NCTM Regional Conference & Exposition Denver Colorado

8 – 9 October 2010Session 106

This session includes a selection of problems used in grades K – 3 classrooms in Singapore. Look at how these problems are used to achieve different instructional goals. See how these problems play a role in helping children develop a strong foundation for subsequent learning.

Colorado Convention Center,

Korbel 3B

Problem Solving in the Singapore Classrooms

Dr Yeap Ban HarMarshall Cavendish

InstituteSingapore

banhar@sg.marshallcavendish.com

www.banhar.blogspot.com

Session 106

The mathematical problem-solving curriculum framework was introduced in Singapore in 1992 in response to recommendations made in An Agenda for Action (in the US) and the Cockcroft Report (in the UK).

Mathematical Problem

Solving

Attitudes

Metacognition

Proc

esse

s

Concepts

Skills

NumericalAlgebraic

GeometricalStatistical

ProbabilisticAnalytical

Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling

Numerical calculationAlgebraic

manipulationSpatial visualization

Data analysisMeasurement

Use of mathematical tools

Estimation

Monitoring of one’s own thinkingSelf-regulation of learning

BeliefsInterest

AppreciationConfidence

Perseverance

intellectual competence

The Singapore mathematics curriculum states that mathematics is an “excellent vehicle for the development and improvement of a person’s intellectual competence” (Ministry of Education 2006). The next few examples show how problem solving can be used to develop visualization, number sense and ability to see patterns as well as to facilitate language development.

example one

SourceEarlybird Kindergarten Mathematics – Kindergarten Textbook in Singapore

PCF Kindergarten Telok Blangah, Singapore

example two

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

example two

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Angela

Bala

Cheng Hao

50

872

example two

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Angela

Bala

Cheng Hao

822

1 unit = 822 ÷ 61 unit = 137Bala has 137 marbles.

600180

42

example two

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Angela

Bala

Cheng Hao

50

872y

y y y y

y

4y + y + (y + 50) = 872

6y + 50 = 872

6y = 872 – 50

y = 822 ÷ 6

y = 137

Angela

4y + y + (y + 50) = 872

Using a box to represent

known quantities.

Using a box to represent unknown

quantities.

Using a letter to represent

unknown quantities.

example three

SourceGrade 4 Lesson on Long Division in Keys Grade School, Manila

SourceGrade 4 Lesson on Long Division in Keys Grade School, Manila

481644816

4000 800

16

4

81

12

8

16

0

16

0

4

example four

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has ? toy cars.His friend has ? toy cars.They have ? toy cars altogether.

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has 10 toy cars.His friend has 12 toy cars.They have ? toy cars altogether.

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has 10 toy cars.His friend has 12 toy cars.They have ? toy cars altogether.

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has 121 toy cars.His friend has 74 toy cars.They have ? toy cars altogether.

121 74

?

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has 20 toy cars.His friend has 74 toy cars.They have ? toy cars altogether.

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has 100 toy cars.His friend has 74 toy cars.They have ? toy cars altogether.

Source2o Basico Lesson on Model Drawing in Escuela Republica de Guatemala, Chile

Hugo has ? toy cars.His friend has 74 toy cars.They have 100 toy cars altogether.

example five

SourceMy Pals Are Here! Maths – Grade 1 Textbook in Singapore

example six

Use five consecutive whole numbers so that the vertical sum is equal to the horizontal sum. Start with 1 to 5.

SourceResearch Lesson at a Professional Development Course in Singapore

Use five consecutive whole numbers so that the vertical sum is equal to the horizontal sum. Start with 1 to 5.

15

4

3 2 2 1 53

4

31 52

4

32

6

4 5 3 4 52

6

62 53

4

Princess Elizabeth Primary School, Singapore

24

6

3 5

Princess Elizabeth Primary School, Singapore

Use the digits 0 to 9 not more than once to make a correct multiplication sentence.

xexample seven

SourceTeacher Professional Development Course in Singapore

1 2x 56 0

4 3x 28 6

2 9x 38 7

1 5x 46 0

1 2x 78 4

1 5x 23 0

1 8x 23 6

1 8x 35 4

1 8x 47 2

1 4x 79 8

1 2x 89 6

responses

problem solving for

various instructional

goals

We have seen the use of problem solving to teach a basic concept or skill, to consolidate learning as well as to provide opportunities for students to apply what they know.

problem solving to

teach a new concept or

skill

PK – K

G 1

G 2

G 3G 4

PK – K

G 1

G 2

G 3G 4

visualization

visualization

metacognition

number sense

problem solving to

consolidate a skill or

concept

xreasoning

generalization

problem solving for

students to apply their knowledge

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Problem Solving in the Singapore Classrooms

Slides are available at

www.banhar.blogspot.com

Da Qiao Primary School, Singapore