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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.
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