Mathematics Explained for Primary Teachers

432 Pages·2010·13.113 MB·English

by  Derek Haylock

Mathematics
Explained
for

primary teachers
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Mathematics
Explained
for

primary teachers
4th edition
Derek Haylock
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© Derek Haylock 2010
First edition published 1995
Second edition published 2001
Third edition published 2005, reprinted 2006, 2007, 2008, 2009
This fourth edition published 2010
Apart from any fair dealing for the purposes of research or private study, or
criticism or review, as permitted under the Copyright, Designs and Patents Act,
1988, this publication may be reproduced, stored or transmitted in any form, or
by any means, only with the prior permission in writing of the publishers, or in
the case of reprographic reproduction, in accordance with the terms of licences
issued by the Copyright Licensing Agency. Enquiries concerning reproduction
outside those terms should be sent to the publishers.
SAGE Publications Ltd
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Library of Congress Control Number: 2010922538
British Library Cataloguing in Publication data
A catalogue record for this book is available from the British Library
ISBN 978-1-84860-196-3
ISBN 978-1-84860-197-0 (pbk)
Typeset by C&M Digitals (P) Ltd, Chennai, India
Printed and bound in Great Britain by Ashford Colour Press Ltd
Printed on paper from sustainable resources
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Contents
About the author vii
Acknowledgements viii
The student workbook and the website ix
Introduction xi
SECTION A MATHEMATICAL UNDERSTANDING 1
1 Primary teachers’ insecurity about mathematics 3
2 Mathematics in the primary curriculum 12
3 Learning how to learn mathematics 24
SECTION B USING AND APPLYING MATHEMATICS 35
4 Key processes in mathematical reasoning 37
5 Modelling and problem solving 51
SECTION C NUMBER AND ALGEBRA 63
6 Number and place value 65
7 Addition and subtraction structures 83
8 Mental strategies for addition and subtraction 97
9 Written methods for addition and subtraction 109
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vi Mathematics Explained for primary teachers
10 Multiplication and division structures 123
11 Mental strategies for multiplication and division 138
12 Written methods for multiplication and division 153
13 Remainders and rounding 164
14 Multiples, factors and primes 176
15 Squares, cubes and number shapes 187
16 Integers: positive and negative 198
17 Fractions and ratios 207
18 Calculations with decimals 219
19 Proportions and percentages 235
20 Algebra 248
21 Coordinates and linear relationships 265
SECTION D SHAPE, SPACE AND MEASURES 275
22 Measurement 277
23 Angle 295
24 Transformations and symmetry 303
25 Classifying shapes 315
26 Perimeter, area and volume 328
SECTION E STATISTICS 339
27 Handling data 341
28 Comparing sets of data 361
29 Probability 379
Answers to self-assessment questions 390
References 405
Index 411
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About the Author
Derek Haylock is an education consultant and author. He worked for over 30 years in
teacher education, both initial and in-service, and was Co-Director of Primary Initial
Teacher Training and responsible for the mathematics components of the primary pro-
grammes at the University of East Anglia (UEA), Norwich. He has considerable practical
experience of teaching and researching in primary classrooms. His work in mathematics
education has taken him to Germany, Belgium, Lesotho, Kenya, Brunei and India. He
now works as an education consultant for a number of organizations, including the
Training and Development Agency for Schools. As well as his extensive publications in
the field of education, he has written seven books of Christian drama for young people
and a Christmas musical (published by Church House/National Society).
Other books in education
Haylock, D. (1991) Teaching Mathematics to Low Attainers 8–12. London: Sage Publications.
Haylock, D. (2001) Numeracy for Teaching. London: Sage Publications.
Haylock, D. and McDougall, D. (1999) Mathematics Every Elementary Teacher Should Know.
Toronto: Trifolium Books.
Haylock, D. and D’Eon, M. (1999) Helping Low Achievers Succeed at Mathematics. Toronto:
Trifolium Books.
Browne, A. and Haylock, D. (eds) (2004) Professional Issues for Primary Teachers. London: Sage
Publications.
Haylock, D. with Thangata, F. (2007) Key Concepts in Teaching Primary Mathematics. London:
Sage Publications.
Haylock, D. and Cockburn, A. (2008) Understanding Mathematics for Young Children: A Guide
for Foundation Stage and Lower Primary Teachers, Fully Revised and Expanded Edition.
London: Sage Publications.
Haylock, D. with Manning, R. (2010) Student Workbook for Mathematics Explained for Primary
Teachers. London: Sage Publications.
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Acknowledgements
My thanks and genuine appreciation are due to the many trainee teachers and primary
school teachers with whom I have been privileged to work on initial training and in-
service courses in teaching mathematics: for their willingness to get to grips with under-
standing mathematics, for their patience with me as I have tried to find the best ways of
explaining mathematical ideas to them, for their honesty in sharing their own insecuri-
ties and uncertainties about the subject – and for thereby providing me with the material
on which this book is based. I also acknowledge my indebtedness to Marianne Lagrange,
Matthew Waters, Jeanette Graham and their colleagues at Sage Publications for their
unflagging encouragement and professionalism. And, finally, my thanks are due to my
wife, Christina, without whose support I could not have even contemplated writing a
fourth edition of this book.
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The Student Workbook
and the Website
To accompany this book there are two sources of supporting material. The first is the
Student Workbook for Mathematics Explained for Primary Teachers (Haylock with
Manning, 2010). This book, written with my colleague at UEA, Ralph Manning, has been
produced specifically to accompany this fourth edition. For each of Chapters 6–29 of
Mathematics Explained the workbook provides a set of tasks related to the mathematical
content of that chapter, together with answers and further explanation. The tasks are of
three kinds: checking understanding; using and applying; and learning and teaching.
The second is the Mathematics Explained for Primary Teachers website (www.
sagepub.co.uk/haylock). Included on this website are 45 of the 62 check-ups from my
book, Numeracy for Teaching (Haylock, 2001). This material relates directly to the
demands of the Numeracy Test that must be passed by trainee teachers in England as a
prerequisite for Qualified Teacher Status. Where relevant I indicate towards the end of
various chapters the Check-Ups available on the website that can be used by readers
looking for further practice – but with a focus on the application of the mathematical
knowledge and skills to the job of being a teacher. In addition, the website contains a
comprehensive glossary of the key terms used in this fourth edition of Mathematics
Explained for Primary Teachers. This combines all the glossaries at the ends of
chapters into a single list in alphabetical order.
Along with other relevant information, web links and assorted material, the website
will also provide details of how the content of this book, chapter by chapter, links to
primary school national curricula for England, Wales and Scotland and the level descrip-
tions within each attainment target.
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