Table Of ContentMathematics in Early Years
Education
This fourth edition of the bestselling Mathematics in Early Years Educationprovides
an accessible introduction to the teaching of mathematics in the early years. Covering
all areas of mathematics – number and counting, calculation, pattern, shape,
measures and data handling – it provides a wide range of practical acti vities and
guidance on how to support young children’s mathematical development. There is
also guidance on managing the transition to KS1 and a strong emphasis throughout
on creating home links and working in partnership with parents.
This new edition has been fully updated to incorporate the latest research and
thinking in this area and includes:
(cid:2) why mathematics is important as a way of making sense of the world
(cid:2) how attitudes to mathematics can influence teaching and learning
(cid:2) how children learn mathematics and what they are capable of learning
(cid:2) how technology can support maths teaching
(cid:2) maths phobia and the impact society has on maths teaching
(cid:2) material on sorting, matching and handling data
(cid:2) the importance of educating about finance in today’s world
(cid:2) ideas for observation and questioning to assess children’s understanding
(cid:2) examples of planned activities
(cid:2) suggestions for language development
(cid:2) assessment criteria.
This textbook is ideal for those training to be teachers through an undergraduate or
PGCE route, those training for Early Years Professional Status and those studying
early childhood on foundation or honours degrees, as well as parents looking to
explore how their young children learn mathematics. This will be an essential text
for any early years practitioner looking to make mathematics interesting, exciting
and engaging in their classroom.
Ann Montague-Smith was formerly Principal Lecturer in Primary Education at
University College Worcester, UK.
Tony Cotton was previously Associate Dean and Head of Education at Leeds
Metropolitan University, UK. Since 2012, he has been working as a freelance writer
and education consultant. Tony has over 15 years’ experience teaching maths
education and 10 years’ experience teaching mathematics in schools.
Alice Hansen worked extensively in England and abroad as a primary school
teacher, Principal Lecturer in Initial Teacher Education, author and consultant
before becoming the director of Children Count Ltd, a highly successful educational
consultancy business.
Alison J. Price was formerly Principal Lecturer in Primary Teacher Education at
Oxford Brookes University, UK.
Mathematics
in Early Years
Education
Fourth edition
Ann Montague-Smith, Tony Cotton,
Alice Hansen and Alison J. Price
Fourth edition published 2018
by Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
and by Routledge
711 Third Avenue, New York, NY 10017
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2018 Ann Montague-Smith, Tony Cotton, Alice Hansen and Alison J. Price
The right of Ann Montague-Smith, Tony Cotton, Alice Hansen and Alison J. Price
to be identified as authors of this work has been asserted by them in accordance
with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
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.
Trademark notice: Product or corporate names may be trademarks or registered
trademarks, and are used only for identification and explanation without intent to
infringe.
First edition published by David Fulton Publishers 1997 as Mathematics in Nursery Education
Second edition published by Routledge in 2007 as Mathematics in Nursery Education
Third edition published by Routledge 2012
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 for this book has been requested
ISBN: 978-1-138-63192-2 (hbk)
ISBN: 978-1-138-73112-7 (pbk)
ISBN: 978-1-315-18910-9 (ebk)
Typeset in Melior
by Fish Books Ltd.
Contents
List of illustrations vii
Introduction xi
1 Learning mathematics in early years settings 1
2 Planning, organising and assessing for mathematics 24
3 Number and counting 48
4 Calculating and problem-solving with number 81
5 Pattern 116
6 Shape and space 153
7 Measures: making comparisons 189
8 Sorting, matching and handling data 223
Glossary 248
References and further reading 252
Index 265
v
List of illustrations
List of figures
1.1 Babies from birth are interested in number, patterns, regularity
and shape 7
1.2 Relationships between the elements of mathematical experiences 16
1.3 Pictographic recording: ‘Mummy duck (centre) said quack and
four came back’ 20
1.4 Iconic and early symbolic recording: 10 ribbons and 3 (the marks
‘read’ 3, 1, 2) 20
1.5 A whiteboard and pen allowed exploration of numerals 21
1.6 ‘Five ducks’: this four-year-old shows a good knowledge of numerals 22
2.1 ‘One, two, three, it’s four!’ – using a puppet to make mistakes and
model misconceptions 28
2.2 An example of a weekly planning sheet for mathematics 33
2.3 Poster showing key vocabulary and questions for number and
counting 34
2.4 Example of an activity plan (based on an activity from Chapter 7) 39
2.5 Record of experiences in number and counting 41
3.1 The number line 49
