Teaching Mathematics: Foundations to Middle Years, 2nd Edition
by:
Di Siemon, Kim Beswick, Kathy Brady, Julie Clark, Rhonda Faragher, Elizabeth Warren
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OXFORD UNIVERSITY PR,06.11.15
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ISBN: 0195523822 ISBN13: 9780195523829

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Teaching Mathematics: Foundations to Middle Years connects readers to the bigger picture of mathematics. This comprehensive resource is designed to help preservice 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 book'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 preservice teachers feel positive about mathematics and their role in teaching it. New to this edition  Additional and updated practical activities for preservice teachers to take straight into the classroom  More student work examples throughout to help link theory to practice and more references to the Australian Curriculum  'Teaching Challenges' feature explores examples of students' miscomprehension, likely difficulties, error identification and analysis in student work  'Consider and Discuss Your Maths' and 'Consider and Discuss Your Teaching' questions and tasks differentiate between learning mathematical content and learning to teach maths in the classroom  All 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 CONTENTS: Part 1: Setting the Scene 1. Understanding School Mathematics Introduction What is mathematics? Goals of school mathematics Affordances and constraints Conclusion 2. Learning Mathematics Introduction What does it mean to learn mathematics? Learning and understanding mathematics Developing your own theory of mathematics learning 3. Teaching Mathematics Introduction What does it mean to teach mathematics? Connections among beliefs How can we know we are teaching? Knowledge for teaching mathematics Effective mathematics teaching Part 2: Understanding the Challenges and Opportunities 4. Thinking Mathematically Learning and doing mathematics Making a start with mathematical thinking General processes for problem solving and reasoning Helping learners to think mathematically Conclusion 5. Communicating Mathematically Introduction The language of mathematics Language and culture Communicating in the mathematics classroom Conclusion 6. Representing Mathematically What are mathematical representations? Traditional representations The importance of mathematical language and recording Using representations to build abstract thinking Choosing and using materials and models Choosing materials and models for the classroom Multirepresentational learning environments Conclusion 7. Assessing and Reporting Assessment is about testing, right? Assessment of learning Assessment for learning Reporting Conclusion 8. Understanding Diversity Who are diverse learners? Language of diversity Diversifying the curriculum Supporting diverse learners Conclusion Part 3: Exploring the Big Ideas in Mathematics 9. Numeracy in the Curriculum What is numeracy? Numeracy across the curriculum Critical numeracy Conclusion 10. Developing a Sense of Number and Algebra Understanding number sense Number sense in practice Developing a sense of number Conclusion 11. Developing a Sense of Measurement and Geometry Linking measurement and geometry What is measurement? Developing measurement sense Geometry Spatial sense How geometry is learned Conclusion 12. Developing a Sense of Statistics and Probability Introduction Statistical literacy What is statistics? What is probability? Conclusion Part 4: Laying the Basis for F4 Mathematics 13. Algebraic Thinking: F4 What is pattern and structure? Why is pattern and structure important? Early algebraic thinking Functional thinking Conclusion 14. Number Ideas and Strategies: F2 The origins of number Research on early number learning Playing with number The numbers 0 to 10 A sense of numbers beyond 10 Scaffolding solution strategies Conclusion 15. Place Value: F4 Prerequisite ideas and strategies Understanding tens and ones Introducing threedigit numeration Developing fourdigit numeration Extending to tens of thousands and beyond Conclusion 16. Additive Thinking: F4 Why additive thinking? The development of additive thinking Contexts for addition and subtraction Additive solution strategies Problem solving Conclusion 17. Multiplicative Thinking: F4 Introduction What is multiplicative thinking? Why is multiplicative thinking important? Initial ideas, representations and strategies Building number fact knowledge and confidence Computation strategies Problem solving Conclusion 18. Fractions and Decimal Fractions: F4 Introduction Making sense of fractions Developing fraction knowledge and confidence Introducing decimal fractions Consolidating understanding Conclusion 19. Measurement Concepts and Strategies: F4 Why is teaching measurement important? Measurement concepts in the curriculum Measurement learning sequence Approaches to developing an understanding of length Approaches to developing an understanding of time Conclusion 20. Geometric Thinking: F4 Classifying spatial objects Relationships between spatial objects Developing dynamic imagery Location Geometric reasoning Conclusion 21. Statistics and Probability: F4 Introduction Grappling with uncertainty The development of students' thinking about probability Representing data Understanding distributions Part 5: Extending Mathematics to the Middle Years: 59 22. Number: Fractions, Decimals and Reals: 59 Building the number line Whole numbers Extending our placevalue system Integers Scientific notation The rationals The reals Density of the number line Conclusion 23. Additive Thinking: 59 Ways of working with addition and subtraction Algorithms Fractions Decimals Integers 24. Multiplicative Thinking and Proportional Reasoning: 59 Introduction Meanings for multiplication and division Working with an extended range of numbers What is proportional reasoning? Addressing the multiplicative gap Conclusion 25. Algebraic Thinking: 59 What is algebraic thinking? Why is algebra important? Arithmetic, algebraic thinking and problem structure Meaningful use of symbols Model approachusing the length model Equivalence and equations Algebraic laws Introducing the distributive law Simplifying expressions and equations Functional thinking Conclusion 26. Measurement Concepts and Strategies: 59 Extending measurement concepts Area Developing area formulae Volume and capacity Mass Money Conclusion 27. Geometric Thinking: 59 Working with spatial objects Geometric proof Transformational geometry NonEuclidean geometry Location Learning geometry in the middle years Conclusion 28. Statistics and Probability: 59 Data investigation Data representations Data measures Variation Describing chance events Conclusion Part 6: Entering the Profession 29. Becoming a Professional Teacher of Mathematics Looking forward Standards for mathematics teaching Final words of advice
