singapore mathematics workshop on 8 july 2011 (not presented)

11

Singapore Mathematics Singapore Mathematics FrameworkFramework

22

Mathematical Problem Mathematical Problem SolvingSolving

1.1. SkillsSkills

2.2. ConceptsConcepts

3.3. ProcessProcess

4.4. AttitudesAttitudes

5.5. MetacognitionMetacognition

33

1) Skills1) Skills

Numerical CalculationNumerical Calculation Algebraic ManipulationAlgebraic Manipulation Spatial VisualisationSpatial Visualisation Data AnalysisData Analysis MeasurementMeasurement Use of Mathematical ToolsUse of Mathematical Tools EstimateEstimate

44

2) Concepts2) Concepts

NumericalNumerical AlgebraicAlgebraic GeometricalGeometrical StatisticalStatistical ProbabilityProbability AnalyticalAnalytical

55

3) Process3) Process

ReasoningReasoning CommunicationCommunication ConnectionConnection

66

4) Attitude4) Attitude

BeliefsBeliefs InterestInterest AppreciationAppreciation ConfidenceConfidence PerserverancePerserverance

77

5) Metacognition5) Metacognition

Monitoring of one’s thinkingMonitoring of one’s thinking Self regulation of learningSelf regulation of learning

88

Skills (Numerical Calculation)Skills (Numerical Calculation)

AdditionAddition

99

Skills (Numerical Calculation)Skills (Numerical Calculation)

SubtractionSubtraction

1010

Skills (Numerical Calculation)Skills (Numerical Calculation)

MultiplicationMultiplication

1111

Skills (Numerical Calculation)Skills (Numerical Calculation)

DivisionDivision

1212

Skills (Algebraic Manipulation)Skills (Algebraic Manipulation)

ExampleExample

12a x 812a x 8 == (10a + 2a) x (10a + 2a) x 88

== 80a + 16a80a + 16a

== 96a96a

1313

Skills (Spatial Visualisation)Skills (Spatial Visualisation)

Using ModelUsing Model

1414

Skills (Data Analysis)Skills (Data Analysis)

Table & GraphTable & Graph

ManipulativesManipulatives

1515

Skills (Measurement)Skills (Measurement)

3m + 3cm3m + 3cm== 300cm + 3cm300cm + 3cm

== 303cm303cm

1616

Skills (Use of Mathematical Skills (Use of Mathematical tools)tools)

1717

Skills (Estimation)Skills (Estimation)

50 49 = 7

1818

Concepts (Numerical)Concepts (Numerical)

AdditionAddition

1919

Concepts (Numerical)Concepts (Numerical)

SubtractionSubtraction

2020

Concepts (Numerical)Concepts (Numerical)

MultiplicationMultiplication

2121

Concepts (Numerical)Concepts (Numerical)

DivisionDivision

2222

Concepts (Algebraic)Concepts (Algebraic)

2323

Concepts (Geometric)Concepts (Geometric)

2424

Concepts (Statistical)Concepts (Statistical)

It is a science of It is a science of collecting, collecting, organising, organising, interpreting and interpreting and analysing data.analysing data. Collection of DataCollection of Data

Using a Using a questionnairequestionnaire

Through Through observationobservation

Through Through interviewinterview

By measuringBy measuring Using electronic Using electronic

means and the means and the internetinternet

The data collected The data collected can be organised can be organised in the form of table in the form of table and then and then presented in presented in graphical forms graphical forms such assuch as PictogramPictogram Bar graphBar graph Pie chartsPie charts Line graphLine graph histogramhistogram

2525

Concepts (Statistics – Concepts (Statistics – Average)Average)

2626

Concepts (Probability)Concepts (Probability)

Find the Find the probability probability of each of of each of the the followingfollowing

Obtaining a tail by Obtaining a tail by tossing a fair coin.tossing a fair coin.

Obtaining a prime Obtaining a prime number by tossing number by tossing a six-sided fair die.a six-sided fair die.

Choosing Choosing randomly a correct randomly a correct answer from a 4-answer from a 4-choice question.choice question.

2727

Concepts (Analytical)Concepts (Analytical)

2828

Selected Grade 1 QuestionsSelected Grade 1 Questions

2929

WebsitesWebsites

http://www.thesingaporemaths.com/http://www.thesingaporemaths.com/ http://www.singaporemath.com/Defahttp://www.singaporemath.com/Defa

ult.aspult.asp http://www.edcrisch.com/edcrisch/wehttp://www.edcrisch.com/edcrisch/we

b/Index.aspb/Index.asp http://www.moe.edu.sg/http://www.moe.edu.sg/ http://www.testpapers.com.sg/index.http://www.testpapers.com.sg/index.

htmlhtml http://www.sgbox.com/http://www.sgbox.com/ http://http://

www.topschoolexampapers.comwww.topschoolexampapers.com//