Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Seminar at Harvard Graduate School of Education 15 April 2010

2,123
views

Published on

Seminar at Harvard Graduate School of Education 15 April 2010

Seminar at Harvard Graduate School of Education 15 April 2010

Published in: Education

1 Like
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total Views
2,123
On Slideshare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
83
0
Likes
1
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. Theoretical Underpinnings of Singapore Math
Seminar at Harvard Graduate School of Education
Yeap Ban-Har, Ph.D.
National Institute of Education
Nanyang Technological University
Singapore
banhar.yeap@nie.edu.sg
• 2. Catholic High School (Primary)
• 3. introduction
Wellington Primary School
Lesson Study Problem
Wellington Primary School
Move 3 sticks to make 3 squares.
Move 3 sticks to make 3 squares.
Move 3 sticks to make 3 squares.
Move 3 sticks to make 2 squares.
Move 3 sticks to make 2 squares.
Move 3 sticks to make 2 squares.
• 10. A Problem from Singapore Grade 6 National Test
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?
• 11. 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
Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.
12
Jim
12
18
12
12
12
12
Ken
3 parts ïƒ  12 + 12 + 12 + 12 + 18 = 66
1 part ïƒ  22
Half of the sweets Ken bought = 22 + 12 = 34
So Ken bought 68 sweets.`
• 12. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
How many girls wore swimming goggles on that day?
A Problem from a Singapore Classroom
Fairfield Methodist Primary School
• 13.
• 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
How many girls wore swimming goggles on that day?
• 14. 88
34
54
• 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
How many girls wore swimming goggles on that day?
• 15. 34 â€“ 20 = 14
54 â€“ 34 = 20
34
54
• 16. 3 x 7 = 21
21 girls wear goggles.
A Curriculum That Helps Average Students Reach High Achievement
• 17. TIMSS 2007
Trends in International Mathematics and Science Studies
1995
2003
2007
38
41
38
High
70
74
73
Intermediate
89
92
91
Low
96
98
97
North Vista Primary School
• 18. TIMSS 2007
Trends in International Mathematics and Science Studies
Average
Indonesia
Thailand
Malaysia
Singapore
2
3
0
40
2
High
15
12
4
70
18
Intermediate
46
44
14
88
50
Low
75
66
48
97
82
Method Used in Singapore Textbooks
• 19. Beliefs
Interest
Appreciation
Confidence
Perseverance
Monitoring of oneâ€™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
• 20. Every Child Counts
• 21. effective
mathematics
teaching
BinaBangsa School, Indonesia
• 22. Primary Mathematics 1A
Pedagogical Principle:
Bruner
• 23. Number Bonds
PCF Kindergarten TelokBlangah
• 24. Number Bonds
PCF Kindergarten TelokBlangah
• 25. Bruner
The concrete ïƒ  pictorial ïƒ  abstract approach is used to help the majority of learners to develop strong foundation in mathematics.
Division
National Institute of Education
• 26. Division
Princess Elizabeth Primary School
• 27. My Pals Are Here! Mathematics 1B
• 28. Catholic High School (Primary)
• 29. mathz4kidz Learning Centre, Penang, Malaysia
brunerâ€™s theory
concrete
A lesson from Earlybird Kindergarten Mathematics
• 30. mathz4kidz Learning Centre, Penang, Malaysia
concrete
experiences
• 31. from
concrete
to
pictorial
mathz4kidz Learning Centre, Penang, Malaysia
• 32. from
pictorial
to
abstract
All Kids Are Intelligent Series
• 33. mathz4kidz Learning Centre, Penang, Malaysia
symbols
• 34. using
concrete
materials
Professional Development in AteneoGrade School, Manila, The Philippines
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
• 35. Primary Mathematics (Standards Edition) 2A
Pictorial Before Abstract
• 36. bruner
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
• 37. skempâ€™s
theory
conceptual
understanding
BinaBangsa School, Semarang, Indonesia
• 38. Keys Grade School, Manila, The Philippines
• 39. Keys Grade School, Manila, The Philippines
• 40. Skemp
Understanding in mathematics
relational
(conceptual)
instrumental
(procedural)
conventional
Teaching for conceptual understanding is given emphasis in Singapore Math.
Pedagogical Principle:
Skemp
Primary Mathematics Standards Edition Grade 6
• 41. Fraction Division
Primary Mathematics Standards Edition Grade 6
• 42. skemp
Scarsdale Middle School New York
• 43. Dienes
Dienes encouraged the use of variation in mathematics education â€“ perceptual variability and mathematical variability.
Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition
Primary Mathematics Standards Edition Grade 1
• 44. Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition Grade 1
• 45. Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition Grade 2
• 46. 1 h = 60 min
60 Ã· 4 = 15
15 x 3 = 45
Â¾ x 60 = 45
Primary Mathematics Standards Edition Grade 5
• 47. Mathematical Variation
16
Primary Mathematics Standards Edition Grade 5
• 48. 16
Mathematical Variation
30
Primary Mathematics
• 49. Mathematical Variation
Primary Mathematics Standards Edition Grade 2
• 50. Earlybird Kindergarten Mathematics
Standards Edition
dieneâ€™s
theory
of
variation
• 51. dieneâ€™s
theory
of
variation
• 52. dienes
Princess Elizabeth Primary School, Singapore
• 53. Emphasis on pictorial representation and systematic variation to enhance conceptual understanding
• 54. Fuchun Primary School, Singapore
interaction
Vygotskyâ€™s Theory
Children Learn in Social Situations
• 55. conclusion
PCF Kindergarten PasirRis
• 56. Mathematics is an excellent vehicle for the development and improvement of a personâ€™s intellectual competence ..
Ministry of Education 2006
DaQiao Primary School
• 57. Patterns
BinaBangsa School Bandung, Indonesia
• 58. Patterns
BinaBangsa School Bandung, Indonesia
• 59. Visualization
Yangzheng Primary School
• 60. Communication
PathlightSchool
• 61. Primary Mathematics Syllabus 2007
Primary 2
Wellington Primary School
• 62. Balestier Hill
Primary School
Fuchun Primary School
Primary Mathematics Syllabus 2007
• 63. Princess Elizabeth Primary School
• 64. â€œChildren are trulythe future of our nation. â€œ
Irving Harris
• 65. TEDS-M Elementary Teachers
Content Knowledge
TEDS-M Elementary Teachers
Pedagogical Content Knowledge
• 66. TEDS-M Middle School Teachers
Content Knowledge
TEDS-M Middle School Teachers
Pedagogical Content Knowledge