Meeting the Needs of Your Most Able Pupils in Maths (The Gifted and Talented Series)

160 Pages·2007·1.8 MB·English

by  McClure Piggott

M1027 - MATHS TEXT.qxp:RAY Q7 2/11/07 10:47 Page i
Meeting the Needs
of Your Most Able Pupils:
MATHEMATICS
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Meeting the Needs
of Your Most Able Pupils:
MATHEMATICS
Lynne McClure and Jennifer Piggott
First published 2007 by
Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN
Simultaneously published in the USA and Canada by
Routledge
270 Madison Ave, New York, NY 10016
Routledge is an imprint of Taylor & Francis, an informa business
This edition published in the Taylor & Francis e-Library, 2007.
“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.”
Copyright © Lynne McClure and Jennifer Piggott 2007
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
A catalog record has been requested
ISBN 0-203-93538-1 Master e-book ISBN
ISBN 13: 978 1 84312 328 6 (pbk)
ISBN 13: 978 0 203 93538 5 (ebk)
ISBN 10: 1 84312 328 2 (pbk)
ISBN 10: 0 203 93538 1 (ebk)
All rights reserved. No part of this book may be reprinted or 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.
Every effort has been made to contact copyright holders for their permission. The publishers
would be grateful to hear from any copyright holder who is not acknowledged here and will
undertake to rectify any omissions in future editions of the book. Crown Copyright material
is reproduced with the permission of the Controller of HMSO and the Queen’s Printer for
Scotland.
Series production editors: Sarah Fish and Andrew Welsh
Typeset by Servis Filmsetting Ltd, Manchester
Printed and bound in Great Britain
by Bell & Bain Ltd, Glasgow
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Contents
Foreword – Professor John Mason vii
Acknowledgements ix
Contributors to the series x
Online content on the Routledge website xii
Introduction 1
1. Our more able pupils – the national scene 3
Making good provision for the most able – what’s in it for schools? 4
National initiatives since 1997 5
Every Child Matters: Change for Childrenand the Children Act 2004 10
Higher Standards, Better Schools for All(Education White Paper,
October 2005) 11
Self-evaluation and inspection 13
Resources for teachers and parents of more able pupils 14
Summary 16
2. Policy in action 17
Why have a policy? 17
Where to start? 18
Issues to bear in mind 19
The initial audit 21
The main body of the policy 26
The action plan 35
Where next? 37
3. Identifying able mathematicians 38
Some important questions 38
What do we mean by ‘able’? 41
Strategies for identification 43
Requirements 49
4. Classroom provision 53
Introduction 53
The heart of it – assessment and evaluation 54
Down to business – meeting the needs of able mathematicians
in the classroom 58
Acceleration 60
Extension 64
Enrichment 67
Reflections 69
v
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Meeting the Needs of Your Most Able Pupils: MATHEMATICS
S
C
TI What is a problem and what is problem solving? 70
A
M
Putting theory into practice – some examples 73
E
H
T Homework 84
A
M
Action research 84
s:
pil Resources 85
u
e P Conclusion 85
bl
A
t
os 5. Beyond the classroom 87
M
r Introduction 87
u
Yo Acceleration 88
f
o
s Enrichment and extension 90
d
e Competitions 92
e
N
e Other support for teachers 93
h
t
g
n
ti 6. Case studies 96
e
e
M Compacting the Key Stage 3 curriculum 96
Primary–secondary transition 100
Continuing professional development 104
Cross-curriculum and support for other subjects 106
Provision beyond the school 108
Home–school liaison 110
Underachieving mathematicians 113
Bullying 116
Dual exceptionality 118
Asperger syndrome 121
Exceptionally able 124
Appendices 127
Appendix 1.1 Institutional quality standards in gifted and talented
education 128
Appendix 2.1 Basic audit form 134
Appendix 2.2 Detailed audit form 135
Appendix 2.3 Departmental monitoring and evaluation guidelines 136
Appendix 2.4 Outline form to support action planning 141
Appendix 3.1 Mathematical ability 142
Appendix 3.2 Key review questions 143
References 144
vi
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Foreword
Reasonable people adapt themselves to the world; unreasonable ones persist
in trying to adapt the world to themselves. Therefore all progress depends on
unreasonable people.
(adapted from George Bernard Shaw, Man and Superman)
Great talents are the most lovely and often the most dangerous fruits on the
