MATHEMATICS Nov / Dec 2006 Brought to you by: Our dedicated team of trainers A.L. Khoo, BSc. (UM) S.S. Tee, MEd. BSc. (UTM) P.Y. Loke, MSc. BSc. (USM)

MATHEMATICSNov / Dec 2006

Brought to you by:Our dedicated team of trainersA.L. Khoo, BSc. (UM)S.S. Tee, MEd. BSc. (UTM)P.Y. Loke, MSc. BSc. (USM)

INTRODUCTION

Why learn math? Solve problems and make sound

decisions Explain how we solve a problem and why

do we make a particular decision (Ministry of Education, Ontario)

INTRODUCTION

When is the best time to start? “Research in recent decades shows that

preschoolers have more potential to develop "informal math knowledge" than was previously realized.”

(Art Baroody, a professor of education)

INTRODUCTION

How to learn math effectively? Concrete-to-representational-to-abstract

(real-to-abstract) Able to perform the math skills and truly

understand math concepts at the abstract level

Help passive learners to make meaningful connections

INTRODUCTION

• How computer helps in learning math? Math computer programs demonstrate

concepts, instruct, and remediate student errors and misunderstandings from preschool through college.

Useful for teaching basic skills in an entertaining way. (Access Center, U.S. Department of Education)

1A: NUMBER 1-5

Concrete: Teacher asks:

Which part of your body only has ‘one’? Children show nose and mouth (guided). Children watch story of 1 from the

software.

1A: NUMBER 1-5

Representational (semi-concrete) Game: Passing the chips.

Teacher pastes numeral 1 on the board. Children pass a few chips (different quantity of dots and objects) around. When the music stops, the children with the chip of 1 dot or 1 object need to paste the chip on the board.

1A: NUMBER 1-5

Abstract Teacher draws a few circles on the floor,

and writes a number in each circle. Children must stand inside the correct circle when a number is called.

1A: NUMBER BONDING Concrete

Teacher puts two objects on a table. Two children have to take all the objects. Each child must take at least one. Teacher shows the number of objects that each child has.

Activity: give other concrete examples of how teacher may teach number bonding in the classroom.

1A: COMPARISON

Activity Teacher arranges six chairs as below:

Teacher gets five children to sit on the first set of chairs, while two children sit on the second set. Children guess which group has many children.

1A: SHAPES

Concrete Teacher introduces different shapes from

real objects. Clock Pencil box Square notepad, etc

Children take turns to feel the shapes. Blindfold the children to guess the shape

by feeling the objects.

1A: SHAPES

Representational Teacher draws shapes on a manila

cardboard and cut out the shapes. Children feel two-dimensional shapes. Children name the shapes.

Concrete Children bring some colourful clothes

from home. Introduce colours. Categorise the clothes

according to the colours. Ask questions.

1A: COLOURS

1A: CONDITION CORRESPONDENCE

Concrete Teacher gets the children to show a few things

Bags Shirts Books, etc

Then, get the children look for things of different colours Blue bag Red shirt Yellow book, etc

2A: NUMBER 0-10

Concrete Materials: cups, plates, forks and spoons. Introduce quantity of ‘1’ for cup, plate,

fork and spoon. Is this one spoon? No, it isn’t. (show 2

spoons) Is this one spoon? Yes, it is. (show 1

spoon)

2A: NUMBER 0-10

Representational Materials: 2 sets of number flash cards Group children in pairs Teacher shows a dot card One child will say the number, the

partner will look for the correct number card

2A: NUMBER 0-10

Abstract Think of an activity that can evaluate the

understanding of the number concept.

Get children to get anything from the classroom that have the quantity of 5.

2A: NUMBER BONDING

Concrete Materials: counters, number chips,

board. A

B1 B2

2A: NUMBER BONDING

Representational materials: number chips (group), dot

chips (each child 1) Teacher calls two numbers. Children find partner. Get the number

chip (answer).

2A: ADDITION

Concrete Describe a situation where children are

able to imagine. Incorporate concrete materials in your story.

Introduce ‘+’ after children understand the situation.

2A: ADDITION

Representational Software

Abstract Add by using number bonding.

2A: SUBTRACTION Concrete

Materials: 2 balls Describes a situation. Children act it out.

Representational Software

Abstract Subtract by using number bonding.

3A: PLACE VALUE

Start with exchange game

Situation: You have come to a planet called Zac. People in the planet use blue chips for trading. But you only have red chips in your pocket! Luckily, you can exchange your red chips to blue chips at Zac Bank. You can exchange three red chips with a blue chip.

3A: PLACE VALUE Exchange game 2 Material: red and blue chips, place value

mat End of the lesson, get children to think:

How many red chips they need to get one blue chip?

How many blue chips they can get if you have 10 red chips? (etc)

One blue chip is equal to ____ red chips? Ten red chips is equal to ____blue chips?

3A: ADDITION

<10 Counting on from one addend Count by moving some objects from one

addend to another Use known facts (number bonding)

>10 Vertical addition Use known facts (number bonding)

3A: SUBTRACTION

Take away objects and then count to subtract

Subtract by ‘counting up’ from one addend

Use known facts (number bonding) Vertical subtraction

3A: MONEY

Human Wave (Counting in tens ) Shopping in the supermarket