ARK Schools, London

Dr Yeap Ban Har [email protected]

Marshall Cavendish Institute Singapore

Presentation slides are available at www.banhar.blogspot.com

Singapore MathsTHE ESSENTIALSLondon June 2011

Kembangan PCF Kindergarten

Curriculum for all learners• Struggling students learn

enough• Average students perform

advanced skills• Advanced students are

challenged

Kembangan PCF Kindergarten

Advanced

Intermediate

Low

High

Gra

de 4

19

95

38

70

89

96

TIMSSTrends in International Mathematics and Science Studies

Gra

de 8

19

9942

77

94

99

Gra

de 4

20

03

Gra

de 8

20

07

38

73

91

97

40

70

88

97

Singapore Mathematics: Focus on Thinking

excellentvehicleanforthe

development&improvement of

a person’s intellectual

competenciesMinistry of Education Singapore 2006

an identical

Allan puts some brown sugar on a dish.The total weight of the brown sugar and the dish is 110 g.Bella puts thrice the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.

Find the weight of the brown sugar that Bella puts on the dish.

110 g

290 g

110 g180 g

2 units = 180 g

1 unit = 90 g

3 units = 270 g

Bella puts 270 g brown sugar on the dish.

an identical

Allan puts some brown sugar on a dish.The total weight of the brown sugar and the dish is 110 g.Bella puts thrice the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.

Find the weight of the brown sugar that Bella puts on the dish.

110 g

290 g

110 g180 g

3 units = 180 g

1 unit = 60 g

3 units = 180 g

Bella puts 180 g brown sugar on the dish.

Singapore MathVisualization

1 2 3 4 5 6

11 10 9 8 7

12 13 14 15 16

21 20 19 18 17

22 23 24 25 26

1 2 3 4 5

9 8 7 6

10 11 12 13

17 16 15 14

18 19 20 21

Professional Development in Santiago de Chile

Singapore MathPatterns

Archipelschool De Tweemaster – Kameleon

The Netherlands

In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992.

Mathematical Problem

Solving

Attitudes

Metacognition

Proc

esse

s

Concepts

Skills

NumericalAlgebraic

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

Professional Development in ARK Schools, London

Professional Development in Santiago de Chile

Problem Solving in Learning Basic Concepts and Skills

Reference: Primary Mathematics (Standards Edition)


Singapore MathLearn New Concept Through

Problem Solving

Singapore MathDrill-and-Practice Through

Problem Solving

Singapore MathApplying Knowledge in

Problem Solving

The CPA ApproachFocus on Thinking

makes abstract concepts accessible to learners who are not yet ready for abstraction

builds fundamental intellectual competencies required for learners to handle abstraction

Textbook

Reference: My Pals Are Here! Maths

1. Setting Up the Task

Each person should get 12 animals. I have given you some. How many more do you need?

Pupils had opportunities to work independently as the teacher attended to other pupils.

2. Development (1)

Put four animals into one cup. Note only one cup is given.This mirrors drawing rings around four objects.

Put four animals into a second cup.

Students should have positive experiences during the lesson.

How many animals are there altogether? How many animals are there in one cup? How many cups do we use?

3. Development (2)

This is like the workbook tasks except that the magnets can be moved. Built-in remedial strategy.

Variations on the arrangements of magnets to increase the level of visualization required.

Pupils needs to monitor the number of magnets as well as to manage their visualization process.

4. Extension

5. Development (3) The use of colour to show the group. Built-in remedial strategy.

CPA Approach

Links between concrete and pictorial representation must be carefully constructed.

Remedial steps are built into instruction


51 – 17

51 x 351 + 26

3 units = 18

1 unit = 6

8 units = 8 x 6 = 48

There were 48 coins at first.

SingaporeMathsThe Essentials

Da Qiao Primary School, Singapore