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Mahasarakham Rajabhat University Transforming The Mathematics Classroom Dr Yeap Ban Har Principal Marshall C avendish Institute Singapore Director for Curriculum &amp; Professional Development Pathlight School Singapore 12 – 13 August 2010. Princess Elizabeth Primary School.

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MahasarakhamRajabhat University

Transforming The Mathematics Classroom

Dr Yeap Ban Har

Principal

Marshall Cavendish Institute

Singapore

Director for Curriculum & Professional Development

Pathlight School

Singapore

12 – 13 August 2010

Princess Elizabeth Primary School

CHIJ Our Lady of Good Counsel

Day 1

Catholic High School (Primary)

Keys Grade School, Manila

Beliefs

Interest

Appreciation

Confidence

Perseverance

Monitoring of one’s own thinking

Self-regulation of learning

Attitudes

Metacognition

Numerical calculation

Algebraic manipulation

Spatial visualization

Data analysis

Measurement

Use of mathematical tools

Estimation

Mathematical Problem Solving

Reasoning, communication & connections

Thinking skills & heuristics

Application & modelling

Skills

Processes

Concepts

Numerical

Algebraic

Geometrical

Statistical

Probabilistic

Analytical

Mathematics Curriculum Framework
Problem

John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm.

How much of the copper wire was left?

Problem

John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm.

How much of the copper wire was left?

150 cm – 19 cm x 5

= 150 cm – 95 cm = 55 cm

55 cm of the copper wire was left.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Why Teach Mathematics

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

Ministry of Education, Singapore 2006

Problem

Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.

How many cookies did Mrs Hoon sell?

210

Jerome Bruner

210

Pictorial Representation

Symbolic Representation

Problem

Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim.

Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4.

How many sweets did Ken buy?

Problem

Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim.

Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4.

How many sweets did Ken buy?

Chocolates

Sweets

Jim

12

Ken

12

12

12

12

18

Teaching Place Value

Activity

• Combine your sets of digit cards. Shuffle the cards.
• Take turns to draw one card at a time.
• Place the card on your place value chart.
• Once you have placed the card in a position, you cannot change its position anymore.
• The winner is the one who makes the greatest number.

### Place Value

Key Concept: The value of digits depends on its place or position.

Teaching Division

Keys Grade School, Manila

Teaching Division

Keys Grade School, Manila

Practising Multiplication

My number is 2!

The product is 12.

National Institute of Education

Practising Multiplication
• Use one set of the digit cards to fill in the five spaces.
• Make a correct multiplication sentence where a two-digit number multiplied by a 1-digit number gives a 2-digit product.
• Make as many multiplication sentences as you can.
• Are the products odd or even?

x

Practicing Subtraction

Activity 4

• Think of a number larger than 10 000 but smaller than 10 million.
• Jumble its digits up to make another number.
• Find their difference.
• Write the difference on a piece of paper. Circle one digit. Add up the rest of the digits.
• Tell me the sum of the rest of the digits and I will tell you the digit you circled.

Example

• 72 167
• 27 671
• 72 167 – 27 671 = 44 496
• 44 496
• 4 + 4 + 4 + 6 = 18
• Tell me 18.

Problem Solving

Scarsdale School District, New York, USA

Arrange cards numbered 1 to 10 so that the trick shown by the instructor can be done.

Teachers solved the problems in different ways.

Scarsdale School District, New York, USA

Scarsdale School District, New York, USA

The above is the solution. What if the cards used are numbered 1 to 9? 1 to 8? 1 to 7? 1 to 6? 1 to 5? 1 to 4?

MahasarakhamRajabhat University

Transforming The Mathematics Classroom

Dr Yeap Ban Har

Principal

Marshall Cavendish Institute

Singapore

Director for Curriculum & Professional Development

Pathlight School

Singapore

12 – 13 August 2010

Princess Elizabeth Primary School

CHIJ Our Lady of Good Counsel

Day 2

Catholic High School (Primary)

Keys Grade School, Manila

effective

mathematics

teaching

learning theories

BinaBangsa School, Indonesia

Bruner

Division

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

National Institute of Education, Singapore

Division

Princess Elizabeth Primary School, Singapore

mathz4kidz Learning Centre, Penang, Malaysia

bruner’s theory

concrete

A lesson from Earlybird Kindergarten Mathematics

from

pictorial

to

abstract

All Kids Are Intelligent Series

concrete

using

materials

Professional Development in AteneoGrade School, Manila, The Philippines

Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

Multiplication

Catholic High School (Primary), Singapore

bruner

Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

conceptual

skemp’s

theory

understanding

BinaBangsa School, Semarang, Indonesia

Skemp

Understanding in mathematics

relational

(conceptual)

instrumental

(procedural)

conventional

Teaching for conceptual understanding is given emphasis in Singapore Math.

