Mathematics Through Play in the Early Years
Publication Year: 2011
Teaching mathematics to young children in creative ways is made easy with this Second Edition of a wonderful book, which offers the reader clear advice and lots of exciting ideas to use in any early years setting.By showing how to introduce mathematical concepts through play-based activities, Mathematics Through Play in the Early Years is in tune with current thinking about best practice in teaching, and with the requirements of the Early Years Foundation Stage and current Numeracy strategy.
- Front Matter
- Back Matter
- Subject Index
- Chapter 1: Why Play?
- Chapter 2: Creating and Using a Mathematical Environment
- Chapter 3: Creative Recording and Mathematical Graphics
- Chapter 4: Counting and Using Number
- Chapter 5: Pattern
- Chapter 6: Shape and Space
- Chapter 7: Measurement
- Chapter 8: Planning, Organizing and Assessing Independent Play
- Chapter 9: Parents as Partners: Involving Parents in Mathematics and Play
Education at SAGE[Page ii]
SAGE is a leading international publisher of journals, books, and electronic media for academic, educational, and professional markets.
Our education publishing includes:
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Find out more at: http://www.sagepub.co.uk/education
© Kate Tucker, 2010
First edition published 2005
Reprinted 2006 (twice), 2007
Second 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 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.
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About the Author[Page vi]
Trained for working with nursery and lower primary-aged children, Kate Tucker specializes in early years teaching with a particular interest in early years mathematics. She is an early years teacher at Two Moors Primary School, Tiverton, Devon where she is also Head of Foundation Stage and Key Stage 1. Kate Tucker has taught children aged three to eight for over 20 years and has written widely on early years mathematics and Foundation Stage practice. She has worked with Devon Education Services as Leading Maths Teacher, Foundation Stage Leading Maths Teacher and Leading Foundation Stage Teacher, and she has also taught the mathematics module for Early Childhood Studies B.Ed students at the University of Plymouth.
Much of this book would not have been possible without the early years children of Bickleigh-on-Exe Church of England Primary School and Two Moors Primary School, Tiverton, Devon. Members of the Family Learning Group at Two Moors Primary School have also made a valued contribution, for which I am most grateful. For this second edition, I would like to thank Roy Kerrigan for his support, Vicki Davidson for her input on parental involvement and Mia Horrell and Martin Preston for their support and interest. I would also like to thank Sue Rogers for her encouragement at the outset, Shirley Brooks for her tremendous contribution to playful mathematics, David Goode for his cooperation, Catherine Lawes for her interest in early years maths and ICT, and Vicky Viney for her drawings. Finally, my thanks go to those members of the Devon Mathematics Team who have given me opportunities to develop my own early years practice.
Some time ago, I visited a student teacher in a reception class where I observed a group of children learning about ‘length’. After a whole-class discussion about ‘long things and short things’ the children were sent away in groups to complete a worksheet. This consisted of a column of hand-drawn objects or things of varying lengths, for example, a snake, a pencil and a shoe. Alongside these were written the words ‘long’ and ‘short’. The task for the children was to draw a line from each object to the correct word. After about 10 minutes I joined a small boy, aged four and new to school. I asked him how he was getting on and what he was doing. He replied ‘don't know … it's too hard’. He was clearly miserable and bored. I left the classroom wondering, what knowledge did he gain from this activity? Perhaps a feeling of failure and the view that school learning is hard? I don't wish to over-dramatise the effect of this brief snapshot of classroom life nor to be overly critical of the teacher in question. Rather I want to emphasise that in the current educational climate where practitioners are under enormous pressure to meet prescribed learning objectives and government targets, and to produce hard evidence of work undertaken, it is all too easy to lose sight of the learning needs of these young children. Perhaps most importantly, this example serves as a (painful) reminder that the activities we plan may not always achieve our intentions for children's learning. It reminds us too of the need to find appropriate ways to enable children to experience mathematics in ways which make ‘human sense’ (Donaldson, 1978).
