mathematicsteaching & learning

in singapore schools

Yeap Ban HarNational Institute of Education

Nanyang Technological University

Mathematics Education Seminar Series

Boston College14 April 2010

Slides can be downloaded from www.mathz4kidz.com

The lecture focuses on selected aspects of mathematics education in Singapore that have significant impact on high achievement of its students. It provides selected insights on the role of curriculum development, structures in the education system that support curriculum implementation, textbooks, teacher training, assessment and testing, and societal expectations on student outcomes.

Da Qiao Primary School

Overview ofEducation System

• Grades 1 – 6 (compulsory education)• Primary School Leaving Examination Grade 6• Grade 7 – 10• General Certificate of Education Ordinary Level

Grade 10• Grade 11 – 12 or Polytechnic• General Certificate of Education Advanced Level

Grade 12 or Diploma

There are variations for advanced and struggling students.

curriculum

Pre-service Practicum

Fuchun Primary School

emphasis onproblem solving

Reference: Singapore Ministry of Education 2006

rationaleThe rationale of teaching mathematics is that it is

“a good vehicle for the development and improvement of a person’s intellectual

competence”.

Wellington Primary School

Thinking Schools Learning Nations

This initiative was introduced in 1997. Since then Ministry of Education in Singapore has been injecting various initiatives into the system. These initiatives are intended to give schools the impetus to refine their programs to include the development of generic competencies.

national test

North Vista Primary School

emphasis onproblem solvingnationaltest

in the

Example of 1-point Items Example of 2-point Items

Which of the following numbers is the largest?(1) 6.59(2) 6.95(3) 6.509(4) 6.905

Adrian and Bala shared the total cost of a present. Adrian paid $15 more than 3/8 of the cost of the present. Bala paid $25. How much did the present cost?(1) $160 (2) $64 (3) $40 (4) $16

A movie started at 11.45 a.m. The movie was 2 hours 25 minutes long. What time did the movie end?

Prawns are sold at $1.35 per 100 g at a market. What is the price of 1.5 kg of prawns?

In the figure below, ABCD is a square, AED is an equilateral triangle and BFD is a straight line. Find <AFD

Reference: Singapore Examinations & Assessment Board 2004-2008

A B

CD

EF

Item Type Point Per Item Total Points

Multiple-Choice 1 20%

15 items 2

Short- Answer 1 30%

20 items 2

Long-Answer 350%

13 items 4

5

Reference: Singapore Examinations & Assessment Board

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?

chocolate cookies

almond cookies

210

1/5

5/83/8

3/8 – 1/5 = 7/40 210

1/40 30

32/40 960 She sold 960 cookies.

Parents Up In Arms Over PSLE Mathematics Paper TODAY’S 10 OCT 2009

SINGAPORE: The first thing her son did when he came out from the Primary School Leaving Examination (PSLE) maths paper on Thursday this week was to gesture as if he was "slitting his throat". "One look at his face and I thought 'oh no'. I could see that he felt he was condemned," said Mrs Karen Sng. "When he was telling me about how he couldn't answer some of the questions, he got very emotional and started crying. He said his hopes of getting (an) A* are dashed."

Not for the first time, parents are up in arms over the PSLE Mathematics paper, which some have described as "unbelievably tough" this year. As recently as two years ago, the PSLE Mathematics paper had also caused a similar uproar. The reason for Thursday's tough paper, opined the seven parents whom MediaCorp spoke to, was because Primary 6 students were allowed to use calculators while solving Paper 2 for the first time. …

Said Mrs Vivian Weng: "I think the setters feel it'll be faster for them to compute with a calculator. So the problems they set are much more complex; there are more values, more steps. But it's unfair because this is the first time they can do so and they do not know what to expect!" …"The introduction of the use of calculators does not have any bearing on the difficulty of paper. The use of calculators has been introduced into the primary maths curriculum so as to enhance the teaching and learning of maths by expanding the repertoire of learning activities, to achieve a better balance between the time and effort spent developing problem solving skills and computation skills. Calculators can also help to reduce computational errors." …Another common gripe: There was not enough time for them to complete the paper. A private tutor, who declined to be named, told MediaCorp she concurred with parents' opinions. "This year's paper demanded more from students. It required them to read and understand more complex questions, and go through more steps, so time constraints would have been a concern," the 28-year-old said.

chocolates

Jim

Ken

sweets

12

12

3 parts 12 + 12 + 12 + 12 + 18 = 661 part 22

Half of the sweets Ken bought = 22 + 12 = 34So Ken bought 68 sweets.

