teaching mathematicsfocusing on problem solving

Dr Yeap Ban HarMarshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

www.banhar.blogspot.comwww.banhar.com

Today’s discussion is based on lessons taken from a Singapore textbook series. The goal is to see how mathematics teaching can be made to focus on problem solving and how the lessons can be differentiated for struggling and advanced students.

Photographs of the session is available on Facebook

focusing on problem solving

mathematicsoffundamentalprinciplesteaching & learning

Revi

ew

concrete

pictorial

abstract

concrete

pictorial

abstract

variations

variations

variations

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

focusing on problem solving

exampleone

focusing on problem solving

Show 32 using base ten blocks.

Do 32 – 9 .

focusing on problem solving

Show 32 using base ten blocks.

Do 32 – 9 .

focusing on problem solving

focusing on problem solving

focusing on problem solving

focusing on problem solving

Show 32 using base ten blocks.

Do 32 – 9 .

focusing on problem solving

focusing on problem solving

exampletwo

focusing on problem solving

This piece of paper represents 1.

Divide it into four equal parts.

St Edward’s School, Vero Beach, Florida

focusing on problem solving

focusing on problem solving

Initial Concrete

Experience

Subsequent Pictorial

Representation

focusing on problem solving

Eventual Symbolic

Representation

focusing on problem solving

focusing on problem solving

examplethre

e

Fuchun Primary School, Singapore

focusing on problem solving

Ratio 2.8 3.0 3.1 3.2 3.3 3.5 3.8Frequency 1 3 5 7 18 4 1

Fuchun Primary School, Singapore

focusing on problem solving

focusing on problem solving

examplefour

focusing on problem solving

focusing on problem solving

examplefive

focusing on problem solving

focusing on problem solving

focusing on problem solving

examplesix

focusing on problem solving

Reference: My Pals Are Here! Maths

focusing on problem solving

Reference: Primary Mathematics (Standards Edition)

focusing on problem solving

Reference: Primary Mathematics (Standards Edition)

focusing on problem solving

examplesev

en

focusing on problem solving

Kyla

Jake $9

$28

?

?$28 – $9 = $19

Kyla has $19.

focusing on problem solving

apples

oranges 90

pears 15

38

apples

oranges 90

pears 15 23

apples

oranges ?

pears 15

90 + 15 = 1055 units

1 unit 105 ÷ 5 = 21

23

There were (21 + 21 + 23) apples, hence oranges.There were 44 oranges used.