Rajabhat Mahasarakham organised this workshop titled Transforming the Mathematics Classroom. The goal is to get teachers to think about teaching mathematics to encourage thinking, to develop visualization and to enhance the ability to observe patterns rather than mathematics as a subject that requires memorization, carrying out meaningless procedures and doing tedious computations.

1. MahasarakhamRajabhat University Transforming The Mathematics Classroom Dr Yeap Ban Har Principal Marshall Cavendish Institute Singapore Director for Curriculum & Professional Development Pathlight School Singapore 12 – 13 August 2010 Princess Elizabeth Primary School CHIJ Our Lady of Good Counsel Day 1 Catholic High School (Primary) Keys Grade School, Manila

2. Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Mathematics Curriculum Framework

3. Mathematics Problems in Singapore Primary 6 National Test

4. Problem John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?

5. Problem John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left? 150 cm – 19 cm x 5 = 150 cm – 95 cm = 55 cm 55 cm of the copper wire was left.

6. Problem In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ. Find MPN.

7. Problem In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ. Find MPN.

8. Problem In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ. Find MPN.

9. Problem In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ. Find MPN.

10. Problem In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ. Find MPN.

11. Why Teach Mathematics Mathematics is an “excellent vehicle to develop and improve a person’s intellectual competence”. Ministry of Education, Singapore 2006

12. Problem Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left. How many cookies did Mrs Hoon sell? 210

13. Jerome Bruner 210 Pictorial Representation Symbolic Representation

14. Problem Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?

15. Problem Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy? Chocolates Sweets Jim 12 Ken 12 18 12 12 12

16. Bar Model Methodin Singapore Textbooks

17. My Pals Are Here Mathematics

18. My Pals Are Here Mathematics

19. My Pals Are Here Mathematics

20. My Pals Are Here Mathematics

21. My Pals Are Here Mathematics

22. My Pals Are Here Mathematics

23. My Pals Are Here Mathematics

24. Lessons toDevelop New Concepts

25. Teaching Place Value Activity Combine your sets of digit cards. Shuffle the cards. Take turns to draw one card at a time. Place the card on your place value chart. Once you have placed the card in a position, you cannot change its position anymore. The winner is the one who makes the greatest number.

26. Place Value Key Concept: The value of digits depends on its place or position.

27. Teaching Division Keys Grade School, Manila

28. Teaching Division Keys Grade School, Manila

29. Lessons to Practise Skills

30. Practising Multiplication My number is 2! The product is 12. National Institute of Education

31. Practising Multiplication Use one set of the digit cards to fill in the five spaces. Make a correct multiplication sentence where a two-digit number multiplied by a 1-digit number gives a 2-digit product. Make as many multiplication sentences as you can. Are the products odd or even? x

32. Practicing Subtraction Activity 4 Think of a number larger than 10 000 but smaller than 10 million. Jumble its digits up to make another number. Find their difference. Write the difference on a piece of paper. Circle one digit. Add up the rest of the digits. Tell me the sum of the rest of the digits and I will tell you the digit you circled. Example 72 167 27 671 72 167 – 27 671 = 44 496 44 496 4 + 4 + 4 + 6 = 18 Tell me 18.

33. Lessons forProblem Solving

34. Problem Solving

35. Problem Solving Scarsdale School District, New York, USA Arrange cards numbered 1 to 10 so that the trick shown by the instructor can be done.

36. Teachers solved the problems in different ways. Scarsdale School District, New York, USA

37. Scarsdale School District, New York, USA The above is the solution. What if the cards used are numbered 1 to 9? 1 to 8? 1 to 7? 1 to 6? 1 to 5? 1 to 4?

38. Conceptual Understanding

39. Conceptual Understanding of Division of Whole Number by a Fraction

40. Conceptual Understanding of Multiplication of Fractions

41. Day 1