mahasarakham rajabhat university day 2

CHIJ Our Lady of Good Counsel

Catholic High School (Primary)

Keys Grade School, Manila

Mahasarakham Rajabhat University

Transforming The

Mathematics Classroom

Dr Yeap Ban Har

PrincipalMarshall Cavendish

InstituteSingapore

Director for Curriculum & Professional

DevelopmentPathlight School

Singapore

12 – 13 August 2010

Day 2

Princess Elizabeth Primary School

mathematicsteaching

effective

Bina Bangsa School, Indonesia

learning theories

Bruner

Bruner

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

Division

bruner’s theoryconcrete

mathz4kidz Learning Centre, Penang, Malaysia

A lesson from Earlybird Kindergarten Mathematics

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

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

usingmaterials

Professional Development in Ateneo Grade School, Manila, The Philippines

Catholic High School (Primary), Singapore

Multiplication

Pictorial Before Abstract

Primary Mathematics (Standards Edition) 2A

bruner

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

conceptual

Bina Bangsa School, Semarang, Indonesia

skemp’s

understandingtheory

Keys Grade School, Manila, The Philippines

Keys Grade School, Manila, The Philippines

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

Spiral Within and

Between Grades

visualizationfocus on

Wellington Primary School, Singapore

bar model method

Advanced

Intermediate

Low

High

Aver

age

Indo

nesi

a

Thai

land

2 30

15 124

46 4414

75 6648

Grade 8

Method Used in Singapore Textbooks

TIMSS 2007Trends in International Mathematics and Science Studies

Mal

aysi

a

Sing

apor

e

402

7018

8850

9782

Wellington Primary School, Singapore

Ministry of Education Singapore 2006

an excellent vehicle for the development and improvement of

a person’s intellectual competence

“

”

educationmathematics

Move 3 sticks to get two squares.

Move 3 sticks to get two squares.

Wellington Primary School, Singapore

Wellington Primary School, Singapore

Wellington Primary School, Singapore

Wellington Primary School, Singapore

Wellington Primary School, Singapore

Wellington Primary School, Singapore

“…development and improvement of a person’s

intellectual competencies...” such as visualization

Singapore Ministry of Education 2006

Primary Mathematics Standards Edition

and early gradesmodel method

in kindergarten

Ali has 3 sweets. Billy has 5 sweets.How many sweets do they have altogether?

upper gradesmodel method

in

Cheryl has $20 less than David.Cheryl and David have $148 altogether,Find the amount of money Cheryl has.

Cheryl

David 20

$148

Cheryl has $20 less than David.Cheryl and David have $148 altogether,Find the amount of money Cheryl has.

Cheryl

David 20

$148 - $20 = $128

$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

David 20

$148

Cheryl

David 20

$148 + $20 = $168

20

$168 ÷ 2 = $84

David has $84.

Cheryl has $64.

Cheryl has $20 less than David.Cheryl and David have $148 altogether,Find the amount of money Cheryl has.

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? 

A

B

156 kg

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? 

A

B 28

156 kg

72 kg

3 units = 156 kg – 72 kg = 84 kg

1 unit = 28 kg

Each shop sold 64 kg of rice.

Siti

Rahim

29 kg

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?

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?

Siti

Rahim

29 kg

11 kg

11 kg 18 kg

2 units = 18 kg1 unit = 9 kg

Rahim’s clothes is 9 kg.The suitcase is 2 kg.

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

Siti

Rahim x y

x y y yx + y = 11

x + 3y = 29

2y = 29 – 11 = 18

y = 18 ÷ 2 = 9

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?

pedagogiesengaging

Rajabhat Mahasarakham University, Thailand

bar model method

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.Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand

Rajabhat Mahasarakham University, Thailand