Thi is Day 1 of a three-day professional development for teachers in Hawaii. Today, we focus on the fundamenatals - thinking and learning theories basic to Singapore Math. There was also an Open Lesson with Grade 4 students.

1. Professional Development for Singapore Math (Upper Grades) Yeap Ban Har banhar@sg.marshallcavendish.com Pearl City, Hawaii Day 1 8 August 2011 Presentations are available at www.banhar.blogspot.com

2. Professional Development for Singapore Math (Upper Grades) Day 1 Session 1 Open Lesson CPA Approach

3. Nanakuli Elementary School, Hawaii, USA

4. Nanakuli Elementary School, Hawaii, USA

5. Nanakuli Elementary School, Hawaii, USA

6. concrete pictorial abstract The CPA Approach is one of the fundamentals of Singapore Math. Nanakuli Elementary School, Hawaii, USA

7. Nanakuli Elementary School, Hawaii, USA

8. concrete The CPA Approach is one of the fundamentals of Singapore Math.

9. pictorial The CPA Approach is one of the fundamentals of Singapore Math.

10. pictorial / abstract 16 16 ÷ 4 The CPA Approach is one of the fundamentals of Singapore Math.

11. pictorial / abstract 16 3 x 4 The CPA Approach is one of the fundamentals of Singapore Math.

12. abstract 4 34×16 16 16 ÷ 4 The CPA Approach is one of the fundamentals of Singapore Math.

13. abstract 4 34×16 16 3 x 4 The CPA Approach is one of the fundamentals of Singapore Math.

14. Professional Development for Singapore Math (Upper Grades) Day 1 Session 2 Examples from Fractions CPA Approach

15. The Concept of Equal Parts in Fractions

16.  The Concept of Equal Parts in Fractions

18. 

20. conceptual understanding Another emphasis of Singapore Math is the focus on conceptual understanding.

21. Let’s learn some math…. What can be counted together i.e. added? What can’t?

24. “A curriculum as it develops should revisit these basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.” Jerome Bruner 1960 The Process of Education One feature of Singapore Math is the spiral approach.

25. Emphasis on Systematic Variation One feature of Singapore Math is the spiral approach and systematic variation.

29. This represents 1 156 = 116

30. This represents 1 76 =

31. This represents 1 76 = 116

32. Professional Development for Singapore Math (Upper Grades) Day 1 Session 3 Fraction Division CPA Approach