new jersey singapore math administrators symposium east brunswick

Expe

rienc

ing

Sing

apor

e M

ath

Experiencing Singapore MathN e w a r k E a s t B r u n s w i c k

Yeap Ban HarMarshall Cavendish Institute

Singapore

[email protected]

Slides are available atwww.banhar.blogspot.com

Expe

rienc

ing

Sing

apor

e M

ath

Land 270 sq miles

People 4.7 million

GDP per capita 1965 USD510 2010 USD43,300

in current USD

Junyuan Secondary School, Singapore

introduction

General Overview of Singapore and its Education System

General Overview of Singapore and its Education System

Students 500 000

Teachers 30 000

Principals & Vice-Principals 900

Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) 15 Mixed-Level Schools

The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.

Canossa Convent Primary School, Singapore

High achievement was not a given. In 1960, among 30 615 candidates who sat for the first Primary School Leaving Examination, 45% of the candidates passed.

Keon Ming Public School, Singapore

Expe

rienc

ing

Sing

apor

e M

ath

Score 1960-1970s 1980s 1990s 2000s

500 Japan JapanKorea

Hong Kong

JapanKorea

SingaporeHong Kong

JapanKorea

Hong KongSingapore

400 Thailand SingaporeThailand

The Philippines

MalaysiaThailand

MalaysiaThailand

300 IndonesiaThe Philippines

IndonesiaThe Philippines

Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table.

"Solving problems is central to mathematical proficiency and is articulated to a varying degree across the international curricula. Singapore applies the highest degree of specificity to it, placing it at the centre of all mathematical learning.“

Review of the National Curriculum in England Research Report UK Department for Education

Expe

rienc

ing

Sing

apor

e M

ath

1992Introduction of Problem-

Solving Curriculum

1997Thinking SchoolsLearning Nation

1982Introduction of Singapore mathematics

textbooks as they are known today.

2001Introduction of textbooks published by

private publishers and approved by Ministry of Education.

2007New editions of textbooks are

published with the introduction of the revised curriculum.

Mathematics is “an excellent vehicle for the

development and improvement of a person’s intellectual competence”.

Ministry of Education Singapore 2006

Page 1

Expe

rienc

ing

Sing

apor

e M

ath

Page 4

Expe

rienc

ing

Sing

apor

e M

ath

Experiencing Singapore MathSpiral Approach


Singapore

[email protected]


543 + 274 =

37 + 24 =

One day, 543 cars and 274 buses pass through a toll booth. How many cars and buses pass through the toll booth?

Math in Focus Grade 2

543

274

cars

buses

543 + 274 =

543 274

cars buses

emphasis spiral

Expe

rienc

ing

Sing

apor

e M

ath

Expe

rienc

ing

Sing

apor

e M

ath

Experiencing Singapore MathVisual Approach


Singapore

[email protected]


110 g

290 g Page 2

110 g

??

2 units = 290 g – 110 g = 180 g

1 units = 180 g 2 = 90 g

3 x 90 g = 270 gBella puts 270 g sugar on the dish.

Escuela de Guetamala, Chile

Expe

rienc

ing

Sing

apor

e M

ath

x + 2x = 12

Expe

rienc

ing

Sing

apor

e M

ath

King Solomon Academy, London

Expe

rienc

ing

Sing

apor

e M

ath

Edgewood Elementary School, New York

Expe

rienc

ing

Sing

apor

e M

ath

Globe Academy, London

Expe

rienc

ing

Sing

apor

e M

ath

3x – 2 = 8

Globe Academy, London

Expe

rienc

ing

Sing

apor

e M

ath

Experiencing Singapore MathInitial Concrete Experiences & Building Conceptual Understanding


Singapore

[email protected]


Expe

rienc

ing

Sing

apor

e M

ath

Relational Understanding R Skemp

Concrete Introduction J Bruner


what & how

Page 08Page 13

Expe

rienc

ing

Sing

apor

e M

ath

Share 3 fourths equally among 3.

3 fourths 3 = 1 fourth

Page 5

Expe

rienc

ing

Sing

apor

e M

ath

Share 3 fourths equally between 2.

3 fourths 2 = 6 eighths 2= 3 eighths

Share 3 fourths equally among 4.

3 fourths 4 = 12 sixteenths 4= 3 sixteenths

Expe

rienc

ing

Sing

apor

e M

ath

12 cookies 4

12 pieces 4

12 sixteenths 4

12 tenths 4

12 x 4

12 cookies 4 cookies

12 pieces 4 pieces

12 x 4 x

34

÷1434

÷12

Page 13

Expe

rienc

ing

Sing

apor

e M

ath

Expe

rienc

ing

Sing

apor

e M

ath

Concrete to Visual J Bruner

Variation Z Dienes

Human Intelligences H Gardner


visualization

Page 11

Math in Focus

Expe

rienc

ing

Sing

apor

e M

ath

Da Qiao Primary School, Singapore

Expe

rienc

ing

Sing

apor

e M

ath

See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey.See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in Singapore on Higher-Order Thinking Skills. Paper presented at International Conference on School Mathematics Textbooks Shanghai, China.

Expe

rienc

ing

Sing

apor

e M

ath

Primary Mathematics (Third Edition)

Visuals are used to teach concepts – distributive property of multiplication – without using formal terms.

Expe

rienc

ing

Sing

apor

e M

ath

Primary Mathematics (Third Edition)