Learning to Teach Mathematics in the Secondary School: a Companion to School Experience / Edited by Sue Johnston-Wilder...[Et Al.]

LEARNING TO TEACH MATHEMATICS IN THE SECONDARY SCHOOL What is the role of mathematics in the secondary classroom? What is expected of a would-be maths teacher? How is mathematics best taught and learnt? Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in modern secondary school classrooms. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, including: I the role of ICT I planning mathematics lessons I Assessment for LearningNEW I including special-needs pupils I using mathematics in contextNEW I teaching mathematics post-16 I communicating mathematically I professional development. Already a major text for many university teaching courses, this fully revised third edition takes into account new developments in the National Curriculum as well as recent changes to the standards for Qualified Teacher Status. Featuring two brand new chapters, a glossary of useful terms, addresses for resources and organisations, and tasks designed to prompt critical reflection and support thinking and writing at Masters level, this book will help you make the most of school experience, during your training, your NQT year and beyond. Designed for use as a core textbook, this new edition of Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all trainee and practising teachers of secondary mathematics. Sue Johnston-Wilder is Associate Professor at the University of Warwick; she works with PGCE students and in-service teachers in the West Midlands. She has previously taught at King’s College London and the Open University. Peter Johnston-Wilder is Associate Professor at the University of Warwick. David Pimm is Professor of Mathematics Education at the University of Alberta, Edmonton, Canada. Clare Lee leads the Mathematics PGCE programme at the Open University and works with in-service teachers nationally. She was previously a research fellow for the King’s Formative Assessment Project. LEARNING TO TEACH SUBJECTS IN THE SECONDARY SCHOOL SERIES Series Editors: Susan Capel, Marilyn Leask and Tony Turner Designed for all students learning to teach in secondary schools, and particularly those on school-based initial teacher training courses, the books in this series complement Learning to Teach in the Secondary School and its companion, Starting to Teach in the Secondary School. Each book in the series applies underpinning theory and addresses practical issues to support student teachers in school and in the training institution in learning how to teach a particular subject. Learning to Teach in the Secondary Learning to Teach Mathematics in School, 5th edition the Secondary School, 3rd edition Edited by Susan Capel, Marilyn Leask Edited by Sue Johnston-Wilder, and Tony Turner Peter Johnston-Wilder, David Pimm and Clare Lee Learning to Teach Art and Design in the Secondary School, 2nd edition Learning to Teach Modern Foreign Edited by Nicholas Addison and Languages in the Secondary School, Lesley Burgess 3rd edition Norbert Pachler, Ann Barnes and Learning to Teach Citizenship in the Kit Field Secondary School, 2nd edition Learning to Teach Music in the Edited by Liam Gearon Secondary School, 2nd edition Learning to Teach Design and Edited by Chris Philpott and Technology in the Secondary School, Gary Spruce 2nd edition Learning to Teach Physical Education Edited by Gwyneth Owen-Jackson in the Secondary School, 3rd edition Learning to Teach English in the Edited by Susan Capel Secondary School, 3rd edition Learning to Teach Religious Education in Edited by Jon Davison and the Secondary School, 2nd edition Jane Dowson Edited by L. Philip Barnes, Andrew Wright Learning to Teach Geography in the and Ann-Marie Brandom Secondary School, 2nd edition Learning to Teach Science in the David Lambert and David Balderstone Secondary School, 3rd edition Edited by Jenny Frost Learning to Teach History in the Secondary School, 3rd edition Learning to Teach Using ICT in the Edited by Terry Haydn, James Arthur, Secondary School, 2nd edition Martin Hunt and Alison Stephen Edited by Marilyn Leask and Norbert Pachler Learning to Teach ICT in the Secondary Starting to Teach in the Secondary School School, 2nd edition Edited by Steve Kennewell, Edited by Susan Capel, Ruth Heilbronn, John Parkinson and Howard Tanner Marilyn Leask and Tony Turner LEARNING TO TEACH MATHEMATICS IN THE SECONDARY SCHOOL A companion to school experience 3rd Edition Edited by Sue Johnston-Wilder, Peter Johnston-Wilder, David Pimm and Clare Lee First edition published 1999 by Routledge Second edition published 2005 by Routledge Third edition published 2011 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Avenue, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2010. