
Teaching Mathematics
Foundations to Middle Years
OUP Australia and New Zealand (Publisher)
2nd Edition
Published on 6. November 2015
Book
Paperback/Softback
800 pages
978-0-19-552382-9 (ISBN)
Description
Teaching Mathematics: Foundations to Middle Years connects readers to the bigger picture of mathematics. This comprehensive textbook designed to help pre-service teachers gradually build mathematical knowledge and become confident about teaching the subject to a range of age groups, in diverse learning environments. Spanning Foundations to 9 mathematics curriculum, the books unique structure explores the different stages of how children learn maths and how
to teach maths, before drilling down to specific strands and skills by age group.
Updated to draw on the revised Australian Curriculum, the second edition is rich with student work examples, practical activities and a wealth of teaching and learning tools to ensure pre-service and practising educators feel positive about mathematics and their role in teaching it.
to teach maths, before drilling down to specific strands and skills by age group.
Updated to draw on the revised Australian Curriculum, the second edition is rich with student work examples, practical activities and a wealth of teaching and learning tools to ensure pre-service and practising educators feel positive about mathematics and their role in teaching it.
More details
Edition
2nd Revised edition
Language
English
Place of publication
Melbourne
Australia
Publishing group
Oxford University Press Australia
Target group
Professional and scholarly
College/higher education
Edition type
Revised edition
Illustrations
b/w illus.
Dimensions
Height: 249 mm
Width: 204 mm
Thickness: 27 mm
Weight
1450 gr
ISBN-13
978-0-19-552382-9 (9780195523829)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Dianne Siemon is a Professor of Mathematics Education in the School of Education at RMIT University
Kim Beswick is a Professor in mathematics education at the University of Tasmania
Kathy Brady is the Head of the Student Learning Centre and a mathematics and numeracy educator at Flinders University
Julie Clark is an Associate Professor in mathematics education in the School of Education at Flinders University
Rhonda Faragher is a Senior Lecturer in the Faculty of Education and Arts at the Australian Catholic University (Brisbane)
Elizabeth Warren is a Professor in Mathematics Education at the Australian Catholic University (Brisbane)
Kim Beswick is a Professor in mathematics education at the University of Tasmania
Kathy Brady is the Head of the Student Learning Centre and a mathematics and numeracy educator at Flinders University
Julie Clark is an Associate Professor in mathematics education in the School of Education at Flinders University
Rhonda Faragher is a Senior Lecturer in the Faculty of Education and Arts at the Australian Catholic University (Brisbane)
Elizabeth Warren is a Professor in Mathematics Education at the Australian Catholic University (Brisbane)
Author
ProfessorProfessor, RMIT University
ProfessorProfessor, University of Tasmania
Head, Student Learning CentreHead, Student Learning Centre, Flinders University
Associate ProfessorAssociate Professor, Flinders University
Senior LecturerSenior Lecturer, Australian Catholic University
ProfessorProfessor, Australian Catholic University
Content
Part 1: Setting the Scene1. Understanding School MathematicsIntroductionWhat is mathematics?Goals of school mathematicsAffordances and constraintsConclusion2. Learning MathematicsIntroductionWhat does it mean to learn mathematics?Learning and understanding mathematicsDeveloping your own theory of mathematics learning3. Teaching MathematicsIntroductionWhat does it mean to teach mathematics?Connections among beliefsHow can we know we are teaching?Knowledge for teaching mathematicsEffective mathematics teachingPart 2: Understanding the Challenges and Opportunities4. Thinking MathematicallyLearning and doing mathematicsMaking a start with mathematical thinkingGeneral processes for problem solving and reasoningHelping learners to think mathematicallyConclusion5. Communicating MathematicallyIntroductionThe language of mathematicsLanguage and cultureCommunicating in the mathematics classroomConclusion6. Representing MathematicallyWhat are mathematical representations?Traditional representationsThe importance