Understanding and Teaching Primary Mathematics
Autor Tony Cottonen Limba Engleză Paperback – 17 sep 2024
This fifth edition has been completely updated to include the latest developments in learning and teaching mathematics, including mastery approaches, a Singapore approach and the use of manipulatives in the primary classroom. There are new activities for you to use in your teaching and links to the dedicated website, which contains materials to develop a personal portfolio, more activities to use in your classroom and presentations and podcasts to support your further professional development to reflect the latest research developments. It covers all areas of the mathematics curriculum and will allow you to become a confident teacher of mathematics through developing your own subject knowledge.
Tony draws on his many years of experience teaching mathematics and working with early career teachers to share classroom activities which will support you in learning mathematics through engaging in mathematical activity with your learners.
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Specificații
ISBN-13: 9781032596532
ISBN-10: 1032596538
Pagini: 422
Ilustrații: 340
Dimensiuni: 189 x 246 x 25 mm
Greutate: 1 kg
Ediția:5
Editura: Taylor & Francis
Colecția Routledge
Locul publicării:Oxford, United Kingdom
ISBN-10: 1032596538
Pagini: 422
Ilustrații: 340
Dimensiuni: 189 x 246 x 25 mm
Greutate: 1 kg
Ediția:5
Editura: Taylor & Francis
Colecția Routledge
Locul publicării:Oxford, United Kingdom
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Public țintă
Postgraduate and Professional Practice & DevelopmentCuprins
Contents
Preface to fifth edition
Acknowledgements
Chapter 1: Teaching and Learning Primary Mathematics
Introduction
Starting point
Why is mathematical subject knowledge important?
What is good mathematical subject knowledge?
What makes a good teacher of mathematics?
How will this book develop my subject knowledge
A framework for teaching mathematics
Foundations for learning mathematics
Organisation of the book
The companion website
Summary
Chapter 2: What Should I Know? What Do I Know?
Introduction
Starting point
Auditing your current knowledge
Summary
Going further
Chapter 3: Recent developments in mathematics teaching
Introduction
Growth mindset
Cognitive load theory
What is Singapore mathematics?
A history of teaching for mastery
What is teaching for mastery?
Developing teaching for mastery in your classroom
Mathematical thinking
Variation
Summary
Going further
Chapter 4: Problem Solving Using Mathematics
Introduction
Progression in problem solving using mathematics
Big ideas
Teaching points
In practice
Assessing problem solving using mathematics
Cross-curricula teaching of problem solving
Summary
Reflections on this chapter
Going further
Chapter 5: Counting: place value; fractions, decimals and percentages
Introduction
Progression in counting: place value; fractions, decimals and percentages
Big ideas
Teaching points
In practice
Assessing counting: place value; fractions, decimals and percentages
Cross-curricula teaching of counting: place value; fractions, decimals and percentages
Summary
Reflections on this chapter
Going further
Chapter 6: Knowing and using number facts
Introduction
Progression in knowing and using number facts
Big ideas
Teaching points
In practice
Assessing knowing and using number facts
Cross-curricula teaching of knowing and using number facts
Summary
Reflections on this chapter
Going further
Chapter 7: Calculation: addition, subtraction, multiplication and division
Introduction
Progression in calculation: addition, subtraction, multiplication and division
Big ideas
Teaching points
In practice
Assessing calculation: addition, subtraction, multiplication and division
Cross-curricula teaching of calculation: addition, subtraction, multiplication and division
Summary
Reflections on this chapter
Going further
Chapter 8: Algebra
Introduction
Progression in algebra
Big ideas
Teaching points
In practice
Assessing algebra
Cross-curricula teaching of algebra
Summary
Reflections on this chapter
Going further
Chapter 9: Geometry: Properties of shapes; position and direction
Introduction
Progression in properties of shapes; position and direction
Big ideas
Teaching points
In practice
Assessing properties of shapes; position and direction
Cross-curricula teaching of properties of shapes; position and direction
Reflections on this chapter
Going further
Chapter 10: Measurement
Introduction
Progression in measurement
Big ideas
Teaching points
In practice
Assessing measurement
Cross-curricula teaching of measurement
Reflections on this chapter
Going further
Chapter 11: Statistics and Handling Data
Introduction
Progression in statistics and handling data
Big ideas
Teaching points
In practice
Assessing statistics and handling data
Cross-curricula teaching of statistics and handling data
Reflections on this chapter
Going further
Chapter 12: Teaching and Learning Mathematics in the Early Years
Introduction
Starting point
Problem solving, reasoning and numeracy
Young children learning number
Young children learning measures
Young children learning shape and space
Young children learning algebra
Creating a mathematically rich environment
Assessment in the early years
Summary
Refections on this chapter
Chapter 13: Issues of Inclusion
Introduction
Starting point
Children with special educational needs
Pupils learning English as an additional language (EAL)
Pupils with social, emotional and mental health needs
Autistic pupils
Pupils with developmental coordination disorder (DCD or dyspraxia)
Dyslexic pupils
Pupils with dyscalculia
Pupils who are gifted and talented
Multicultural and anti-racist approaches
Summary
Reflections on this chapter
Chapter 14: ICT and the Use of Calculators in Teaching and Learning Mathematics
Introduction
Starting point
Progression in using calculators
A calculator aware curriculum
The appropriate use of personal computers and other devices
Summary
Reflections on this chapter
Preface to fifth edition
Acknowledgements
Chapter 1: Teaching and Learning Primary Mathematics
Introduction
Starting point
Why is mathematical subject knowledge important?
