Experiencing Singapore MathSingapore Math Administrators Symposium Chicago 27 – 29 January 2011

Yeap Ban Har banhar@sg.marshallcavendish.com

www.marshallcavendish.com/education/mci

Session Mathematics as a Thinking Tool Importance of Initial Concrete Experiences Emphasis on Conceptual Understanding

Experiencing Singapore Math

a thinkingtool

mathematics

thinkingRevision of the Curriculum

19922001

20072013

curriculum and standards

Advanced

Intermediate

Low

High

Ind

onesi

a

Th

aila

nd

2 30

15 124

46 4414

75 6648

Grade 8

Method Used in Singapore Textbooks

TIMSS 2007Trends in International Mathematics and Science Studies

Mala

ysi

a

Sin

gapor

e

402

7018

8850

9782

Inte

rnati

onal

Experiencing Singapore Math

A C

G E

B

H

F

D

In the diagram, ACEG and BDFH are squares. AB, CD, EF and GH are of the same length. The ratio of AB : BC is 2 : 1.

What fraction of square ACEG is shaded?

Grade 6 National Test Item Singapore Examination and Assessment Board 2010

Experiencing Singapore Math

A C

G E

B

H

F

D

Experiencing Singapore Math

A C

G E

B

H

F

D

concreteintroduction

“… in which at some simple level a set of ideas or operations were introduced in a rather intuitive way …”

Bruner 1975, p.3-4

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Traditional Gift from Singapore ‘Five Stones’

Session From Concrete to Pictorial

Experiencing Singapore Math

emphasis visualization

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Session Bar Model Method Where Does It All Lead To?

Experiencing Singapore Math

emphasis visualization

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Dolphin show

Bird show

1235

275

1235 – 275 = ?

1235 – 235 – 40 = 960

960

1235 + 960 = ?

2235 – 40 = 2235 – 35 – 5 = 2195

2195 people attend both shows.

Experiencing Singapore Math

2 units = $24

1 unit = $12The book costs $12.

2 units = $24

Experiencing Singapore Math

Experiencing Singapore Math

3 units = $24

1 unit = $8The book costs $16.

3 units = $24

2 units = $16

Experiencing Singapore Math

3 units = $24

1 unit = $8

The book costs $32 ÷ 3 = $10.67. $24

4 units = $32

emphasis variation

emphasis variation

Session Variation, Not Repetition Teach Less, Learn More

Experiencing Singapore Math

Experiencing Singapore Math

emphasis variationconnections

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

Experiencing Singapore Math

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

Session Current Developments

in Mathematics Instruction in Singapore

Experiencing Singapore Math

thinkingRevision of the Curriculum

19922001

20072013

curriculum and standards

thinkingtextbooks

thinkingpedagogy

PERI Report

2010

engagementpedagogy

engagementpedagogy

thinkingnational test of a group of children are boys.

of the boys and 210 girls chose to go on a school trip.

of the children chose not to go on the school trip.

How many children chose to go on the school trip?

4

3

6

5

5

1

210

5

1

8

3 40

7

5

1

8

3

21040

7

3040

1 9603032

40

32

960 children chose to go.

technologynational test

A type of candy costs 40 cents each.Find the largest number of candies that can be bought with $95.

$95 ÷ 40 cents = 367.5

The largest number of candies that can be bought is 367.

strugglingsystem-wide strategies learners

learning support programs

foundation programs

lessonstudyprofessional development

Singapore Math Summer InstituteWorchester State University, MA 6-8 July 2011

where content meets pedagogyDr Yeap Ban Har Dr Richard Bisk Several Other Singapore Presenters

Contact melissaooi@sg.marshallcavendish.com