Seoul Foreign School Plenary Session

Dr Yeap Ban Har yeapbanhar@gmail.com

Marshall Cavendish Institute Singapore

Presentation slides are available at

www.banhar.blogspot.com

Professional Development Singapore Mathematics

Seoul 9 – 11 July 2012

www.mcinstitute.com.sg www.facebook.com/MCISingapore

MAP101

FUNDAMENTALS

of singapore

m a t h

Slides are available at

www.banhar.blogspot.com

Mayflo

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Introduction

This course is an overview of Singapore

Math. It includes the what and how of

teaching mathematics.

Curriculum document is available at http://www.moe.gov.sg/

Singapore Ministry of Education 1997

THINKING SCHOOLS

LEARNING NATION

is singapore what

mathematics

key focus singapore

mathematics of

problem solving

thinking

excellent vehicle

an

for the development & improvement of a person’s intellectual

competencies Ministry of Education Singapore 2006

conceptual understanding

FUNDAMENTALS

of singapore

m a t h

Slides are available at

www.banhar.blogspot.com

Mayflo

wer P

rima

ry S

chool, S

inga

pore

Singapore Math

Visualization

110 g

290 g

110 g 180 g

Bella puts 180 g brown sugar on the dish.

110 g

290 g

110 g 180 g

2 units = 180 g

1 unit = 90 g

3 units = 270 g

Bella puts 270 g brown sugar on the dish.

on an identical dish

Singapore Math is based on the CPA Apporach.

Pictorial representations can be more concrete

(pictures) or more abstract (diagrams such as bar

model).

An alternate way to solve the brown sugar

problem:

Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.

Bar models were introduced to overcome the pervasive problems students had with word problems – even the basic ones.

Such word problems are used to help

students

Deal with information

Handle and clarify ambiguity – one

dish or two

Develop visualization – bar models

are used extensively

Practice mental strategies – numbers

used are not difficult to compute

Singapore Math

Visualization

Procedural & Conceptual

Understanding Singapore Math places an emphasis on

both. Procedures are explained in a

conceptual way. For example, long

division is seen simply as breaking

large numbers into smaller ones before

dividing.

Using number bonds to make

sense of long division

Over-emphasizing

procedural knowledge

Balancing procedural knowledge with conceptual understanding

Differentiated Instruction for advanced learners – how does one get the result

of 51 3 from 60 3.

Singapore Math

Patterns & Generalization

Task Extension for

Advanced Learners

C H E R Y L

C H E R Y L 1

C H E R Y L 2

C H E R Y L 3

C H E R Y L 4

C H E R Y L 5

C H E R Y L 6

C H E R Y L 7

C H E R Y L 8

C H E R Y L 9

C H E R Y L

C H E R Y L

C H E R Y L

C H E R Y L

C H E R Y L

C H E R Y L

Which letter is 99?

Method 1 The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located.

Method 2 The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.

Method 3 Numbers ending with 9 are at E. So, 99 is at E too.

Method 4 The position for 99 can be found by writing out all the numbers but this is not efficient method.

D A V I D

Method 1 The letters under A and I are even. So 99 cannot be there.

Method 2 The positions of numbers ending with 9 form a diagonal pattern.

Method 3 The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out.

Method 4 The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out.

Method 5 Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.

Method 2 The positions of numbers ending with 9 form a diagonal pattern. The methods were the ones that participants in Chile came up with.

Another Method In a course done in December 2010 with a group of Chilean teachers, there was a method that involves division. For Cheryl, it was 99 10. For David, it was 99 8. Are you able to figure out that method?

Singapore Math

Patterns & Generalization

Singapore Mathematics: Focus on Problem Solving

CPA Approach based on Jerome Bruner was used to learn division of fractions – using paper folding and subsequent drawing.

Singapore Mathematics: Focus on Conceptual Understanding

Singapore Math

Learn New Concept Through

Problem Solving

Textbook Study

Observe the various meanings of

multiplication from Grade 1 to Grade

3.

Multiplication Facts

We do a case study on multiplication

facts. We will see the use of an anchor

task to engage students for an

extended period of time.

Strategy 1

Get 3 x 4 from 2 x 4

Strategy 2

Doubling

Strategy 3

Get 7 x 4 from 2 x 4 and 5 x 4

Strategy 4

Get 9 x 4 from 10 x 4

Strategy 1

Get 3 x 4 from 2 x 4

Strategy 3

Get 9 x 4 from 4 x 4 and 5 x 4

This is essentially the distributive

property. Do we introduce the

phrase at this point?

Strategy 2

Doubling

Strategy 4

Get 9 x 4 from 10 x 4

Unusual Response

Get 4 x 8 from 4 x 2. Can it be done? Does the number

of cups change? Does the number of counters per cup

change?

Differentiated Instruction

These are examples of how the lesson can be

differentiated for advanced learners.

Prior to learning multiplication, students

learn to make equal groups using concrete

materials. Marbles is the suggested

materials.

After that they represent these concrete

situations using, first, drawings ..

Open Lesson in Chile

… and, later, diagrams. Students also

write multiplication sentences in

conventional symbols.

First, equal groups –

three groups of four.

Second, array –

Three rows of four

Third, four multiplied three

times ….

Textbook Study

Observe how equal group

representation evolves into array and

area models. Also observe how the

multiplication tables of 3 and 6 are

related on the flights of stairs.

They begin with equal group representation.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

In Primary 2, students learn

multiplication facts of 2, 5, 10 and 3

and 4. In Primary 3, they learn the

multiplication facts of 6, 7, 8 and 9.

Later, the array meaning of

multiplication is introduced.

Square tiles are subsequently used to lead to

the area representation of multiplication.

Open Lesson at Broomfield, Colorado

Students who were already good in the skill of multiplying two-digit number

with a single-digit number were asked to make observations. They were

asked “What do you notice? Are there some digits that cannot be used ta

all?”

Singapore Math

Drill-and-Practice Through

Problem Solving

Singapore Math

Three-Part Lesson

Singapore Math

Three-Part Lesson

Singapore Math

Three-Part Lesson

FUNDAMENTALS

of singapore

m a t h

Slides are available at

www.banhar.blogspot.com

Mayflo

wer P

rima

ry S

chool, S

inga

pore

The following slides are for additional

tasks that are discussed on the second

day for Grades 5 – 8

Marcus gave ¼ of his coin collection to his sister

and ½ of the remainder to his brother.

As a result, Marcus had 18 coins.

Find the number of coins in his collection at first.

3 units = 18

8 units = ???

Marcus had 48 coins at first.