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.
Teaching Mathematics: Foundations to Middle Years connects readers to the bigger picture of mathematics. This comprehensive resource is designed to help pre-service teachers gradually build mathematically 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 bookâ€™s unique structure explores the different stages of how children learn maths and how to teach maths, before drilling down to the 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 teachers feel positive about mathematics and their role in teaching it.New to this editionAdditional and updated practical activities for pre-service teachers to take straight into the classroomMore student work examples throughout to help link theory to practice and more references to the Australian Curriculumâ€˜Teaching Challengesâ€™ feature explores examples of studentsâ€™ miscomprehension, likely difficulties, error identification and analysis in student workâ€˜Consider and Discuss Your Mathsâ€™ and â€˜Consider and Discuss Your Teachingâ€™ questions and tasks differentiate between learning mathematical content and learning to teach maths in the classroomAll chapters updated to draw on contemporary mathematics education research and current theories on the teaching and learning of mathematics and with reference to the current revised Australian Curriculum
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)
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 environmentsConclusion 7. 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 Fâ€“4 Mathematics13. Algebraic Thinking: Fâ€“4What is pattern and structure?Why is pattern and structure important?Early algebraic thinkingFunctional thinkingConclusion14. Number Ideas and Strategies: Fâ€“2The origins of numberResearch on early number learningPlaying with numberThe numbers 0 to 10A sense of numbers beyond 10Scaffolding solution strategiesConclusion15. Place Value: Fâ€“4Prerequisite ideas and strategiesUnderstanding tens and onesIntroducing three-digit numerationDeveloping four-digit numerationExtending to tens of thousands and beyondConclusion16. Additive Thinking: Fâ€“4Why additive thinking?The development of additive thinkingContexts for addition and subtractionAdditive solution strategiesProblem solvingConclusion17. Multiplicative Thinking: Fâ€“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: Fâ€“4IntroductionMaking sense of fractionsDeveloping fraction knowledge and confidenceIntroducing decimal fractionsConsolidating understandingConclusion19. Measurement Concepts and Strategies: Fâ€“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: Fâ€“4Classifying spatial objectsRelationships between spatial objectsDeveloping dynamic imageryLocationGeometric reasoningConclusion 21. Statistics and Probability: Fâ€“4IntroductionGrappling with uncertaintyThe development of studentsâ€™ thinking about probabilityRepresenting dataUnderstanding distributionsPart 5: Extending Mathematics to the Middle Years: 5â€“9 22. Number: Fractions, Decimals and Reals: 5â€“9Building the number lineWhole numbersExtending our place-value systemIntegersScientific notationThe rationalsThe realsDensity of the number lineConclusion23. Additive Thinking: 5â€“9Ways of working with addition and subtractionAlgorithmsFractionsDecimalsIntegers24. Multiplicative Thinking and Proportional Reasoning: 5â€“9IntroductionMeanings for multiplication and divisionWorking with an extended range of numbersWhat is proportional reasoning?Addressing the multiplicative gapConclusion25. Algebraic Thinking: 5â€“9What is algebraic thinking?Why is algebra important?Arithmetic, algebraic thinking and problem structureMeaningful use of symbolsModel approachâ€”using the length modelEquivalence and equationsAlgebraic lawsIntroducing the distributive lawSimplifying expressions and equationsFunctional thinkingConclusion26. Measurement Concepts and Strategies: 5â€“9Extending measurement conceptsAreaDeveloping area formulaeVolume and capacityMassMoneyConclusion27. Geometric Thinking: 5â€“9Working with spatial objectsGeometric proofTransformational geometryNon-Euclidean geometryLocationLearning geometry in the middle yearsConclusion28. Statistics and Probability: 5â€“9Data investigationData representationsData measuresVariationDescribing chance eventsConclusionPart 6: Entering the Profession 29. Becoming a Professional Teacher of MathematicsLooking forwardStandards for mathematics teachingFinal words of advice
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.
Gradually builds mathematic knowledge and confidence about teaching maths. It covers both how to teach maths (Parts 1,2 and 6) and the maths strands (Parts 3, 4, 5) with a focus on building pre-service teachers own maths knowledge to be more confident in their own skills and abilities. Blends research and theory with practice highlights best practice teaching approaches from research and rich with student work examples and activities that can be taken into a range of learning environments Practical with lots of activities that pre-service teachers can take straight into the classroom Comprehensive and flexible structure: Most competitors are organised by theme, Siemon is structured by age group, working from bigger picture (how students learn and how to teach) down to the more specific skills (maths content). Flexible structure allows lecturers to teach subject how they wish. Breadth and depth of content: covers F 9, no other Australian book covers early primary through to the middle years (key competition only cover primary). This allows the book to be used throughout a degree, across multiple units, while on practicum and into their future classrooms.
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