This was the presentation at Shinglee's New Syllabus Mathematics textbook launch.

1. d r y e a p b a n h a r
R E D E S I G N I N G T H E
S E C O N DA RY
M AT H E M AT I C S
C L A S S RO O M
T h e P r o b l e m - S o l v i n g
A p p r o a c h

2. d r y e a p b a n h a r
S l i d e s a r e a v a i l a b l e a t
w w w . b a n h a r . l o g s p o t . c o m

3. • key findings from Japanese research on features of
effective mathematics lessons
• different types of lessons can be taught using a
problem-solving approach
• providing students with enriching learning
experiences that equip them with competencies
useful not just for mathematics but beyond
• three-part lesson format

4. wha t
how
SINGAPORE MATHEMATICS
CURRICULUM
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5. FOCUS ON
p r o b l e m s o l v i n g
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6. p r o b l e m s o l v i n g

7. w w w . b a n h a r . b l o g s p o t . c o m

8. w w w . b a n h a r . b l o g s p o t . c o m

9. FOCUS ON
t h i n k i n g
S o u r c e : S i n g a p o r e E x a m i n a t i o n a n d A s s e s s m e n t B o a r d
Hong & Jeya Problem

10. S o u r c e : S i n g a p o r e E x a m i n a t i o n a n d A s s e s s m e n t B o a r d

11. Every minute Hong travelled 15 m more than Jeya.
Travel time = 240  15 = 16 min
Distance = 70 m x 16 = 700 m + 350 m + 70 m
= 1120 m
(a) Hong cycled 240 m more than Jeya.
(b) Jeya cycled 1120 m.

12. FOCUS ON
t h i n k i n g
w w w . b a n h a r . b l o g s p o t . c o m
Mathematics is “an excellent
vehicle for the development and
improvement of a person’s
intellectual competence”.
Ministry of Education Singapore 2006

13. 1992
Introduction of Problem-
Solving Curriculum
1997
Thinking Schools
Learning Nation
1982
Introduction of Singapore mathematics
textbooks as they are known today. 2001
Introduction of textbooks published by
private publishers and approved by
Ministry of Education.
2007
New editions of textbooks are
published with the introduction of the
revised curriculum.
Mathematics is “an excellent
vehicle for the development and
improvement of a person’s
intellectual competence”.
Ministry of Education Singapore 2006
2013
New editions of textbooks are
published with the revision of the
curriculum.

14. Competencies
for the 21st
Century

15. wha t
how
introduction
w w w . b a n h a r . b l o g s p o t . c o m
SINGAPORE MATHEMATICS
CURRICULUM

16. Elements of Problem-Solving Classrooms
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17. Elements of Problem-Solving Classrooms
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18. Elements of Problem-Solving Classrooms
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19. Elements of Problem-Solving Classrooms
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Lesson  Date:
x
y
x
2x

20. Anchor Tasks
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21. Anchor Tasks
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x
y
x
2x

22. Anchor Tasks
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23. 
k e y q u e s t i o n
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24. 
p o l i s h i n g p e b b l e s
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25. 
c o l l e c t i v e a h a !
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26. Extended
Engagement
with One
Task
Teach Less, Learn More
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27. Extended
Engagement
with One
Task
Teach Less, Learn More
w w w . b a n h a r . b l o g s p o t . c o m

28. Extended
Engagement
with One
Task
Teach Less, Learn More
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a b

29. Extended
Engagement
with One
Task
Teach Less, Learn More
w w w . b a n h a r . b l o g s p o t . c o m
a b
(a + b)2

30. Extended
Engagement
with One
Task
Teach Less, Learn More
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a b
(a + b)2
= b2 + …

31. Extended
Engagement
with One
Task
Teach Less, Learn More
w w w . b a n h a r . b l o g s p o t . c o m
a b
(a + b)2
= b2 + a2 + …

32. Extended
Engagement
with One
Task
Teach Less, Learn More
w w w . b a n h a r . b l o g s p o t . c o m
a b
(a + b)2
= b2 + a2 + ab + ab
= …

33. Extended
Engagement
with One
Task
Teach Less, Learn More
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34. effective mathematics lessons are based on an
anchor task
Teach Less, Learn More
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This is essentially teaching through problem solving.

35. effective mathematics lessons are based on an
anchor task
Teach Less, Learn More
w w w . b a n h a r . b l o g s p o t . c o m
How does an anchor task benefit struggling learners?
How does an anchor task benefit advanced learners?
differentiated
instruction

36. guided practice
independent
practice
teacher models
teacher scaffolds
independent work
Lesson Structure

37. anchor task
guided practice
independent practice
Lesson Structure
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38. anchor task
guided practice
independent practice
Instructional Model
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model
scaffold
observe | independent work

39. 
i n s t r u c t i o n b e t w e e n d e s k s
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40. 
s u m m i n g u p
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41. 
b o a r d w r i t i n g
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42. Lesson to develop concepts
Lesson to consolidate concepts
Lesson to apply concepts
Lesson Types
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43. Anchor Task for Consolidation-Type Lessons
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48. T h r e e T y p e s o f L e s s o n s
- D e v e l o p i n g c o n c e p t s
- C o n s o l i d a t i n g c o n c e p t s
- A p p l y i n g c o n c e p t s
T h r e e P a r t s t o A L e s s o n
- A n c h o r T a s k
- G u i d e d P r a c t i c e
- I n d e p e n d e n t P r a c t i c e
T h r e e I n s t r u c t i o n a l
P r a c t i c e
- M o d e l
- S c a f f o l d
- I n d e p e n d e n t