The final plenary lecture is on helping the average and struggling learners.

1. Day 3 Program Pedagogy Strand Helping the Average and Low- Achieving Students Learn Mathematics Content Strand Fractions Classroom Sessions 1 Fractions Classroom Sessions 2 Mental Strategies / Bar Model Institute Closes Day 3

2. PLENARY LECTURE 3  YEAP BAN HAR Helping The Average and Low-Achieving Learners LEARN MATHEMATICS Slides are available at www.banhar.blogspot.com and Marshall Cavendish Institute’s Facebook

4. “Un plan de estudios de la manera que se desarrolla debe revisar estas ideas básicas en varias ocasiones, construyéndose sobre ellos hasta que el estudiante ha comprendido todo el aparato formal que conllevan”. (Bruner 1960 en El Proceso de la Educación). . “A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.” (Bruner 1960 in The Process of Education).

5. TIMSS Trends in International Mathematics and Science Studies Grade 4 2003 Grade 8 2007 Grade 4 1995 Grade 8 1999 38 40 Advanced 38 42 73 70 High 70 77 91 88 Intermediate 89 94 97 97 Low 96 99 Balestier Hill Primary School, Singapore

6. TIMSS 2007 Trends in International Mathematics and Science Studies Indonesia Thailand Malaysia Singapore International Grade 8 Advanced 2 3 0 40 2 High 15 12 4 70 18 Intermediate 46 44 14 88 50 Low 75 66 48 97 82 Sembawang Secondary School, Singapore

7. TIMSS 2007 Trends in International Mathematics and Science Studies USA MA MN International Singapore Grade 4 Advanced 5 22 10 18 41 High 26 63 40 55 72 Intermediate 67 92 77 85 92 Low 90 99 97 97 98 St Edwards School, Florida, USA

8. TIMSS 2007 Trends in International Mathematics and Science Studies USA MA MN International Singapore Grade 8 Advanced 2 16 6 8 40 High 15 52 31 41 70 Intermediate 46 82 67 81 88 Low 75 95 92 97 97

9. TIMSS 2007 Trends in International Mathematics and Science Studies USA MA MN International Singapore Grade 4 Advanced 2 22 10 18 40 High 15 63 40 55 70 Intermediate 46 92 77 85 88 Low 75 99 97 97 97 St Edwards School, Florida, USA

10. TIMSS 2007 Trends in International Mathematics and Science Studies USA MA MN International Singapore Grade 4 Advanced 2 22 10 18 40 High 15 63 40 55 70 Intermediate 46 92 77 85 88 Low 75 99 97 97 97 St Edwards School, Florida, USA

11. At Entry Point

12. Globe Academy, London, UK

13. Building Confidence

14. Globe Academy, London, UK Building Students’ Capacity to Learn Concrete Materials  Independence

15. Globe Academy, London, UK

16. Globe Academy, London, UK Building Teachers’ Capacity to Observe Observation  Conversation

17. Learning Support Program in Singapore Princess Elizabeth School, Singapore

18. At Intermediate Point

19. Globe Academy, London, UK

20. Concrete, Visual Approach Globe Academy, London, UK

21. 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. King Solomon Academy, London, UK

22. Foundation Mathematics Program in Singapore Pathlight School, Singapore

23. Pathlight School, Singapore High Expectations

24. Bukit View Primary School, Singapore

25. Pathlight School, Singapore

26. Pathlight School, Singapore

27. Pathlight School, Singapore

28. The Importance of Concrete, Visual Approach. In this lesson study, the construction of model was done in a concrete manner but the calculation was not. Observe the effects on students who were not entirely successful.

31. From a Classroom Learning Session Pears and apples costs the same. The total cost of 2 apples and 5 pears is $5.60. Find the cost of each fruit. Cost of pears $5.60 Cost of apples

32. From a Classroom Learning Session A pear costs twice as much as an apple. The total cost of 2 apples and 5 pears is $7.20. Find the cost of each fruit. Cost of pears $7.20 Cost of apples

33. From a Classroom Learning Session 2 pears cost as much as 3 apples. The total cost of 2 apples and 5 pears is $5.70. Find the cost of each fruit. Cost of pears $5.70 Cost of apples

34. From a Classroom Learning Session 2 pears cost as much as 3 apples. The total cost of 2 apples and 5 pears is $5.70. Find the cost of each fruit. Cost of pears $5.70 Cost of apples 19 units = $5.70 1 unit = $5.70 ÷ 19 = $0.3  An apple costs 60 cents and a pear cost 90 cents.