tree of humanity. They hang upon the most slender twigs that are easily
snapped off.
(Carl Jung in Psychological Reflections)
There is a plethora of research papers and books in mathematics education, and
a huge collection of resource and support books for teachers. In amongst all
these publications there are a few robust and stable insights. One of these is that
expectation (of the learners, of their teachers, and of their parents or guardians)
is a dominant force in learners’ performance. Another is that when you find
some way of working which is effective for a particular group of learners (low
attaining, unmotivated, high attaining, displaying gifts and talents), it is also
effective with learners who do not obviously fit into that group. Another is that
labelling people reinforces behaviour patterns associated with those
expectations, and hence the expectations themselves, whereas labelling
behaviour enables learners to transcend that way of acting and move on.
Nowhere are these insights more evident than when supporting and
challenging learners who display quick thinking and appreciation of
mathematical structure. Drawing on their practical experience, the authors of
this book not only make a case for, but show how to formulate policies which, if
carried through, will support and foster thinking by all children in a school, not
just the ‘more able’.
One of the principal forces for educational reform worldwide, and certainly in
the UK, has been a desire to do more, more effectively, for learners displaying
interest in and talent for mathematics. Like all learners, they respond to and
thrive on appropriate challenge in a supportive community and in an
atmosphere that promotes curiosity, enquiry, and persistence. The challenge to
schools is to provide such an atmosphere and to promote the emergence of sub-
communities within the school culture. This leads to one of the many tensions
and topics for debate in meeting the opportunities afforded by learners
displaying mathematical ability: do you select, identify, and then construct
special provision for some, or do you build up a community which encourages
and challenges all who choose to join in? The first could be described as
‘targeting’, and is both interventionist and controlling, while the second could be
described as ‘slipstreaming’ and is respectful and empowering. This book
provides solid and practical advice for pursuing practical difficulties and
challenges of both approaches.
vii
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Meeting the Needs of Your Most Able Pupils: MATHEMATICS
S
C
TI As Shaw suggests, learners who create the most disturbance are sometimes
A
M
the ones we need to foster most strongly, and as Jung observes, learners
E
H
T displaying extreme talents may be the most psychologically and socially delicate.
A
M
Whatever the forces operating in young people’s lives, school offers an
s:
pil opportunity to enter and experience a special world of intellectual and social
u
e P challenge, through being in the presence of teachers who themselves have access
bl
A to that world.
t
os The key to effective mathematics teaching lies in the subtle messages riding
M
r on the back of social interactions and expressions of expectations. The socio-
u
Yo mathematical norms of the classroom, also described as mathematical ethos or
f
o
s atmosphere, can have a big impact on learners, as can the nature and style of the
d
e questions asked and the tasks proposed. Being in the presence of teachers who
e
N
e not only appreciate mathematics, but actually think about mathematics
h
g t themselves, contributes to an ambience within which sensitive and reflective
n
ti ways of working with learners can sustain and promote mathematical thinking.
e
e
M This book provides the kind of support and information that school managers
and teachers need in order to be awake to the issues and to make the best
possible provision for all their learners, displaying whatever abilities currently.
JOHNMASON
Professor of Mathematics Education, Open University
Senior Research Fellow, Oxford University
May 2007
viii
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Acknowledgements
This book is written for the many teachers and children we have worked with,
especially our own daughters, Kate, Biddy, Franki, Alice and Roxane, and also our
husbands, Roger and Brian, for their patience and support.
ix