What is good mathematical subject knowledge?
What makes a good teacher of mathematics?
How will this book develop my subject knowledge
A framework for teaching mathematics
Foundations for learning mathematics
Organisation of the book
The companion website
Summary
Chapter 2: What Should I Know? What Do I Know?
Introduction
Starting point
Auditing your current knowledge
Summary
Going further
Chapter 3: Recent developments in mathematics teaching
Introduction
Growth mindset
Cognitive load theory
What is Singapore mathematics?
A history of teaching for mastery
What is teaching for mastery?
Developing teaching for mastery in your classroom
Mathematical thinking
Variation
Summary
Going further
Chapter 4: Problem Solving Using Mathematics
Introduction
Progression in problem solving using mathematics
Big ideas
Teaching points
In practice
Assessing problem solving using mathematics
Cross-curricula teaching of problem solving
Summary
Reflections on this chapter
Going further
Chapter 5: Counting: place value; fractions, decimals and percentages
Introduction
Progression in counting: place value; fractions, decimals and percentages
Big ideas
Teaching points
In practice
Assessing counting: place value; fractions, decimals and percentages
Cross-curricula teaching of counting: place value; fractions, decimals and percentages
Summary
Reflections on this chapter
Going further
Chapter 6: Knowing and using number facts
Introduction
Progression in knowing and using number facts
Big ideas
Teaching points
In practice
Assessing knowing and using number facts
Cross-curricula teaching of knowing and using number facts
Summary
Reflections on this chapter
Going further
Chapter 7: Calculation: addition, subtraction, multiplication and division
Introduction
Progression in calculation: addition, subtraction, multiplication and division
Big ideas
Teaching points
In practice
Assessing calculation: addition, subtraction, multiplication and division
Cross-curricula teaching of calculation: addition, subtraction, multiplication and division
Summary
Reflections on this chapter
Going further
Chapter 8: Algebra
Introduction
Progression in algebra
Big ideas
Teaching points
In practice
Assessing algebra
Cross-curricula teaching of algebra
Summary
Reflections on this chapter
Going further
Chapter 9: Geometry: Properties of shapes; position and direction
Introduction
Progression in properties of shapes; position and direction
Big ideas
Teaching points
In practice
Assessing properties of shapes; position and direction
Cross-curricula teaching of properties of shapes; position and direction
Reflections on this chapter
Going further
Chapter 10: Measurement
Introduction
Progression in measurement
Big ideas
Teaching points
In practice
Assessing measurement
Cross-curricula teaching of measurement
Reflections on this chapter
Going further
Chapter 11: Statistics and Handling Data
Introduction
Progression in statistics and handling data
Big ideas
Teaching points
In practice
Assessing statistics and handling data
Cross-curricula teaching of statistics and handling data
Reflections on this chapter
Going further
Chapter 12: Teaching and Learning Mathematics in the Early Years
Introduction
Starting point
Problem solving, reasoning and numeracy
Young children learning number
Young children learning measures
Young children learning shape and space
Young children learning algebra
Creating a mathematically rich environment
Assessment in the early years
Summary
Refections on this chapter
Chapter 13: Issues of Inclusion
Introduction
Starting point
Children with special educational needs
Pupils learning English as an additional language (EAL)
Pupils with social, emotional and mental health needs
Autistic pupils
Pupils with developmental coordination disorder (DCD or dyspraxia)
Dyslexic pupils
Pupils with dyscalculia
Pupils who are gifted and talented
Multicultural and anti-racist approaches
Summary
Reflections on this chapter
Chapter 14: ICT and the Use of Calculators in Teaching and Learning Mathematics
Introduction
Starting point
Progression in using calculators
A calculator aware curriculum
The appropriate use of personal computers and other devices
Summary
Reflections on this chapter
Recenzii
‘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
‘Cotton’s 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 O’Brien, 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
Tracey Muir, Senior Lecturer in Mathematics Education, University of Tasmania, Australia
‘Cotton’s 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 O’Brien, 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
Notă biografică
Tony Cotton is the editor of Mathematics Teaching, a previous honorary secretary of the ATM and a member of the ATM for over 40 years. He started his career teaching mathematics in secondary schools in Sheffield, then worked as an advisory teacher for anti-racist and multicultural education, before teaching on secondary and primary teacher education courses in Nottingham and Leeds, becoming the head of the School of Education and Childhood at Leeds Metropolitan University. In 2012, he left the University sector to work full time as a writer and freelance educational consultant.
Descriere
Written by an experienced teacher and teacher educator, the best-selling Understanding and Teaching Primary Mathematics combines pedagogy and subject knowledge to build confidence and equip you with all the skills and know-how you need to successfully teach mathematics to children of any age.