Working with young children is challenging and sometimes difficult. We don't always get it right. But recent developments in the early years sector, in particular the implementation of the Early Years Foundation Stage framework (2007), offer a welcome opportunity to revisit some of the most enduring principles regarding young children's learning. First, we know that young children need to be active in their learning – hands on and brains on. Secondly, play is a key way in which young children experience the world through their interaction with materials, concepts and people. Thirdly, significant others play a vital role in helping young children to make sense of the sometimes bewildering world around them. Finally, we need to acknowledge children's active role in shaping teaching and learning experiences in the classroom and particularly in their play. We might, then, think in terms of a co-constructed pedagogy as a negotiated space, based on a reciprocal relationship between children and their educators (Rogers and Evans, 2008). These principles are underpinned by many decades of robust research and inform the ideas presented here in this book in its welcome second edition. Drawing on the most up-to-date reviews of research and practice in primary and early years education, Kate Tucker argues persuasively throughout the book against the ‘worksheet driven’ culture in schools and asks us to consider instead more creative and active ways to nurture children's early mathematical understanding. In light of renewed interest in the play, the book promotes a play-based approach to the teaching of mathematics; one that is both appropriate to the learning needs of young children and, importantly for practitioners that meets curriculum requirements. It is especially good to see that the book acknowledges the potential problem of transition [Page ix]from the Foundation Stage to Key Stage 1, including a consideration of the vexed issue of teaching mixed-aged classes. Here she argues against a watered-down National Numeracy Strategy for children in reception in favour of an active play-based approach for all. This is illustrated through the many practical examples and ideas designed to help practitioners to move beyond the worksheet to more creative interpretations of the curriculum. Play is at the heart of this, sometimes initiated by the child and sometimes a collaborative endeavour between child and adult. This reciprocal relationship is vital, Kate argues, if we want children to learn in a meaningful and lasting way and make connections with other areas of knowledge and understanding. We are reminded also of the Reggio Emilia approach, where mathematics is but one of the so-called ‘hundred languages’ of children (Edwards, 1998). The present book conveys the message that providing children with opportunities to record their mathematical knowledge and understanding through a variety of media and forms of representation will help them to make personally meaningful connections with other areas of knowledge and show practitioners what they know in authentic ways.
At a time when the Early Years workforce is both expanding and becoming more diverse, practitioners in all settings and at all stages of their training will find this book a highly accessible and useful read. It is packed with ideas based on sound knowledge about how young children learn best. And the strength of this book is that it is firmly grounded in real classrooms with real children: it is worth noting that the ideas in the book are tried and tested in the author's classroom. I have been privileged on many occasions to visit Kate's classroom and have observed at first hand the many benefits to the children of learning mathematics through playful activities, not least the sense of fun and enjoyment it engenders.
Finally, as more four-year-olds than ever are placed in primary school classrooms (Rogers and Rose, 2007) it is imperative that young children receive experiences that capture and nurture their natural curiosity and motivation to learn. Young children are powerful, creative and competent, and we must capitalize on this in our teaching. This book will certainly help practitioners to have courage to move beyond the ‘worksheet’ into more exciting and creative mathematical territory for both themselves and the children.London, Institute of Education,References[Page x]1978) Children's Minds. London: Fontana.(1998) The Hundred Languages of Children: The Reggio Emilia Approach,, and (2nd Edition. London: Ablex Publishing.DfES (2007) Statutory Framework for the Early Years Foundation Stage. Nottingham: Department for Education and Skills.2008) Inside Role Play in Early Childhood Education: Researching Children's Perspectives. London: Routledge.and (2007) Ready for Reception? The advantages and disadvantages of single-point entry to school, Early Years, 27, 1, pp. 47–63. http://dx.doi.org/10.1080/09575140601135130and (
Appendices[Page 148][Page 149][Page 150]Photocopiable 1: Independent play[Page 151][Page 152]Photocopiable 2: Independent play in the outside play area[Page 153]Photocopiable 3: Observation sheet for Independent playPhotocopiable 4: Record and assessment sheet for review time
Algorithm A step-by-step procedure for solving a specific problem, such as an addition, subtraction, multiplication or division problem. Array An ordered collection of objects or numbers, often presented in rows or columns. Cardinal The number that indicates how many there are in a set. CD Creative development. CLL Communication, language and literacy. Complementary addition The mathematical operation that finds out how many more are needed to make a given number. ELG Early Learning Goals. FS Foundation Stage ICT Information and Communication Technology. IWB Interactive whiteboard KUW Knowledge and understanding of the world Lit Literacy Ordinal A number denoting the position in a sequence, such as 1st, 2nd, 3rd, etc. Partition The act of dividing a set of of objects into two subsets. PD Physical development. PE Physical Education. Pictogram A visual representation of data pictures to denote the nature of the information it represents. PNS Primary National Strategy. PSRN Problem solving, resoning and number. [Page 155] R Reception. RE Religious Education. Rotation The movement of an object about a fixed point. Schema Repeated patterns of behaviour in young children. Sequence Objects, shapes or numbers arranged in a line, such as cow, sheep, pig. When this is repeated several times, it forms a repeating pattern. Sukkot Jewish autumn festival during which families build a three-sided shelter (sukkah) with a roof made of branches and greenery in their garden. It reminds them of the Jews' journey from Egypt to Israel. Symmetry A picture or object that has ‘sameness’ on two sides. Tessellation Fitting shapes together without leaving gaps. Translation Movement along a straight line. Yl/2 Year 1/2.
