Being Alongside: For the Teaching and Learning of Mathematics PDF
Preview Being Alongside: For the Teaching and Learning of Mathematics
Being Alongside Being Alongside For the Teaching and Learning of Mathematics Alf Coles University of Bristol, UK A C.I.P. record for this book is available from the Library of Congress. ISBN: 978-94-6209-210-5 (paperback) ISBN: 978-94-6209-211-2 (hardback) ISBN: 978-94-6209-212-9 (e-book) Published by: Sense Publishers, P.O. Box 21858, 3001 AW Rotterdam, The Netherlands https://www.sensepublishers.com/ Printed on acid-free paper All Rights Reserved © 2013 Sense Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfi lming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifi cally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. DEDICATION To three generations of my family: Iona, Arthur, Iris ~ Niki ~ Walt and Flo v TABLE OF CONTENTS Preface ix Timeline of Teaching and Research Activity xi Acknowledgements xiii Part One 1. Introduction 3 2. Enactivism 11 3. A Cyclical Enquiry 25 Part Two 4. On Using Video 37 5. On Teacher Learning 53 6. Re-looking at Teacher Discussions 65 Part Three 7. On Metacognition 79 8. The Story of Teacher A 89 9. Heightened Listening 101 Part Four 10. Conclusion 115 Appendix 1 121 Appendix 2 129 Appendix 3 147 Appendix 4 149 References 163 Index 169 vii PREFACE This is a book of a research project in one mathematics department in a secondary school in the UK. It is written in four parts. In the first, I set up the context for the study, my research stance and the methodology used. In the second part, I report on and analyse the use made, by the mathematics department, of video recordings of mathematics lessons in the school. In the third part, I analyse a set of video recordings of one teacher (Teacher A) who taught mathematics in the school. Through looking at the practice of Teacher A, I arrive at a re-framing of the concept of metacognition. I then look at the similarities and differences between the way meetings were run when working on video with teachers and the classroom practice of Teacher A. This comparison leads me to the idea of a ‘heightened listening’ as a description of a way of paying attention to discussions. In the final part of the book, I look back over a variety of different distinctions made in the book and draw out some similarities, differences and issues. Appendix 1 contains lesson write-ups of four of the mathematical activities referred to in this book. I suggest you familiarise yourself with these activities and work on them yourself for a while, before reading. In the book, I refer to people, positions and projects I have been involved with as a teacher and researcher since 1994. I therefore also suggest reading the timeline on the following page, to help make sense of the chronology of events. I have adopted the following notation and conventions. Italics used in quotations are always in the original. Italics as part of normal text indicate emphasis. In order to preserve gender anonymity for students, I use ‘they’ and ‘them’ for individuals as well as in the plural. The teacher who is central to this study I label ‘Teacher A’ or TA. Other teachers are labelled TC, TD, etc, and I use initials (AC) for myself. I label students S1, S2, etc. If any student re-appears in the same transcript I give them the same label, but not across different transcripts (unlike the teacher labels which consistently refer to the same person throughout the book). I adopted the following transcript notation, avoiding all other punctuation: [ ] indecipherable speech [text] my best guess at speech [text] note to the reader (.) pause less than 1 second (2) pause of 2 seconds ? rising intonation / / interrupted speech … some words left out from transcription ix PREFACE text speech said as if in the voice of another -: more than one speaker talking at the same time Line endings are chosen, where possible, to indicate phrasing. I used line numbers when this was useful reference for analysis. Where it is not already made explicit in the text, transcripts are dated and labeled either “Lesson” or “TD/TB” (which would indicate a Teacher Discussion, focused on a lesson given by Teacher B). x
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