international school saigon pearl
TRANSCRIPT
Seminar on Singapore Math
International SchoolSaigon PearlHo Chi Minh City
www.banhar.blogspot.com
Yeap Ban-Har, Ph.D.Singapore
[email protected] Qiao Primary School, Singapore
The examples used in this course are take n from Math in Focus The Singapore Approach unless otherwise specified.
Catholic High School (Primary), Singapore
introduction
Wellington Primary School, Singapore
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
Example 1
Example 2
John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left? 19 cm x 5 = 95 cm150 cm – 95 cm = 105 cm
Example 3Singapore Examinations & Assessment Board
105 cm of copper wire was left.
mathematicalproficiencies
Kilpatrick, Swafford & Findell 2001
• Procedural fluency• Conceptual reasoning• Strategic competence• Adaptive reasoning• Productive disposition
strands of
Philosophy of the Education System
thinking schoolslearning nationMinistry of Education 1997
Rationale for Teaching Mathematics
“an excellent vehiclefor the development and improvement
Ministry of Education 2006
of a person’sintellectual competence”
their understandingin a variety ofcomplex situations
mathz4kidz Learning Centre, Penang, Malaysia
This whole shape
stands for 1.
Trends inMathematics& Science Studiesapply
and knowledge
What does this stand
for?
Trends inMathematics& Science Study
explaintheir reasoningmathz4kidz Learning Centre, Penang, Malaysia
mathematicalliteracy
OECD Program for International Student Assessment (PISA)
… capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual’s life …
in early grades basics
Princess Elizabeth Primary School, Singapore
Development of
Number Sense
Number Bonds is emphasized prior to the learning of addition.
Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5.
Earlybird Kindergarten Mathematics Series
Number Bonds
PCF Telok Blangah Kindergarten, Singapore
One duck is big. Six ducklings are small.
PCF Telok Blangah Kindergarten, Singapore
PCF Telok Blangah Kindergarten, Singapore
PCF Telok Blangah Kindergarten, Singapore
PCF Telok Blangah Kindergarten, Singapore
Number Bonds
PCF Telok Blangah Kindergarten, Singapore
Number Bonds
PCF Telok Blangah Kindergarten, Singapore
Number Bonds
PCF Telok Blangah Kindergarten, Singapore
Basic Facts
Basic Facts
Basic Facts
Basic Facts
Basic Facts
Basic Facts
Primary Mathematics Standards Edition
National Institute of Education
mathematicsteachingeffective
Bina Bangsa School, Indonesia
Spiral Within and
Between Grades
mathematicsteachingeffective
Bina Bangsa School, Indonesia
Bruner
Bruner
The concrete pictorial abstract approach is used to help the majority of learners to develop strong foundation in mathematics.
National Institute of Education, Singapore
Division
Princess Elizabeth Primary School, Singapore
Division
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
Catholic High School (Primary), Singapore
Multiplication
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
skempScarsdale 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
mathematicsteachingeffective
Bina Bangsa School, Indonesia
Pedagogical Principle:
Dienes
Pedagogical Principle:
Dienes
Primary Mathematics Standards Edition
Pedagogical Principle:
Dienes
Dienes
Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability.
Primary Mathematics Series Standards Edition
variationtheoryof
diene’s
Earlybird Kindergarten Mathematics Series Standards Edition
Can you see how Dienes’ idea is used in designing these tasks?
dienesPrincess Elizabeth Primary School, Singapore
thinking problem solvingbruner’s cpa approachconceptual understanding
diene’s variations
Emphasis on pictorial
representation and systematic variation to
enhance conceptual
understanding
conclusion
PCF Kindergarten Pasir Ris, Singapore
Instructional Models
• Coaching• Modeling• Providing• Explaning
Da Qiao Primary School, Singapore
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?
Grade SixNational Test Item
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.
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
“Children are truly the future of our
nation. “Irving Harris