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)

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 B1B2

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