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E-raamat: Understanding and Teaching Primary Mathematics in Australia

, , (Leeds Metropolitan University, UK)
  • Formaat: 338 pages
  • Ilmumisaeg: 30-Aug-2022
  • Kirjastus: Routledge
  • Keel: eng
  • ISBN-13: 9781000638639
  • Formaat - EPUB+DRM
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  • Formaat: 338 pages
  • Ilmumisaeg: 30-Aug-2022
  • Kirjastus: Routledge
  • Keel: eng
  • ISBN-13: 9781000638639

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"Written by experienced teacher educator and author, Tony Cotton, and two Australian primary teachers, Jess Greenbaum and Michael Minas, Understanding and Teaching Primary Mathematics in Australia combines pedagogy and mathematics subject knowledge to build teachers' confidence both in their mathematical subject knowledge and in their ability to teach mathematics effectively. The book covers all the key areas of the Australian National Curriculum for mathematics from teaching number and calculation strategies to exploring geometry and statistics. There are also chapters which deal with the teaching of mathematics in the Early Years; inclusive approaches to mathematics teaching and teaching mathematics using ICT. Stimulating, accessible and containing a wealth of practical ideas you can use in your classroom, Understanding and Teaching Primary Mathematics in Australia is an essential purchase for graduate and practicing teachers alike"--

Written by experienced teacher educator and author, Tony Cotton, and two Australian primary teachers, Jess Greenbaum and Michael Minas, Understanding and Teaching Primary Mathematics in Australia combines pedagogy and mathematics subject knowledge to build teachers’ confidence both in their mathematical subject knowledge and in their ability to teach mathematics effectively.

The book covers all the key areas of the Australian Curriculum for mathematics from teaching number and calculation strategies to exploring geometry and statistics. There are also chapters that deal with the teaching of mathematics in the Early Years, inclusive approaches to mathematics teaching and teaching mathematics using ICT.

Stimulating, accessible and containing a wealth of practical ideas for use in the classroom, Understanding and Teaching Primary Mathematics in Australia is an essential text for graduate and practicing teachers alike.



Adapted for Australian pre- and in-service teachers, the book covers all the key areas of the Australian Curriculum: Mathematics, from teaching number and calculation strategies, to exploring geometry and statistics.

Arvustused

Understanding and Teaching Primary Mathematics in Australia is a valuable resource that addresses each strand of the Australian Curriculum: Mathematics in rich and comprehensive ways. The conversational tone of the commentary weaves a meaningful blend of theory and practice that is likely to resonate with many preservice teachers.

Nicole Maher, University of Tasmania, Australia.

Understanding and Teaching Primary Mathematics provides a valuable resource for both in-service and pre-service teachers. It combines both pedagogy and content knowledge to build fundamental mathematical understandings with practical suggestions on how this knowledge is enacted in the classroom. I will definitely be using it in my undergraduate teaching courses and strongly recommend it to other mathematics teacher educators.

Tracey Muir, Senior Lecturer in Mathematics Education, University of Tasmania, Australia

Cottons narrative throughout the book will support teachers and student teachers to make links between mathematical content knowledge and pedagogy. The book weaves theory, content and pedagogy through examples of real-life teaching experiences. Teachers and student teachers alike will find this book and its companion features an informative and useful resource for professional and personal development.

Karen Major, Professional Teaching Fellow in Primary Mathematics, University of Auckland, New Zealand

Once again, Tony Cotton has produced a very accessible and engaging book which will be a great support to trainee teachers from a range of teaching routes, including School Direct and Teach First. The book gives insight into a range of activities and resources which can be used in class, providing comprehensive links to National Curriculum requirements. It supports these with an in-depth analysis of some of the issues related to the teaching of mathematics, such as subject knowledge and pedagogy. Portfolio tasks and self-audits are provided, which will help to develop and enrich practice. This book is altogether a very practical classroom support which will be an invaluable resource for those seeking to enhance their own practice.

Keith Brentnall, Senior Lecturer in Primary Mathematics, Northumbria University, UK

Our students find Understanding and Teaching Primary Mathematics accessible and engaging, helping them to understand the "Big Ideas" in primary mathematics. This new edition provides up-to-date links to the new National Curriculum and the latest research which will keep all our students up to date with primary mathematical developments. The content closely supports both the BA and PGCE Primary Education mathematics courses and is referred to throughout the year. This book will continue to be a key text for all our primary BA and PGCE students.

