Being Alongside: For the Teaching and Learning of Mathematics

174 Pages·2013·3.662 MB·English

by  Alf Coles

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
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No part of this work may be reproduced, stored in a retrieval system, or transmitted
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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