Understanding and Teaching Primary Mathematics

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.

• ContentsPreface to fifth editionAcknowledgementsChapter 1: Teaching and Learning Primary MathematicsIntroductionStarting pointWhy 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 knowledgeA framework for teaching mathematicsFoundations for learning mathematicsOrganisation of the bookThe companion websiteSummaryChapter 2: What Should I Know? What Do I Know?IntroductionStarting pointAuditing your current knowledgeSummaryGoing furtherChapter 3: Recent developments in mathematics teachingIntroductionGrowth mindsetCognitive load theoryWhat is Singapore mathematics?A history of teaching for masteryWhat is teaching for mastery?Developing teaching for mastery in your classroomMathematical thinkingVariationSummaryGoing furtherChapter 4: Problem Solving Using MathematicsIntroductionProgression in problem solving using mathematicsBig ideasTeaching pointsIn practiceAssessing problem solving using mathematicsCross-curricula teaching of problem solvingSummaryReflections on this chapterGoing furtherChapter 5: Counting: place value; fractions, decimals and percentagesIntroductionProgression in counting: place value; fractions, decimals and percentagesBig ideasTeaching pointsIn practiceAssessing counting: place value; fractions, decimals and percentagesCross-curricula teaching of counting: place value; fractions, decimals and percentagesSummaryReflections on this chapterGoing furtherChapter 6: Knowing and using number factsIntroductionProgression in knowing and using number factsBig ideasTeaching pointsIn practiceAssessing knowing and using number factsCross-curricula teaching of knowing and using number factsSummaryReflections on this chapterGoing furtherChapter 7: Calculation: addition, subtraction, multiplication and divisionIntroductionProgression in calculation: addition, subtraction, multiplication and divisionBig ideasTeaching pointsIn practiceAssessing calculation: addition, subtraction, multiplication and divisionCross-curricula teaching of calculation: addition, subtraction, multiplication and divisionSummaryReflections on this chapterGoing furtherChapter 8: AlgebraIntroductionProgression in algebraBig ideasTeaching pointsIn practiceAssessing algebraCross-curricula teaching of algebraSummaryReflections on this chapterGoing furtherChapter 9: Geometry: Properties of shapes; position and directionIntroductionProgression in properties of shapes; position and directionBig ideasTeaching pointsIn practiceAssessing properties of shapes; position and directionCross-curricula teaching of properties of shapes; position and directionReflections on this chapterGoing furtherChapter 10: MeasurementIntroductionProgression in measurementBig ideasTeaching pointsIn practiceAssessing measurementCross-curricula teaching of measurementReflections on this chapterGoing furtherChapter 11: Statistics and Handling DataIntroductionProgression in statistics and handling dataBig ideasTeaching pointsIn practiceAssessing statistics and handling dataCross-curricula teaching of statistics and handling dataReflections on this chapterGoing furtherChapter 12: Teaching and Learning Mathematics in the Early YearsIntroductionStarting pointProblem solving, reasoning and numeracyYoung children learning numberYoung children learning measuresYoung children learning shape and spaceYoung children learning algebraCreating a mathematically rich environmentAssessment in the early yearsSummaryRefections on this chapterChapter 13: Issues of InclusionIntroductionStarting pointChildren with special educational needsPupils learning English as an additional language (EAL)Pupils with social, emotional and mental health needsAutistic pupilsPupils with developmental coordination disorder (DCD or dyspraxia)Dyslexic pupilsPupils with dyscalculiaPupils who are gifted and talentedMulticultural and anti-racist approachesSummaryReflections on this chapterChapter 14: ICT and the Use of Calculators in Teaching and Learning MathematicsIntroductionStarting pointProgression in using calculatorsA calculator aware curriculumThe appropriate use of personal computers and other devicesSummaryReflections on this chapter

‘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