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2011 Sue Johnston-Wilder, Peter Johnston-Wilder, David Pimm and Clare Lee for selection and editorial material. Individual chapters © the contributors. All rights reserved. No part of this book may be reprinted, reproduced or utilised in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Learning to teach mathematics in the secondary school: a companion to school experience / edited by Sue Johnston-Wilder...[et al.]. p. cm. Includes bibliographical references and index. 1. Mathematics—Study and teaching (Secondary)—United States. I. Johnston-Wilder, Sue. QA13.L43 2011 510.71’2—dc22 2010009231 ISBN 0-203-84412-2 Master e-book ISBN ISBN13: 978-0-415-56559-2 (hbk) ISBN13: 978-0-415-56558-5 (pbk) ISBN13: 978-0-203-84412-0 (ebk) This book is dedicated to our children, the maths students of the next generation: Robin, Beth, Jaclyn, Daniel, Alex, Alastair, Olivia, Rhiannon and Steve and is offered in memory of Jill Bruce, Rita Nolder, Christine Shiu and Gill Hatch, inspirational teacher-researchers who died before their time. CONTENTS Introduction to the series x Illustrations xii Tasks xiv Notes on contributors xvii Acknowledgements xx Introduction xxi Introduction to the third edition xxv 1 MATHEMATICS EDUCATION: WHO DECIDES? 1 JOHN WESTWELL I mathematics and you I mathematics and education I competing influences on the mathematics curriculum I agencies for change 2 MATHEMATICS IN THE NATIONAL CURRICULUM 16 JOHN WESTWELL AND ROBERT WARD-PENNY I the scope, prescription and presentation of the curriculum I the development and revision of the curriculum I performance standards and assessment within the curriculum I programmes of study for the curriculum 3 PUPILS LEARNING MATHEMATICS 36 MARIA GOULDING I the social context of learning I theories of learning and knowledge I feelings and motivation I the cognitive dimension 4 DIFFERENT TEACHING APPROACHES 54 DAVID PIMM AND SUE JOHNSTON-WILDER I teaching as listening, asking and telling I forms of classroom organisation I resources and ideas for enhancing your teaching vii I CONTENTS I I I I 5 PLANNING FOR MATHEMATICS LEARNING 79 KEITH JONES AND RUTH EDWARDS I learning from teachers planning mathematics lessons I planning a lesson, planning collaboratively I planning sequences of lessons I planning for out-of-school learning 6 ASSESSMENT FOR LEARNING 101 CLARE LEE I learning intentions and success criteria I feedback I questioning I peer and self-assessment 7 ASSESSMENT AND PUBLIC EXAMINATIONS 123 PETER JOHNSTON-WILDER I in-class assessment I other aspects of in-class assessment I public assessments and examinations I GCSE assessment 8 COMMUNICATING MATHEMATICALLY 146 CANDIA MORGAN I the nature of mathematical language I writing mathematically 9 USING INFORMATION AND COMMUNICATIONS TECHNOLOGY (ICT) 162 SUE JOHNSTON-WILDER AND DAVID PIMM I some background I calculating devices I spreadsheets I graph plotters I graphic calculators I dynamic geometry packages I programming languages – Logo I small teaching programs I the internet and CD-ROMs 10 INCLUSION IN PRACTICE: SPECIAL NEEDS PUPILS IN MAINSTREAM MATHEMATICS 189 MELISSA RODD I inclusion and diversity, disability and special needs I orienting to special needs I classification and characterisation of special educational needs I particular special needs and learning disabilities I speech, language and communication and EAL I sensory/physical impairments I resources for learning I one of a team 11 MATHEMATICS IN CONTEXT 206 CLARE LEE AND ROBERT WARD-PENNY I why do people do mathematics? I skills for learning mathematics in context I strengths and weaknesses of different contexts I problems with using contexts in teaching I teaching mathematics in context I viii I I I I CONTENTS 12 GETTING THE WHOLE PICTURE 225 JOHN WESTWELL AND CLARE LEE I the whole curriculum I the whole person 13 TEACHING MATHEMATICS POST-16 242 GEOFF WAKE I background: 14–19 pathways I knowledge for teaching I qualifications: types and

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