Singapore Math in Rotterdam 2Opleiding Singapore rekenspecialist

Review of Day 1What are some features of Singapore Math and its theoretical underpinnings.

On Day 2, we look at the focus on visualization and the model method.

Review of Day 1

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

Variations

Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.

Math in Focus 2A

Math in Focus 2A

Math in Focus 2A

Zoltan Dienes

The three lessons include mathematical variations within the same grade.

This is referred to as a spiral approach.

It is likely that a teacher will start this unit using the sticks. This is followed by the use of base ten blocks. Finally, non-proportionate materials such as coins are used. In each of these lessons, the teacher is likely to introduce the following five notations in turn – place value chart, expanded notation, number in numerals, number in words and the tens and ones notation.

The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons.

Place Value Chart Expanded Notation

Numerals WordsTens and Ones Notation Primary Mathematics

Zoltan Dienes

This lesson include perceptual variations. This is Dienes’ idea of multiple embodiment. The

mathematical concept is constant while the materials used to embody it are varied.

Jerome Bruner

Bruner advised teachers to use the CPA Approach in teaching mathematics.

Richard SkempSkemp distinguished between instrumental

understanding from relational understanding to encourage teachers to teach for conceptual

understanding.

conceptual

Bina Bangsa School, Semarang, Indonesia

skemp’s

understandingtheory

Example 2

Division in Other Grade Levels

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

Keys Grade School, Manila, The Philippines

Keys Grade School, Manila, The Philippines

The Bar Model Methodde strookmodel

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

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

Wellington Primary School

visualization

Primary Mathematics Standards Edition

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 cm

150 cm – 95 cm = 105 cm

There was an interesting discussion on this problem. There was an explanation that a + b + c = 19 cm. Then there was an assumption that a : b : c = 4 : 2 : 1 which was met with rebuttals such as there is no need to know a : b : c as well as the point that a : b : c can be determined by measuring or folding.  

The Bar Model Methodde strookmodel

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

Ali has 3 sweets. Billy has 5 sweets.How many sweets do they have altogether?

Ali

Billy

Ali has 3 sweets. Billy has 5 sweets.How many sweets do they have altogether?

Ali

Billy

Introduction

The focus is on the bar model method.

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Summary

The three basic situations are part-whole, comparison and before-after situations.

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

The class decided that this was

impossible. The teacher asked the class to change this to another

number to make the situation possible. We

discussed when it is 3, 4 and 5

times.

A student gave an incorrect solution

for the second part. The teacher asked students to write a question

for which this would be a correct

solution.

Summary

We discussed how to use students’ responses to make the lesson focus on depth. We also saw how a

problem can be modified to challenge learners.

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

School Assessment

women

men

School Assessment

women

men 12

45

School Assessment

women

men 12

45

6 6

?

women

men

Further Practice for Model Method

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping

Materials developed by Poon Yain Ping