Pedagogical Principle:

Skemp

Primary Mathematics Standards Edition Grade 6

skemp

Scarsdale Middle School, New York

### Spiral Approach

Spiral

Spiral Within Grade

Grade 2

• Lesson 1 347 + 129
• Lesson 2 182 + 93
• Lesson 3 278 + 86

Spiral Between Grade

• Grade 1 Adding up to 100
• Grade 2 Adding up to 1000
• Grade 3 Adding up to 10000
Spiral

Spiral Between Grade

• Grade 2 Add 1/5 and 2/5
• Grade 3 Add 1/5 and 1/10
• Is adding 1/5 and 1/10 the same as adding 1/5 and 3/10?
• Grade 4 Add 3/5 and 4/5
• Add 5/6 and 1/3
• Grade 5 Add 2/5 and 1/4
• Add 4/5 and 3/4
• Add 1 ¾ and 2 ½

focus on

visualization

bar model method

Wellington Primary School, Singapore

TIMSS 2007

Trends in International Mathematics and Science Studies

Average

Indonesia

Thailand

Malaysia

Singapore

Grade 8

Advanced

2

0

3

2

40

High

15

4

12

18

70

Intermediate

46

14

44

50

88

Low

75

48

66

82

97

Method Used in Singapore Textbooks

education

mathematics

an excellent vehicle for the development and improvement of a person’s intellectual competence

Wellington Primary School, Singapore

Ministry of Education Singapore 2006

“…development and improvement of a person’s intellectual competencies...” such as visualization

Singapore Ministry of Education 2006

model method

in kindergarten

and early grades

Ali has 3 sweets.

Billy has 5 sweets.

How many sweets do they have altogether?

model method

in

upper grades

Cheryl has \$20 less than David.

Cheryl and David have \$148 altogether,

Find the amount of money Cheryl has.

Cheryl

\$148

20

David

Cheryl has \$20 less than David.

Cheryl and David have \$148 altogether,

Find the amount of money Cheryl has.

Cheryl

\$148 - \$20

= \$128

20

David

\$128 ÷ 2 = \$64

Cheryl has \$64.

How about David? \$84

Cheryl has \$20 less than David.

Cheryl and David have \$148 altogether,

Find the amount of money Cheryl has.

Cheryl

\$148

20

David

Cheryl has \$20 less than David.

Cheryl and David have \$148 altogether,

Find the amount of money Cheryl has.

20

Cheryl

\$148 + \$20 = \$168

20

David

\$168 ÷ 2 = \$84

David has \$84.

Cheryl has \$64.

At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

156 kg

A

B

72 kg

At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

3 units = 156 kg – 72 kg = 84 kg

1 unit = 28 kg

Each shop sold 64 kg of rice.

156 kg

A

28

B

72 kg

Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes.

What is the mass of Rahim’s clothes?

What is the mass of the suitcase?

29 kg

Siti

Rahim

11 kg

Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes.

What is the mass of Rahim’s clothes?

What is the mass of the suitcase?

29 kg

11 kg

18 kg

Siti

2 units = 18 kg

1 unit = 9 kg

Rahim

Rahim’s clothes is 9 kg.

The suitcase is 2 kg.

11 kg

We can also find the mass of Siti’s clothes (27 kg) if required.

Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes.

What is the mass of Rahim’s clothes?

What is the mass of the suitcase?

x + y = 11

x + 3y = 29

x

y

y

y

Siti

2y = 29 – 11 = 18

x

y

Rahim

y = 18 ÷ 2 = 9

engaging

pedagogies

bar model method

RajabhatMahasarakham University, Thailand

Start with any number of beans.

Take turns to remove beans from the table.

Either take one or two beans.

The one who take the last one or two beans wins the game!

How many npn-congruent quadrilaterals of area 5 square units can be drawn on the geo-paper? The vertices must be on the dots.

RajabhatMahasarakham University, Thailand