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Teaching Mathematics : Foundations to Middle Years - Di Siemon

Teaching Mathematics

Foundations to Middle Years

Paperback

Published: 6th November 2015
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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 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 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 pre-service teachers feel positive about mathematics and their role in teaching it.

New to this edition

  • Additional and updated practical activities for pre-service 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
About the Author

Dianne Siemon: Professor of Mathematics Education, School of Education, RMIT
Kim Beswick: Professor of Mathematics Education, School of Education, University of Tasmania
Kathy Brady: Head of the Student Learning Centre, Flinders University
Julie Clark: Associate Professor of Mathematics Education, School of Education, Flinders University
Rhonda Faragher: Senior Lecturer, Faculty of Education and Arts, Australian Catholic University
Elizabeth Warren: Professor in Mathematics Education, Faculty of Education and Arts, Australian Catholic University

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
Multi-representational 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 F–4 Mathematics
13. Algebraic Thinking: F–4
What is pattern and structure?
Why is pattern and structure important?
Early algebraic thinking
Functional thinking
Conclusion

14. Number Ideas and Strategies: F–2
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: F–4
Prerequisite ideas and strategies
Understanding tens and ones
Introducing three-digit numeration
Developing four-digit numeration
Extending to tens of thousands and beyond
Conclusion

16. Additive Thinking: F–4
Why additive thinking?
The development of additive thinking
Contexts for addition and subtraction
Additive solution strategies
Problem solving
Conclusion

17. Multiplicative Thinking: F–4
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: F–4
Introduction
Making sense of fractions
Developing fraction knowledge and confidence
Introducing decimal fractions
Consolidating understanding
Conclusion

19. Measurement Concepts and Strategies: F–4
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: F–4
Classifying spatial objects
Relationships between spatial objects
Developing dynamic imagery
Location
Geometric reasoning
Conclusion

21. Statistics and Probability: F–4
Introduction
Grappling with uncertainty
The development of students’ thinking about probability
Representing data
Understanding distributions

Part 5: Extending Mathematics to the Middle Years: 5–9 
22. Number: Fractions, Decimals and Reals: 5–9
Building the number line
Whole numbers
Extending our place-value system
Integers
Scientific notation
The rationals
The reals
Density of the number line
Conclusion

23. Additive Thinking: 5–9
Ways of working with addition and subtraction
Algorithms
Fractions
Decimals
Integers

24. Multiplicative Thinking and Proportional Reasoning: 5–9
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: 5–9
What is algebraic thinking?
Why is algebra important?
Arithmetic, algebraic thinking and problem structure
Meaningful use of symbols
Model approach—using the length model
Equivalence and equations
Algebraic laws
Introducing the distributive law
Simplifying expressions and equations
Functional thinking
Conclusion

26. Measurement Concepts and Strategies: 5–9
Extending measurement concepts
Area
Developing area formulae
Volume and capacity
Mass
Money
Conclusion

27. Geometric Thinking: 5–9
Working with spatial objects
Geometric proof
Transformational geometry
Non-Euclidean geometry
Location
Learning geometry in the middle years
Conclusion

28. Statistics and Probability: 5–9
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

ISBN: 9780195523829
ISBN-10: 0195523822
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 800
Published: 6th November 2015
Publisher: Oxford University Press Australia
Country of Publication: AU
Dimensions (cm): 24.9 x 20.4  x 2.6
Weight (kg): 1.49
Edition Number: 2
Edition Type: Revised