Brenda Wood, Senior Lecturer in Primary Mathematics, University of Greenwich, UK

This is not only an essential handbook for beginning teachers in the primary phase it is also of tremendous value to secondary maths teachers. Many children struggle to make sense of the fundamental concepts in mathematics and carry confusion through their school years. Tony Cotton demonstrates clearly how teachers can work to (re)construct their learners understanding. This superb handbook connects the findings of research with specific pedagogic approaches and classroom tasks. It will support teachers as they reflect on their classroom practice with their colleagues and mentors. Anyone who is engaged in devising programmes for initial teacher education and for continuing professional development will appreciate the depth of scholarship underpinning this book.

Corinne Angier, Senior Lecturer in Mathematics Education, Sheffield Hallam University, and regional mathematics lead for Teach First, UK

Confidence in the teaching of primary maths is fundamental to successful pupil outcomes and this book provides access to a rich and varied collection of resources to support the novice and experienced teacher at every turn. It combines underpinning theory with relevant and accessible pedagogical approaches which support the development of learners deep mathematical understanding.

Sue OBrien, Principal Lecturer in Primary and Early Years Mathematics, Sheffield Hallam University, UK

This book should be a core text for all teacher training pathways. It reflects the need for in-depth subject knowledge, pedagogical excellence and an enthusiasm for mathematics. The range of issues and challenges addressed forms a substantial basis for developing an understanding of the complexities and expectations of the modern primary classroom. The style is clear and concise, and the integration of ICT support reflects a modern learning environment in an effective and engaging manner.

Nick Tinsdeall, Senior Lecturer in Primary Mathematics, University of Cumbria, UK

This is a comprehensive journey through the key areas of teaching primary mathematics. The inclusion of fundamental big ideas and teaching points, covering mathematical misconceptions, make this a valuable resource for the beginning teacher or more experienced primary practitioners.

Richard Holme, Lecturer in Primary Mathematics, University of Dundee, UK

With ongoing education curriculum reviews and political changes at local and national levels, this new edition of a key textbook is both timely and relevant. Cotton continues to remind us of the importance of the methods shaping the teaching and learning of mathematics from teacher trainees through ongoing professional development for all maths teachers in both domestic and international contexts.