3.2 Piaget’s test of conservation of number: two matched rows of counters 50
3.3 Piaget’s test of conservation of number: second row transformed 50
3.4 Using familiar symbols to record ‘five ducks – I’m nearly 5’ 56
3.5 Numicon tiles 1–10 58
3.6 Different patterns of 5 suggest different ways it can be made up 59
3.7 Different representations of 8 on an abacus, as 5 + 3 and as double –4 59
3.8a and b Ordering numbers: a number jigsaw; numbered flowers pegged
on a line 61
3.9 ‘6, 5, 4’, practising counting backwards from 10 on the number track 63
3.10 Number track highlighting multiples of 2 and a 100 square highlighting
multiples of 5 63
vii
viii List of illustrations
3.11 The boys counted to see how many frogs they managed to flip into
the pool 64
3.12 Using the numbers jigsaw while singing ‘5 little ducks went
swimming one day’ 68
3.13 Notices or name boards by the sand or water play areas encourage
children to count, check and interpret data 69
3.14 Domino match 80
4.1 Using staircase towers and a number line to emphasise ‘one more’,
‘one fewer’ 82
4.2 Exploring two colour partitioning patterns for 6 83
4.3 Partitioning and recombining can be described in terms of subtraction
and addition 84
4.4 Modelling addition by increase on a number line 86
4.5 Subtraction as take away and as difference 86
4.6 Division: 6 ÷ 2 as sharing and as grouping 87
4.7 Fractions: half of a whole circle and half of a set of eight 87
4.8 Addition by counting all 89
4.9 Addition by counting on 90
4.10 Comparing sets: having shared out the frogs 94
4.11 Partitioning: two activities partitioning eight 95
4.12 ‘There was five ladybirds (centre) and only one left so four flew away’ 96
4.13 Addition: rolling two balls down the chute into numbered crates 101
4.14 ‘There, now I have nine houses like on the walk’ 103
4.15 Flip-it for number combinations to 10 107
5.1 Repeating patterns: horizontal, vertical and diagonal 117
5.2 A growing pattern (which relates to the odd numbers 1, 3, 5, 7 …) 117
5.3 Reflective symmetry (top) and rotational symmetry (bottom) in
nature and the built environment 118
5.4 An array showing three rows of 4 and four columns of 3 119
5.5 The original threaded lace is placed above the one to be made 122
5.6 Repeating pattern made with different shaped blocks 123
5.7 Textures and patterns are all around the setting 124
5.8 Pattern in the built environment (a pattern walk through Broseley,
Shropshire) 126
5.9 Exploring making lines with crayon on big paper (three-year-old) 127
5.10 Paint and marbles can be used to produce interesting line patterns 129
5.11 Blot and fold patterns can produce interesting line effects which
show the effect of reflections 130
5.12 Creating a collage sequence on edging paper 130
5.13 Clapping patterns 132
5.14 Growing patterns (1,2,3…; 2,4,6,8…; 1,1,1,2,1,3…) 132
5.15 Cyclic patterns are closed repeating patterns 132
5.16 People patterns: hands up, hands down, hands up, hands down … 140
List of illustrations ix
5.17 Pentatonic scale 142
5.18 Pegboard sequence 144
5.19 100 square highlighting multiples of 2 and 11 145
6.1 All these shapes are closed. They can be squeezed or transformed
into each other 154
6.2 Two examples of triangles; both have three sides yet many children
will not recognise the second as a triangle 156
6.3 A range of triangles (from left to right): equilateral, isosceles,
right-angled and scalene triangles 156
6.4 Children used to seeing shapes in only one orientation will identify
the first two shapes 157
6.5 Non-examples of a triangle 157
6.6 Libby at 14 months enjoys exploring shape 159
6.7 The boys made ‘Transformers’, which can change shape from robots
to machines 164
6.8 Exploring 3D shape through building with wooden blocks 167
6.9 Exploring symmetry in manufactured items 169
6.10 The square piece will fit back into its outline in four ways 169
6.11 Symmetrical pictures made from shape tiles 170
6.12 At the top she announced ‘I’m going to go down the slide backwards’ 170
6.13 The train track enables children to explore movements of straight
and turn 171
7.1 Children who cannot conserve will think the straight line is longer 192
7.2 Visits to the Botanic Gardens and the Natural History Museum 198
7.3 Sand play: ‘It’s full up to the top’ 200
7.4 Covering areas with sponge printing 202
7.5 Exploring capacity indoors and out 204
7.6 Sorting pictures of themselves when younger prompts discussion
about past events 206
7.7 The elastic band can be moved to mark the level for pouring 213
7.8 To make a rocker timer: put a lump of plasticine at the base of
a coffee jar lid 216
8.1 Suitably labelled boxes (words and pictures) offer opportunities
for sorting when tidying up 224
8.2 Table and bar chart of favourite cakes data 225
8.3 Eye colour represented by bricks, pictures, block graph and bar chart 228
8.4 Creating purposeful groups: ‘all these cars open’; ‘for the bathroom’ 231
8.5 Sorting for animals with ears 231
8.6 Using an egg box to compare 1:1 232
8.7 Lines of objects of different sizes are not helpful for comparison 233
8.8 A list in emergent writing: ‘What we need for our game’
(four-year-old) 234
8.9 A simple table recording children’s favourite pets 235
