Plenary Lecture 1 on Fundamentals of Singapore Math. This MCI-WSU Singapore Math Institute is a collaboration between the US university and Marshall Cavendish Institute. 76 participants spent three days with three presenters learning about teaching of whole numbers and fractions.

1. Day 1 Program Opening Pedagogy Strand Fundamentals o Singapore Math Content Strand Counting & Place Value Classroom Sessions 1 Focus on Addition & Subtraction Classroom Sessions 2 Focus on Multiplication & Division Welcome

2. PLENARY LECTURE 1  YEAP BAN HAR Fundamentals of SINGAPORE MATH This lecture provides an overview of the fundamental features of Singapore Math. For teachers new to Singapore Math, it aims to provide a strong foundation to what makes mathematics accessible to all students, and helps students learn it in a way that is useful. For teachers experienced in teaching Singapore Math, the examples are chosen to give subtle insights into the approach. Slides are available at www.banhar.blogspot.com and Marshall Cavendish Institute’s Facebook Bukit View Primary School, Singapore

4. 88 11 units = 88 1 unit = 88 ÷ 11 = 8 6 units = 6 x 8 = 48 5 units = 5 x 8 = 40 The two numbers are 40 and 48.

5. emphasis on visualization One third of a number is equal to one half of another. Their sum is 80. Find the two numbers. 5 units = 80 1 unit = 80 ÷ 5 80 1 unit = 10 + 6 = 16 3 units = 3 x 16 The two numbers are 32 and 48. 3 units = 30 + 18 = 48 2 units = 2 x 16 = 32

6. emphasis on visualization One third of a number is 2 less than one half of another. Their sum is 84. Find the two numbers. 2 84

7. emphasis on visualization One third of a number is 2 less than one half of another. Their sum is 84. Find the two numbers. 2 80 84 2 2 5 units = 80 1 unit = 80 ÷ 5 = 10 + 6 = 16 3 units = 3 x 16 = 45 + 3 = 48 2 units = 2 x 16 = 32 The two numbers are 48 and 36.

8. 88 80 2 84 emphasis on variations

9. The importance of pictorial representations preceding abstract representations The importance of variations – mathematical and perceptual Bruner Dienes Singapore Math as we call it today is simply the result of systematic and consistent application of synthesis of established learning theories.

19. emphasis on generalization

20. emphasis on numbersense 96 80 16 3 x 16 = 30 + 18 96 = 80 + 16 3 x 16 = 32 + 16 3 x 16 = 45 + 3 4 96 8 16

21. school mathematics more than functional mathematics JFK International Airport, USA

23. generalization

24. number sense

25. metacognitionk i n g