## Fundamental Idea

Dr Yeap talks about one of the fundamental ideas in mathematics: that items can only be counted, added, and subtracted if they have the same nouns. He uses a simple example with concrete objects, chocolates and glue sticks to illustrate the point and then shows how it relates to column addition and the addition of fractions.

## Number Bonds

Dr. Yeap explains how young children can use concrete materials and later use pictorial representations as number bonds. Number bonds represent how numbers can be split up into their component parts. Children can explore number bonds using a variety of concrete materials, such as counters with containers and ten frames or with symbols.

## Subtraction

Dr. Yeap explains how standard column subtraction can be taught meaningfully by using children's knowledge of number bonds. Once children can explain how numbers can be split into their component parts, they can adapt their understanding to the conventional column subtraction method.

## Mental Calculations

Dr. Yeap discusses how children can develop an ability to calculate the four operations (addition, subtraction, multiplication and division) in their heads without the use of paper and pencil or calculators.

## Multiplication

Dr. Yeap discusses how children can learn their times tables meaningfully by using visualisation and other strategies.

## Long Division

Dr Yeap discusses how children can learn to do long division meaningfully by first using concrete apparatus, such as base-10 materials, to perform the operations. They can then explore how this idea is represented in the long division algorithm.

## Bar Model 1

Dr. Yeap discusses how diagrams can be used to represent a situation in a problem: such as rectangles representing (unknown) quantities. This method of visualising problems is known as the bar model.

## Bar Model 2

Dr. Yeap gives another example of the bar model: how diagrams can be used to represent situations in a problem.

Dr Yeap Ban Har is the Director of Curriculum and Professional Development at Pathlight School, an autism-oriented K-10 school in Singapore. An experienced educator, Ban Har spent ten years at the National Institute of Education, Singapore, where he was involved in several funded research programmes in mathematics education, and where he taught a range of teacher education courses, including Problem-Solving Heuristics in Primary Mathematics and Curriculum Studies in Primary and Secondary Maths. He works regularly in collaboration with the Curriculum Planning and Development Division of the Ministry of Education in Singapore, and he was part of a team which reviewed the Singapore Maths curriculum for the revised 2013 syllabus.

He continues to teach courses at tertiary institutions such as the National Institute of Education (Singapore), Wheelock College (Boston) and Rajabhat Maha Sarakham University (Thailand). He also sits on the advisory board of the SEED Institute and several schools in Singapore and Asia.

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