4th Edition

Understanding and Teaching Primary Mathematics

By Tony Cotton Copyright 2021
    348 Pages 156 Color Illustrations
    by Routledge

    348 Pages 156 Color Illustrations
    by Routledge

    Written by an experienced teacher and teacher educator with widespread experience of teaching mathematics in the UK and internationally, 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 fourth edition has been fully updated to reflect the latest research developments and initiatives in the field, including a brand-new chapter on ‘Mastery and mathematics’ and ‘The Singapore approach’ which reflects the current international interest in these approaches to learning and teaching mathematics. Extra features also include helpful callouts to the book’s revised and updated companion website, which offers a shared site with a range of resources relevant to both this book and its companion volume, Teaching for Mathematical Understanding.

    Stimulating, accessible and well-illustrated, with comprehensive coverage of subject knowledge and pedagogy, Understanding and Teaching Primary Mathematics is an essential purchase for trainee and practising teachers alike.

    Chapter 1: Teaching and Learning Primary Mathematics

    Chapter 2: What Should I Know? What Do I Know?

    Chapter 3: Recent developments in mathematics teaching: Teaching for mastery

    Chapter 4: Problem Solving Using Mathematics

    Chapter 5: Counting: place value; fractions, decimals and percentages

    Chapter 6: Knowing and using number facts

    Chapter 7: Calculation: addition, subtraction, multiplication and division

    Chapter 8: Algebra

    Chapter 9: Geometry: Properties of shapes; position and direction

    Chapter 10: Measurement

    Chapter 11: Statistics and Handling Data

    Chapter 12: Teaching and Learning Mathematics in the Early Years

    Chapter 13: Issues of Inclusion

    Chapter 14: ICT and the Use of Calculators in Teaching and Learning Mathematics


    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.

    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