teaching mathematics effectively for the 21 st century

Teaching Mathematics Effectively for the 21st Century

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

Nanyang Technological University Singapore

[email protected]

The MPK Lecture

Teaching Mathematics Effectively to

Engage Students for the 21st

Century

Catholic High School (Primary)

introduction

Wellington Primary School

Task

• Move 3 sticks to make 2 squares.

Task

• Move 3 sticks to make 3 squares.

• 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day?

A Problem from Singapore Classroom

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?

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

A Problem from Singapore Classroom

Fairfield Methodist Primary School


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

34

88

54


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

34

54 – 34 = 2034 – 20 = 14

54

3 x 7 = 21

21 girls wear goggles.

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.

Mathematics Curriculum Framework

Mathematical Problem

Solving

Attitudes

Metacognition

Proc

esse

s

Concepts

SkillsNumericalAlgebraic

GeometricalStatistical

ProbabilisticAnalytical

Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling

Numerical calculationAlgebraic

manipulationSpatial visualization

Data analysisMeasurement

Use of mathematical tools

Estimation

Monitoring of one’s own thinkingSelf-regulation of learning

BeliefsInterest

AppreciationConfidence

Perseverance

Advanced

Intermediate

Low

High

38 4138

70 7473

89 9291

96 9897

Grade 4


TIMSSTrends in International Maths and Science Studies

Advanced

Intermediate

Low

High

3 105

24 4026

69 7767

93 9590

Grade 4

Elementary School in Japan


4123

7461

9289

9898

Advanced

Intermediate

Low

High

2 4031

15 7064

46 8885

75 9794

Grade 8

Telok Kurau Primary School


4540

7171

8690

9598

Advanced

Intermediate

Low

High

2 30

15 124

46 4414

75 6648

Grade 8

Effective Methods in Teaching Mathematics


402

7018

8850

9782

mathematicsteaching

effective

Bina Bangsa School, Indonesia

Pedagogical Principle:

BrunerPrinsip Pedagogi:

Bruner

Primary Mathematics 1A

Number Bonds

PCF Kindergarten Telok Blangah

Bruner

The concrete 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.

DivisionPembagian

My Pals Are Here! Mathematics 1B

DivisionPembagian

Photo: Princess Elizabeth Primary School

DivisionPembagian

My Pals Are Here! Mathematics 1B

DivisionPembagian

summary

Elementary School in Chile

Skemp

Understanding in mathematics • relational (conceptual) • instrumental (procedural)• conventional

Teaching for conceptual understanding is given emphasis in Singapore Math.


SkempPrinsip

Pedagogi: Skemp

Primary Mathematics Standards Edition Grade 6

Skemp

Matematika Singapura menitik-beratkan pengajaran pada pemahaman konsep.


SkempPrinsip

Pedagogi: Skemp


Fraction Division

Pembagian 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.

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 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

Primary Mathematics Standards Edition


DienesPrinsip Pedagogi:

Dienes

Dienes

Dienes encouraged the use of variation in mathematics education – perceptual variation and mathematical variation.

Dienes menganjurkan penggunaan variasi dalam pengajaran matematika - variasi persepsi dan variasi matematika.


DienesPrinsip Pedagogi:

Dienes

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

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

Mathematical Variation

Variasi dari segi Matematika

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

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

30


Variasi dari segi Matematika

effective

Keys Grade School , Manila

teaching

Pictorial Before Abstract

Gambar sebelum abstrak

Primary Mathematics Standards Edition

Perceptual Variation

Variasi dari segi persepsi


Variasi dari segi matematika

Emphasis on pictorial

representation and systematic

variation to enhance

conceptual understanding

Penekanan pada pemaparan visualdan variasi sistematis

memperkuat pemahaman konsep

Advanced

Intermediate

Low

High

41

74

92

98

Singapore



40

70

88

97

Advanced

Intermediate

Low

High

10

40

77

95

U S A



6

31

67

92

Advanced

Intermediate

Low

High

16

48

79

94

England



8

35

69

90

Advanced

Intermediate

Low

High

5

26

67

90

International



2

15

46

75

conclusion

PCF Kindergarten Pasir Ris

Mathematics is an excellent vehicle for

the development and improvement of a

person’s intellectual competence ..

Ministry of Education 2006

Fuchun Primary School

Matematika adalah kendaraan / alat yang hebatuntuk membangun dan memperbaiki kompetensi

dan intelektual seseorang …

Bina Bangsa School Bandung

Patterns

Patterns

Bina Bangsa School Bandung

SD Negeri in PalembangVisualization

Teacher Training for LEAP Programme for Public School Teachers in Manila

Visualization

mathz4kidz Learning Centre in MalaysiaCommunication

Pathlight School

Communication

Primary 2 Wellington Primary School

Primary Mathematics Syllabus 2007

Balestier HillPrimary School

Fuchun Primary School

Primary Mathematics Syllabus 2007

Princess Elizabeth Primary School

“Children are truly the future of our

nation. “Irving Harris

teaching mathematics effectively for the 21 st century

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