Yeap Ban Harbanhar.yeap@pathlight.org.sg

Session A4Teaching Kindergarten

and First Grade Math

PCF Kindergarten Telok Blangah Singapore

Princess Elizabeth Primary School Singapore

National Conference

on Singapore

Math Strategies Las Vegas

Slides are available at www.banhar.blogspot.com

PCF Kindergarten Telok Blangah Singapore In Singapore, formal education starts at Primary 1 (Grade 1). Compulsory education is for the first six grades.

overview

• Theories Behind Singapore Math– Jerome Bruner– Zoltan Dienes– Richard Skemp

• Big Ideas in Early Mathematics– Number Bonds & Basic Facts– Visualization– Connections– Communication

PCF Kindergarten Telok Blangah Singapore

introduction

PART 2

PCF Kindergarten Telok Blangah Singapore

The formal education system in Singapore is

uniform with only public schools, a national curriculum, and a single teacher-training institute.

The gaps among children in the first year of primary school are large depending on the kindergarten education they have received. Some children have not attended kindergartens.

St Anthony’s Canossian Primary School, Singapore

Conscious effort not to put the disadvantage children in a position of greater disadvantage.

Textbooks are written for learners of the language, yet challenging for advanced learners.

My Pals Are Here! Mathematics 1

Textbooks are also written simply so that non-specialist teachers can understand the mathematics they are teaching. Hopefully, it is not complicated to put the less educated parents off helping their kids. Children bring their books home every day.

My Pals Are Here! Mathematics 1

Since 2005, Grade 1 and Grade 2 teachers have been asked to adopt the SEED Approach. SEED is the acronym for Strategies for Effective Engagement and Development.

More holistic assessment approaches are favored over written tests.

Hands-on learning have been given added emphasis.

Catholic High School (Primary), Singapore

Further efforts to strengthen primary education is evident. A high-profile committee reviewed primary education in Singapore and made suggestions this stage of education can be further improved.

It recommended, among other things, pedagogies that engage students better.• Learning by Doing• Learning through Inquiry• Learning by Collaborating• Learning by Reflecting• Learning in and about the

Real World

big ideas in early mathematicsin kindergarten through grade one

PART 2

PCF Kindergarten Telok Blangah Singapore

Number Bonds is emphasized prior to the learning of addition.

Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5.

Number Bonds

Earlybird Kindergarten Mathematics

PCF Kindergarten Telok Blangah Singapore

One duck is big. Six ducklings are small.

PCF Kindergarten Telok Blangah Singapore

PCF Kindergarten Telok Blangah Singapore

PCF Kindergarten Telok Blangah Singapore

PCF Kindergarten Telok Blangah Singapore

PCF Kindergarten Telok Blangah Singapore

Number Bonds continues to receive attention in Grade 1.

My Pals Are Here! Mathematics 1

concrete pictorial abstractBRUNER’S THEORY

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PCF Kindergarten Telok Blangah Singapore

Addition Facts are given emphasis in the first six months of grade one.

The children learn it in stages as the textbooks distinguished between Numbers to 10, Numbers to 20, Numbers to 40 and Numbers to 100.

Count On and Count All are used in Numbers to 10.

Kin

derg

arte

n Te

xtbo

ok

Addition Facts

While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20.

Prin

cess

Eliz

abet

h P

rimar

y S

choo

l

Addition Facts & Number Sense

7 + 8

7 + 8

mathematical variationDIENES’ THEORY

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PCF Kindergarten Telok Blangah Singapore

perceptual variationDIENES’ THEORY

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PCF Kindergarten Telok Blangah Singapore

Example on Place Value

Example on Number Bonds

Why are the illustrations in three consecutive tasks are as such?

spiral approach

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PCF Kindergarten Telok Blangah Singapore

An Example

Study how students get to revisit ideas of number bonds as the deal

with number bonds for 6 through 9.

spiral approach

PART 2

PCF Kindergarten Telok Blangah Singapore

Between Grades: Division

• Primary 1– without symbol

• Primary 2– with symbol, no remainder

• Primary 3– with symbol, with remainder– long division to 3-digit

• Primary 4– long division to 4-digit

• Primary 5– include continuous quantities

Within Grade: Whole Numbers

• Number to 10• Numbers to 20• Numbers to 40• Numbers to 100

Within each unit, numbers, place value, comparing, adding and subtracting are dealt with.

This allows students to review materials as they learn new ideas.

spiral approach

PART 2

PCF Kindergarten Telok Blangah Singapore

Whole Numbers in Grade 1

• Basic Review– Children count shapes in the unit on Shapes

• Review to Extend Knowledge– Children learn another use of whole numbers in

the unit on Ordinal Numbers• Pre-requisite

– Children apply counting, comparing, adding and subtracting in the unit on Picture Graphs

conceptual understandingSKEMP’S THEORY

PART 2

PCF Kindergarten Telok Blangah Singapore

17 + 19

16 + 20

Number Sense

Looking for Patterns is introduced through exploration with Shapes. Subsequently, this is done using numbers – in a more abstract context.

Connections

Princess E

lizabeth Prim

ary School

Make Connections to Generalize

In the learning of Numbers to 10, children use square tiles to form patterns of 3 and patterns of 4, for instance.

Illustrations in textbooks were also carefully varied to develop this competency.

Visualization

Connections

Princess E

lizabeth Prim

ary School

Articulating one’s thoughts orally, at first, and in written forms using words, pictures, diagrams and symbols is important.

Communication

Maris S

tella High (P

rimary) S

chool