Richard Race, Senior Lecturer in Education, Roehampton University, UK

Preface to the Australian Edition xi
Acknowledgments xvi
Chapter 1 Teaching and learning primary mathematics
1(14)
Introduction
1(1)
Starting point
2(1)
Why is mathematical subject knowledge important?
3(1)
What is good mathematical subject knowledge?
4(2)
What makes a good teacher of mathematics?
6(1)
How will this book develop my subject knowledge?
7(1)
A framework for teaching mathematics
8(1)
Foundations for learning mathematics
9(1)
Organisation of the book
10(2)
The companion website
12(1)
Summary
12(1)
Going further
12(3)
Chapter 2 What should I know? What do I know?
15(13)
Introduction
15(1)
Starting point
16(1)
Auditing your current knowledge
16(10)
Summary
26(1)
Going further
27(1)
Chapter 3 Problem solving using mathematics
28(33)
Introduction
28(5)
Progression in problem solving using mathematics
33(1)
Big ideas
34(2)
Enquiry and problem solving
36(3)
Representing
39(1)
Reasoning and communication
39(1)
Teaching points
40(10)
In practice
50(2)
Rationale and evaluation
52(1)
Assessing problem solving using mathematics
53(1)
Cross-curricular teaching of problem solving
54(1)
Summary
55(1)
Reflections on this chapter
55(1)
Going further
56(5)
Chapter 4 Number: Counting; place value; fractions, decimals and percentages
61(43)
Introduction
61(1)
Starting point
62(2)
Progression in counting; place value; fractions, decimals, percentages and proportionality
64(2)
Big ideas
66(10)
Teaching points
76(21)
Assessing counting and understanding number
97(1)
Cross-curricular teaching of counting and understanding number
97(1)
Summary
98(1)
Reflections on this chapter
99(1)
Going further
99(2)
Self-audit
101(3)
Chapter 5 Number: Knowing and using number facts
104(27)
Introduction
104(1)
Starting point
105(2)
Progression in knowing and using number facts
107(2)
Big ideas
109(6)
Teaching points
115(10)
Rationale and evaluation
125(1)
Assessing knowing and using number facts
126(1)
Cross-curricular teaching of knowing and using number facts
126(1)
Summary
127(1)
Reflections on this chapter
128(1)
Going further
129(2)
Chapter 6 Number: Calculation (addition, subtraction, multiplication and division)
131(41)
Introduction
131(1)
Starting point
132(3)
Progression in calculation
135(2)
Big ideas
137(22)
Teaching points
159(8)
Assessing calculation
167(1)
Cross-curricular teaching of calculation
168(1)
Summary
168(1)
Reflections on this chapter
169(1)
Going further
169(2)
Self-audit
171(1)
Chapter 7 Patterns and algebra
172(22)
Introduction
172(1)
Starting point
173(2)
Progression in patterns and algebra
175(2)
Big idea
177(5)
Teaching points
182(5)
Rationale and evaluation
187(2)
Assessing algebra
189(1)
Cross-curricular teaching of algebra
190(1)
Summary
190(1)
Reflections on this chapter
191(1)
Going further
191(1)
Self-audit
192(2)
Chapter 8 Geometry: Properties of shapes; position and direction
194(29)
Introduction
194(1)
Starting point
194(5)
Progression in geometry
199(2)
Big ideas
201(6)
Teaching points
207(11)
Rationale and evaluation
218(1)
Assessing geometry
218(1)
Cross-curricular teaching of geometry
219(1)
Summary
220(1)
Reflections on this chapter
220(1)
Going further
221(1)
Self-audit
222(1)
Chapter 9 Measurement
223(22)
Introduction
223(1)
Starting point
224(1)
Progression in measuring
225(3)
Big ideas
228(2)
Teaching points
230(11)
Assessing understanding of measurement
241(1)
Cross-curricular teaching of measurement
241(1)
Summary
242(1)
Reflections on this chapter
242(1)
Going further
243(1)
Self-audit
244(1)
Chapter 10 Statistics and probability
245(22)
Introduction
245(1)
Starting point
246(1)
Progression in statistics and probability
247(2)
Big ideas
249(7)
Teaching points
256(6)
Assessing knowledge of statistics and probability
262(1)
Cross-curricular teaching of statistics and probability
263(1)
Summary
263(1)
Reflections on this chapter
264(1)
Going further
265(1)
Self-audit
266(1)
Chapter 11 Teaching and learning mathematics in the Early Years
267(30)
Introduction
267(6)
Starting point
273(2)
Problem solving, reasoning and numeracy
275(9)
Young children learning geometry
284(3)
Young children learning algebra
287(4)
Assessment in the Early Years
291(3)
Summary
294(1)
Reflections on this chapter
294(1)
Going further
295(2)
Chapter 12 Issues of inclusion
297(21)
Introduction
297(1)
Starting point: further reading
298(4)
Children with special educational needs
302(1)
Gender issues
303(3)
Children learning English as an additional language (EAL)
306(2)
Children with social, emotional and mental health needs
308(1)
Children with autism
308(2)
Children with Developmental Coordination Disorder (DCD or dyspraxia)
310(1)
Children with dyslexia and dyscalculia
311(2)
Multicultural and anti-racist approaches
313(2)
Summary
315(1)
Reflections on this chapter
316(1)
Going further
317(1)
Chapter 13 ICT and the use of calculators in teaching and learning mathematics
318(15)
Introduction
318(1)
Starting point
319(1)
The appropriate use of personal computers and other devices
320(9)
Using ICT during lockdown. What did we learn?
329(1)
Summary
330(1)
Reflections on this chapter
331(1)
Going further
331(2)
Index 333
Tony Cotton was previously Associate Dean and Head of Education at Leeds Metropolitan University, UK. Since 2012, he has been working as a freelance writer and education consultant. He has written widely for mathematics teachers and writes pupil textbooks. Tony has worked internationally developing curricula and running teacher workshops. He currently edits Mathematics Teaching, the journal of the Association of Teachers of Mathematics.

Jess Greenbaum is a primary school mathematics learning specialist in Melbourne, Australia.

Michael Minas is a Melbourne-based education consultant who specialises in working with primary schools in the area of mathematics.