Understanding and Teaching Primary Mathematics

by Tony Cotton

Overview

Written by an experienced teacher and teacher educator with widespread experience of teaching mathematics in the UK and internationally, 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.

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 and 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.

Product Details

ISBN-13:	9781040108987
Publisher:	Taylor & Francis
Publication date:	09/03/2024
Sold by:	Barnes & Noble
Format:	eBook
Pages:	402

About the Author

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 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.

Table of Contents

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

Editorial Reviews

‘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

From the Publisher