Singapore Math at Highline Public Schools March 2013 Session 5 Yeap Ban Har www.banhar.blogspot.com

The Merlion by Yeap Ken Min

John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?

19 cm x 5 = 95 cm 150 cm – 95 cm = 55 cm 55 cm was left.

Lesson 6 12th March 2013

Lesson 6 12th March 2013

Lesson 6 12th March 2013

“… over-emphasising procedural skills without understanding the underlying

mathematical principles should be avoided.”

Ministry of Education 2006

Student Achievement Average Learners Performing

Well

Pathlight School, Singapore

Singapore Math allows

average learners perform at

a high level. The following

are some data from some

international research on

math achievement and

attitude.

East Coast Primary School, Singapore

Score 1960-1970s 1980s 1990s 2000s

500 Japan Hong Kong Japan Korea

Hong Kong Japan Korea

Singapore

Hong Kong Japan Korea

Singapore

400 Thailand The Philippines Singapore Thailand

Malaysia Thailand

Malaysia Thailand

300 Indonesia The Philippines

Indonesia The 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.

mathematics

gra

de f

our

ma

them

atics

Singapore

South Korea

Hong Kong

Taiwan

Japan

Northern Ireland

Belgium

Finland

England

Russia

International

43

39

37

34

30

24

10

12

18

13

4

78

80

80

74

70

59

50

49

49

47

28

94

97

96

93

93

86

89

85

78

82

69

99

100

99

99

99

96

99

98

93

97

90

606

605

602

591

585

562

549

545

542

542

500

adva

nced

hig

h

inte

rmedia

te

low

average

gra

de e

ight

ma

them

atics

South Korea

Singapore

Taiwan

Hong Kong

Japan

Russia

Israel

Finland

United States

England

International

47

48

49

34

27

14

12

4

7

8

3

77

78

73

71

61

47

40

30

30

32

17

93

92

88

89

87

78

68

73

68

65

46

99

99

96

97

97

95

87

96

92

88

75

613

611

609

586

570

539

516

514

509

507

500

adva

nced

hig

h

inte

rmedia

te

low

average

gra

de e

ight

ma

them

atics

Singapore

Malaysia

Thailand

Indonesia

International

48

2

2

0

3

78

12

8

2

17

92

36

26

15

46

99

65

55

43

75

611

440

427

386

500

adva

nced

high

inte

rmedia

te

low

ave

rage

Singapore Math The CPA Approach, The Spiral

Approach and Emphasis on Relational

Understanding Globe Academy, London

J Bruner Enactive, Iconic, Symbolic

Representations

Edgewood Elementary School, New York

Greenville Elementary School, New York

Escuela de Guetamala, Chile

6

6

6

6

J Bruner Spiral Curriculum

Greenville Elementary School, New York

Bina Bangsa School, Indonesia

Z Dienes Play Structured Learning

Practice

Jenaplanschool Cleoplas, The Netherlands

x x x

x

x

L Vygotsky Interaction

Pathlight School, Singapore

Bina Bangsa School, Indonesia

Globe Academy, London

R Skemp Relational and Instrumental

Understanding

Using bar model to introduce solving

algebraic equations

Solve 7 – 3y = 1 .

7

3y 1

Using bar model to introduce solving

algebraic equations

Solve 7 – 3y = 1 .

7

3y 1

J Piager Assimilation, Accommodation

Keys Grade School, Manila

H Gardner Multiple Intelligences

Keys Grade School, Manila

Seely Place Elementary School, New York

Observing patterns and

making generalizations

involves reflection.

Find the value of 12.2 ÷ 4 .

Example 1

Answer : 3.05 [B1]

Singapore National Examination

12.20 4 3

12 0.20

.05

0.20 0

12.20

12 20 hundredths

Number Bond Method

Long Division Method

A show started at 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes?

11 a.m. 1.30 p.m.

2 h 30 min

Answer : 2 h 35 min [B1]

Example 2

Find <y in the figure below.

360o – 210o = 150o

70 o 70 o

70 o

y

Example 3

Cup cakes are sold at 40 cents each. What is the greatest number of cup

cakes that can be bought with $95?

$95 ÷ 40 cents = 237.5

Answer: 237 cupcakes

Example 4

Mr Tan rented a car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days?

$767.40 – 3 x $155 = $302.40

$302.40 ÷ 60 cents per km = 504 km

Example 5

“Mathematical problem solving is central to

mathematics learning.”

Ministry of Education 2006

“… including non-routine, open-ended and real-world

problems.”

Ministry of Education 2006

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.

Trends in International Mathematics and Science

Study TIMSS

Students in the highest international benchmark are able to apply their knowledge in a variety of situations

and able to explain themselves.

“Skill proficiencies include the ability to use technology

confidently, where appropriate, for exploration and problem

solving.”

Ministry of Education 2006

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 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

Example 6

Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.

Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.

(a) Kay puts the frame on 9 squares as shown in the figure below.

3 4 5

11 13

19 20 21

What is the average of the 8 numbers that can be seen in the frame?

Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.

(a) Kay puts the frame on 9 squares as shown in the figure below.

3 4 5

11 13

19 20 21

What is the average of the 8 numbers that can be seen in the frame?

Alternate Method 4 x 24 = 96 96 ÷ 8 = 12

3+4+5+11+13+19+20 = 96 96 ÷ 8 = 12

(b) Lin puts the frame on some other 9 squares. The sum of the 8 numbers that can be seen in the frame is 272. What is the largest number that can be seen in the frame?

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 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

Weiyang started a savings plan by putting 2 coins in a money box every day. Each coin was either a 20-cent or 50-cent coin. His mother also puts in a $1 coin in the box every 7 days. The total value of the coins after 182 days was $133.90. (a) How many coins were there altogether? (b) How many of the coins were 50-cent coins?

Example 7

three keys to successful implementation

assessment

Reference: Department of Education State of New York

Reference: Department of Education State of Hawaii

assessment

teacher preparation

Teacher as a learner (professor as a

model)

Teacher as an observer of learning

(lesson study)

Teacher as reflective practitioner

(professional learning community)

Singapore teachers learn what they need to learn through an

approach that balances content and pedagogy.

teacher preparation

National Institute of Education

Singapore

The practice component is given emphasis – micro teaching,

practicum and lesson study.

teacher preparation

National Institute of Education

Singapore

There is an

emphasis on

teachers

solving the

problems

themselves

during the

course.

teacher preparation

Teachers learn from the

textbooks and teachers

guide.

teacher development

We learn from the Japanese method to help teachers

develop better skills in observing students. This is lesson

study.

teacher development

Princess Elizabeth Primary School

Singapore

TEDS-M Elementary Teachers

Content Knowledge TEDS-M Elementary Teachers

Pedagogical Content Knowledge

TEDS-M Findings

National Institute of Education, Singapore

Fuchun Primary School, Singapore

Edgewood Elementary School, New York

Bina Bangsa School, Indonesia

Keys Grade School, The Philippines

Kranji Secondary School, Singapore

leadership Mayor of Newark gave an inspirational message to

teachers attending professional development on

Singapore Math.

• What can I do as a teacher?

• What can my school do?

• What can the education schools do?

• What government support should be in place?

Slides are available at

www.banhar.blogspot.com

Singapore Math at Highline Public Schools March 2013 Yeap Ban Har yeapbanhar@gmail.com

The Merlion by Yeap Ken Min