of mathematical language and recordingUsing representations to build abstract thinkingChoosing and using materials and modelsChoosing materials and models for the classroomMulti-representational learning environmentsConclusion7. Assessing and ReportingAssessment is about testing, right?Assessment of learningAssessment for learningReportingConclusion8. Understanding DiversityWho are diverse learners?Language of diversityDiversifying the curriculumSupporting diverse learnersConclusionPart 3: Exploring the Big Ideas in Mathematics9. Numeracy in the CurriculumWhat is numeracy?Numeracy across the curriculumCritical numeracyConclusion10. Developing a Sense of Number and AlgebraUnderstanding number senseNumber sense in practiceDeveloping a sense of numberConclusion11. Developing a Sense of Measurement and GeometryLinking measurement and geometryWhat is measurement?Developing measurement senseGeometrySpatial senseHow geometry is learnedConclusion12. Developing a Sense of Statistics and ProbabilityIntroductionStatistical literacyWhat is statistics?What is probability?ConclusionPart 4: Laying the Basis for F-4 Mathematics13. Algebraic Thinking: F-4What is pattern and structure?Why is pattern and structure important?Early algebraic thinkingFunctional thinkingConclusion14. Number Ideas and Strategies: F-2The origins of numberResearch on early number learningPlaying with numberThe numbers 0 to 10A sense of numbers beyond 10Scaffolding solution strategiesConclusion15. Place Value: F-4Prerequisite ideas and strategiesUnderstanding tens and onesIntroducing three-digit numerationDeveloping four-digit numerationExtending to tens of thousands and beyondConclusion16. Additive Thinking: F-4Why additive thinking?The development of additive thinkingContexts for addition and subtractionAdditive solution strategiesProblem solvingConclusion17. Multiplicative Thinking: F-4IntroductionWhat is multiplicative thinking?Why is multiplicative thinking important?Initial ideas, representations and strategiesBuilding number fact knowledge and confidenceComputation strategiesProblem solvingConclusion18. Fractions and Decimal Fractions: F-4IntroductionMaking sense of fractionsDeveloping fraction knowledge and confidenceIntroducing decimal fractionsConsolidating understandingConclusion19. Measurement Concepts and Strategies: F-4Why is teaching measurement important?Measurement concepts in the curriculumMeasurement learning sequenceApproaches to developing an understanding of lengthApproaches to developing an understanding of timeConclusion20. Geometric Thinking: F-4Classifying spatial objectsRelationships between spatial objectsDeveloping dynamic imageryLocationGeometric reasoningConclusion21. Statistics and Probability: F-4IntroductionGrappling with uncertaintyThe development of students' thinking about probabilityRepresenting dataUnderstanding distributionsPart 5: Extending Mathematics to the Middle Years: 5-9 22. Number: Fractions, Decimals and Reals: 5-9Building the number lineWhole numbersExtending our place-value systemIntegersScientific notationThe rationalsThe realsDensity of the number lineConclusion23. Additive Thinking: 5-9Ways of working with addition and subtractionAlgorithmsFractionsDecimalsIntegers24. Multiplicative Thinking and Proportional Reasoning: 5-9IntroductionMeanings for multiplication and divisionWorking with an extended range of numbersWhat is proportional reasoning?Addressing the multiplicative gapConclusion25. Algebraic Thinking: 5-9What is algebraic thinking?Why is algebra important?Arithmetic, algebraic thinking and problem structureMeaningful use of symbolsModel approach-using the length modelEquivalence and equationsAlgebraic lawsIntroducing the distributive lawSimplifying expressions and equationsFunctional thinkingConclusion26. Measurement Concepts and Strategies: 5-9Extending measurement conceptsAreaDeveloping area formulaeVolume and capacityMassMoneyConclusion27. Geometric Thinking: 5-9Working with spatial objectsGeometric proofTransformational geometryNon-Euclidean geometryLocationLearning geometry in the middle yearsConclusion28. Statistics and Probability: 5-9Data investigationData representationsData measuresVariationDescribing chance eventsConclusionPart 6: Entering the Profession 29. Becoming a Professional Teacher of MathematicsLooking forwardStandards for mathematics teachingFinal words of advice