Download - Professional Development Session for Teachers in California by singaporemath.com April 2010
Theoretical Underpinnings of Singapore Math
Sheraton San Diego Mission Valley Hotel, San Diego CA
SingaporeMath.comProfessional Development
Please download from www.mathz4kidz.com
Yeap Ban-Har, Ph.D.National Institute of Education
Nanyang Technological University Singapore
[email protected] Qiao Primary School
Catholic High School (Primary)
overview
video of dice problem
solving problems
instructional models
Bruner’s theory
Skemp’s theory
Dienes’ theory
introduction
Wellington Primary School
Task
• Move 3 sticks to make 3 squares.
Lesson Study Problem Wellington Primary School
Task
• Move 3 sticks to make 3 squares.
Task
• Move 3 sticks to make 3 squares.
Task
• Move 3 sticks to make 2 squares.
Task
• Move 3 sticks to make 2 squares.
Task
• Move 3 sticks to make 2 squares.
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?
A Problem from Singapore Grade 6 National Test
chocolates
Jim
Ken
sweets
12
12
3 parts 12 + 12 + 12 + 12 + 18 = 661 part 22
Half of the sweets Ken bought = 22 + 12 = 34So Ken bought 68 sweets.`
18
12
12
12
12
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?
Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.
• 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
• 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?
34
88
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?
34
54 – 34 = 2034 – 20 = 14
54
3 x 7 = 21
21 girls wear goggles.
A Curriculum That Helps
Average Students
Reach High Achievement
Advanced
Intermediate
Low
High
1995
2003
2007
38 4138
70 7473
89 9291
96 9897
Grade 4
North Vista Primary School
TIMSS 2007Trends in International Mathematics and Science Studies
Advanced
Intermediate
Low
High
Aver
age
Indo
nesi
a
Thai
land
2 30
15 124
46 4414
75 6648
Grade 8
Method Used in Singapore Textbooks
TIMSS 2007Trends in International Mathematics and Science Studies
Mal
aysi
a
Sing
apor
e
402
7018
8850
9782
Mathematics Curriculum Framework
Mathematical Problem
Solving
Attitudes
Metacognition
Proc
esse
s
Concepts
SkillsNumericalAlgebraic
GeometricalStatistical
ProbabilisticAnalytical
Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling
Numerical calculationAlgebraic
manipulationSpatial visualization
Data analysisMeasurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinkingSelf-regulation of learning
BeliefsInterest
AppreciationConfidence
Perseverance
Every Child Counts
mathematicsteaching
effective
Bina Bangsa School, Indonesia
Pedagogical Principle:
Bruner
Primary Mathematics 1A
Number Bonds
PCF Kindergarten Telok Blangah
Number Bonds
PCF Kindergarten Telok Blangah
Bruner
The concrete pictorial abstract approach is used to help the majority of learners to develop strong foundation in mathematics.
National Institute of Education
Division
Princess Elizabeth Primary School
Division
Catholic High School (Primary)
bruner’s theoryconcrete
mathz4kidz Learning Centre, Penang, Malaysia
A lesson from Earlybird Kindergarten Mathematics
concreteexperiences
mathz4kidz Learning Centre, Penang, Malaysia
pictorialconcreteto
from
mathz4kidz Learning Centre, Penang, Malaysia
abstractpictorialto
from
All Kids Are Intelligent Series
symbols
mathz4kidz Learning Centre, Penang, Malaysia
concrete
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
usingmaterials
Professional Development in Ateneo Grade School, Manila, The Philippines
Pictorial Before Abstract
Primary Mathematics (Standards Edition) 2A
bruner
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
conceptual
Bina Bangsa School, Semarang, Indonesia
skemp’s
understandingtheory
Keys Grade School, Manila, The Philippines
Keys Grade School, Manila, The Philippines
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
Fraction Division
Primary Mathematics Standards Edition Grade 6
skemp
Scarsdale Middle School New York
Primary Mathematics Standards Edition
Pedagogical Principle:
Dienes
Dienes
Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability.
Primary Mathematics Standards Edition Grade 1
Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition Grade 1
Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition Grade 2
homeworkAre you able to see how these tasks are varied according to Dienes’ idea of mathematical variability?
16
How is Task 4 different from
Task 5?
Primary Mathematics Standards Edition Grade 5
16
30
What is the given in Task 5? What is the given in Task
6? Are these different?Primary Mathematics Standards Edition Grade 5
variationtheoryof
diene’s
Earlybird Kindergarten Mathematics Standards Edition
Can you see how Dienes’ idea is used in designing these tasks?
dienes
Princess Elizabeth Primary School, Singapore
Emphasis on pictorial
representation and systematic variation to
enhance conceptual
understanding
conclusion
PCF Kindergarten Pasir Ris
Instructional Models
• Coaching• Modeling• Providing• Explaning
Da Qiao Primary School
“Children are truly the future of our
nation. “Irving Harris
This presentation is based on part of one of Singapore pre-service mathematics method courses.
50% of Singapore elementary teachers are not college graduate and they are not trained to be specialists.
The TEDS-M findings provide some evidence into the effectiveness of this form of professional development.
TEDS-M Elementary TeachersContent Knowledge
TEDS-M Elementary TeachersPedagogical Content Knowledge
TEDS-M Middle School TeachersContent Knowledge
TEDS-M Middle School TeachersPedagogical Content Knowledge