This document summarizes a professional development workshop on Singapore Math. It discusses focusing on conceptual understanding and using concrete materials to teach fractions and multiplication. It also covers formative assessment strategies like observation, interviews, and analyzing student work. International test score data is presented comparing countries' performance in 4th and 8th grade mathematics. The workshop emphasizes differentiated instruction for all students including advanced learners.

1. Professional Development in Singapore Math
Focus on Conceptual Understanding
Edgemont Union Free School District
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

2. Seely Place Elementary School, New York

4. Seely Place Elementary School, New York

5. Learning
with concrete materials
www.banhar.blogspot.com

6. Anchor Task |
Show 2 equal parts.

7. SEED Institute, Singapore
Let’s Learn Fractions
Show 2
equal
parts
Edgemont School District, New York

8. Theoretical Underpinnings
Skemp
• relational, instrumental
Bruner
• concrete, pictorial, abstract
Vygotsky
• social interaction
Piaget
• assimilation, accommodation

12. Greenville Elementary School, New York
2,476 x 3
Bruner
CPA Approach

13. Greenville Elementary School, New York
The concrete materials show
2,476 = 2,000 + 400 + 70 + 6
The concrete materials make
students do
partial multiplication
The concrete materials allow
regrouping (18 = 10 + 8)

14. Using Concrete Materials
They are used in tandem with
pictorial and symbolic
representations, not one after
another.
Avoid jargon and employ more
‘revoicing’ i.e. students’
language in early stages of
learning
Concrete material embodies the
essential ideas

15. Assessment
www.banhar.blogspot.com

18. Bruner
CPA Approach

23. Formative Assessment
Level
• Class
• Individual
Criteria
• Collect data to decide if a student
is approaching or has met or has
exceeded expectations
Strategies
• Observation
• Interview
• Written work

24. Basic skill items

25. Conceptual items

26. Direct application

27. Unusual items

28. adv
high
int
low
Singapore
606
43
78
94
99
South Korea
grade four mathematics
ave
605
39
80
97
100
Hong Kong
602
37
80
96
99
Taiwan
591
34
74
93
99
Japan
585
30
70
93
99
Northern Ireland
562
24
59
86
96
Belgium
549
10
50
89
99
Finland
545
12
49
85
98
England
542
18
49
78
93
Russia
542
13
47
82
97
United States
541
13
47
81
96
International
500
4
28
69
90

29. advanced
high
intermediate
low
South Korea
grade eight mathematics
average
613
47
77
93
99
Singapore
611
48
78
92
99
Taiwan
609
49
73
88
96
Hong Kong
586
34
71
89
97
Japan
570
27
61
87
97
Russia
539
14
47
78
95
Israel
516
12
40
68
87
Finland
514
4
30
73
96
United States
509
7
30
68
92
England
507
8
32
65
88
International
500
3
17
46
75

30. Professional Development in Singapore Math
Focus on Differentiated Instruction
Edgemont Union Free School District
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

31. Advanced Learners
• Make a story
• Give another way. Give an
original way.
• Explain to a friend. Write an
explanation. Draw a diagram
to show.
• My friend has an idea. What
do you think of it?
Singapore Math adopts
enrichment model and not
acceleration model.