18

12

12

12

12

18

program implementation

North Vista Primary School

school programsinclude

forall students

enrichment

Wellington Primary School

Telok Kurau Primary School

A lion weighs 135 kg. A cow weigh 87 kg more than the lion. An elephant weighs 139 more than the cow. How heavy is the elephant?

(Primary 2)

A shop sells bicycles for adults and children. The adult bicycles come in 2 color choices: black and white. The children bicycles come in 3 color choices: red, blue and green. Mr Tan wants to buy a bicycle for himself and another one for his son. How many different color choices does he have to buy both bicycles?

A shop sells bicycles for adults and children. The adult bicycles come in 2 color choices: black and white. The children bicycles come in 4 color choices: red, blue, green and purples. Mr Tan wants to buy a bicycle for himself and another one for his son. How many different color choices does he have to buy both bicycles?

A shop sells bicycles for adults and children. The adult and children choose from any of these colors: red, blue, green, yellow and purple. bicycles come in 2 color choices: black and white. The children bicycles come in 3 color choices: red, blue and green. Mr Tan wants to buy a bicycle for himself and another one for his son. How many different color choices does he have to buy both bicycles?

Materials that delve deeper into a basic topic are used as part of the regular program. For example, this school uses a textbook plus teacher-produced worksheets such as this to enrich students’ ideas about multiplication. Lesson Study at Maris Stella High School

(Primary)

Maris Stella High School (Primary)

Maris Stella High (Primary) School

Source: Maris Stella High (Primary) School, Singapore

Raffles Girls’ Primary School

In twice-a-year tests designed by the schools, problems such as this one are given to challenge students. However, there is an expectation that every student makes significant effort to acquire the ability to solve such problems.

complex problem solving

is expected of every student

parental expectations

Tanjong Pagar PCF Kindergarten

parentalexpectations

Seminar for Parents on Problem Solving

system-wide intervention

Northlight School

Fuchun Primary School

presence of‘safety nets’

learning support programat entry point

Princess Elizabeth Primary School

Variation in kindergartensKindergarten is not part of formal schooling.

Pre-school education

varies in types and quality.

Teachers’ qualification ranges from O-Levels to masters degrees in early childhood. Monthly fees range from $65 to more than $1000.

PCF Kindergarten Telok Blangah

Kindergartens that the majority of Singapore children attend are run by grass-root organizations and they struggle to provide a high-quality program due to lack of resources and qualified teachers.

One such provider of kindergarten education is the PCF Kindergartens which has 255 kindergartens out of 485 kindergartens in Singapore.

Variation in kindergartens

Also, 50% of first-graders in Singapore come from non-English speaking environment.

PCF Kindergarten Tanjong Pagar,

foundation mathematicsat halfway point

Princess Elizabeth Primary School

teacher-initiated intervention

Princess Elizabeth Primary School

Da Qiao Primary School

teacher-initiatedintervention

Telok Kurau Primary School

pedagogy

Kuo Chuan Presbyterian Primary School

emphasis onconcrete topictorial to abstract

representations

Catholic High School (Primary)

especially onthe model method

mathz4kidz Learning Center, Malaysia

teacher education

National Institute of Education

teacher trainingpre-service

National Institute of Education

professional developmentin-service

Princess Elizabeth Primary School, Singapore

Hougang Primary School, Singapore

teacher learningfrom textbooks

achievement

Catholic High School (Primary)

Catholic High School (Primary), Singapore

Advanced

Intermediate

Low

High

1995

2003

2007

TIMSS 1995 to 2007

38 4138

70 7473

89 9291

96 9897

Grade 4

Catholic High School (Primary), Singapore

Advanced

Intermediate

Low

High

TAIW

AN

HO

NG

KON

G

SIN

GAP

ORE

TIMSS 2007

24 4140

66 7481

92 9297

99 98100

Grade 4

Northlight School, Singapore

Advanced

Intermediate

Low

High

AVER

AGE

MAL

AYSI

A

SIN

GAP

ORE

TIMSS 2007

2 402

15 7018

46 8850

75 9782

Grade 8