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Professional Development in Singapore Math Focus on Conceptual Understanding E d g e m o n t U n i o n F r e e S c h o o l D i s t r i c t
Yeap Ban Har
Marshall Cavendish Institute Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
Seely Place Elementary School, New York
Seely Place Elementary School, New York
Learning
with concrete materials
www.banhar.blogspot.com
Anchor Task |
Show 2 equal parts.
Let’s Learn Fractions
SEED Institute, Singapore
Show 2
equal
parts
Edgemont School District, New York
Theoretical Underpinnings
Skemp
• relational, instrumental
Bruner
• concrete, pictorial, abstract
Vygotsky
• social interaction
Piaget
• assimilation, accommodation
Bruner CPA Approach
2,476 x 3
Greenville Elementary School, New York
The concrete materials show 2,476 = 2,000 + 400 + 70 + 6
Greenville Elementary School, New York
The concrete materials make students do partial multiplication
The concrete materials allow regrouping (18 = 10 + 8)
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
Assessment
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Bruner CPA Approach
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
Basic skill items
Conceptual items
Direct application
Unusual items
gra
de f
our
ma
them
atics
Singapore
South Korea
Hong Kong
Taiwan
Japan
Northern Ireland
Belgium
Finland
England
Russia
United States
International
43
39
37
34
30
24
10
12
18
13
13
4
78
80
80
74
70
59
50
49
49
47
47
28
94
97
96
93
93
86
89
85
78
82
81
69
99
100
99
99
99
96
99
98
93
97
96
90
606
605
602
591
585
562
549
545
542
542
541
500
adv high int low ave
gra
de e
ight
ma
them
atics
South Korea
Singapore
Taiwan
Hong Kong
Japan
Russia
Israel
Finland
United States
England
International
47
48
49
34
27
14
12
4
7
8
3
77
78
73
71
61
47
40
30
30
32
17
93
92
88
89
87
78
68
73
68
65
46
99
99
96
97
97
95
87
96
92
88
75
613
611
609
586
570
539
516
514
509
507
500
adva
nced
hig
h
inte
rmedia
te
low
average
Professional Development in Singapore Math Focus on Differentiated Instruction E d g e m o n t U n i o n F r e e S c h o o l D i s t r i c t
Yeap Ban Har
Marshall Cavendish Institute Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
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.
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