The ABCDs of Singapore MathLower School Professional Development

St Edward’s SchoolVero Beach FL

www.banhar.blogspot.com

Yeap Ban-Har, Ph.D.Singapore

banhar.yeap@pathlight.org.sg

Da Qiao Primary School

Catholic High School (Primary)

introduction

Wellington Primary School

Classroom Task

• Move 3 sticks to make 3 squares.

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 2 squares.

• Move 3 sticks to make 2 squares.

• Move 3 sticks to make 2 squares.

• 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?

Teacher-Constructed Test Item

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.

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

Philosophy of the Education System

thinking schoolslearning nation

Ministry of Education 1997

their understandingin a variety of

complex situations

mathz4kidz Learning Centre, Penang, Malaysia

This whole shape

stands for 1.

Trends inMathematics& Science Studies

applyand 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 …

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

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

thinking problem solving

bruner’s cpa approachconceptual understanding

diene’s variations

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