


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Perceptual Variation

Primary Mathematics Standards Edition

Variasi dari segi persepsi


Variasi dari segi matematika


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Penekanan pada pemaparan visualdan variasi sistematis

memperkuat pemahaman konsep

Emphasis on pictorial

representation and systematic

p p p

yvariation to enhance

conceptual understanding

Grade

4

Singapore


rade

8

Advanced

Intermediate

High

G

41

74

92

G

40

70

88

Low 98


97


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Grade

4

U S A


rade

8Advanced

Intermediate

High

G

10

40

77

G6

31

67

Low 95


92

Grade

4

England


rade

8

Advanced

Intermediate

High

G

16

48

79

G

8

35

69

Low 94


90


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Grade

4

International


rade

8Advanced

Intermediate

High

G

5

26

67

G2

15

46

Low 90


75

conclusion

PCF Kindergarten Pasir Ris


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Fuchun Primary School

Mathematics is anMathematics is an excellent vehicle for the development and improvement of a person’s intellectual

competence ..

Ministry of Education 2006

Matematika adalah kendaraan / alat yang hebatuntuk membangun dan memperbaiki kompetensi

dan intelektual seseorang …

Bina Bangsa School Bandung

Patterns


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Patterns

Bina Bangsa School Bandung

SD Negeri in PalembangVisualization


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Teacher Training for LEAP Programme for Public School Teachers in ManilaVisualization

mathz4kidz Learning Centre in MalaysiaCommunication


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Pathlight School

Communication

Primary Mathematics Syllabus 2007

Primary 2 Wellington Primary School


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Balestier HillPrimary School

Fuchun Primary School

Primary Mathematics Syllabus 2007

Princess Elizabeth Primary School


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“Children are truly the future of our nation. “

Irving Harris

teaching mathematics eff ti leffectively for the 21st century€¦ · mathematics curriculum...

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