Resources[Page 156]Mrs Mopple's Washing Line (1994) Red FoxJasper's Beanstalk and (1992) Hodder & StoughtonBumpus Jumpus Dinosaurumpus and (2002) OrchardLadybird, Ladybird (1998) Andersen PressThe Gruffalo and (1999) Macmillan Children's BooksJamaica and Brianna and (1994) HeinemannThe Sand Horse and (2002) Andersen PressThe Enormous Crocodile and (1978) CapeRosie's Walk (1992) Random CenturyThe Pet Shop and (1990) HeinemannA Bit More Bert and (2002) PuffinThe Mousehole Cat and (1990) Walker BooksHanda's Hen (2002) Walker BooksHonda's Surprise (1994) Walker BooksThe Story of Little Babaji, and (1997) Ragged BearsNumicon®, Numicon Limited, http://www.numicon.comUseful storybooks depicting counting, cardinal and ordinal numberMy Granny Went to Market: A Round the World Counting Book (1995) Barefoot BooksMr Magnolia (1999) Red FoxHanda's Hen (2002) Walker BooksEngines, Engines (2001) Trafalgar Square[Page 157]1, 2, 3, to the Zoo: A Counting Book (1987) Hamish HamiltonOut for the Count (1991) Frances Lincoln LtdTen Green Monsters (1993) Andersen PressOne Green Island (1996) Walker BooksEmeka's Gift (1995) Frances Lincoln LtdAddition and SubtractionFive Little Ducks (1992) Orchard BooksTen Seeds (2001) Andersen PressMany Hands Counting Book (1999) Walker BooksTen Red Apples (2002) Walker BooksTen Terrible Pirates and (1994) David BennettTwo Little Witches (1996) Walker BooksUsing MoneyA Bargain for Frances (1992) MammothThe Great Pet Sale (1998) Hodder Children's BooksSmall Change (1992) Red FoxBunny Money (1991) Picture CorgiMultiplication and DivisionThe Doorbell Rang (1986) Bodley HeadOne Is a Snail, Ten Is a Crab et al. (2003) Walker BooksBridget Riley. Paintings from the 60s and 70s texts by , and (1999) Serpentine GalleryAfrican, Indian and Islamic Art, http://www.geomatrix.co.ukAndy Goldsworthy produced by and (1990) VikingTom Thumb's Musical Maths (1998) A & C BlackUseful Storybooks Depicting PatternWhat Goes Snap! and (1998) Walker BooksThe Very Hungry Caterpillar (1970) HamiltonKings of Another Country (1992) Oxford University PressNikos the Fisherman (1995) Oxford University PressMrs Mopple's Washing Line (1994) Red FoxTen Bright Eyes (1998) LeveinsonLucy and Tom's 1, 2, 3 (1989) PuffinCurious Clownfish (1990) Frances Lincoln[Page 158]Elmer McKee, (1990) Red FoxMy Mum and Dad Make Me Laugh (1994) Walker BooksThe Big Concrete Lorry (1989) WalkerSnail Trail (2000) AndersenTraffic Jam (1990) Orchard BooksCome Away From the Water, Shirley (1977) CapeJack's Fantastic Voyage (1994) Red FoxKatie Morag and the Two Grandmothers (1985) Bodley Head Community Playthings, http://www.communityplaythings.comMondrian (2001) Midpoint PressBarbara Hepworth and (2001) Tate Gallery PublishingSpy Shapes in Art (2004) CollinsUseful Storybooks Showing Shape and SpaceBrown Rabbit's Shape Book (1994) KingfisherIf At First You Do Not See (1982) SparrowThe Secret Birthday Message (1972) Hamish HamiltonLittle Cloud (1998) PuffinThe Shape of Things (1994) WalkerThe Wheeling and Whirling-Around Book and (1994) WalkerChanges, Changes (1994) Red FoxGrandfather Tang's Story (1991) MacRaeThe Shape Game (2003) DoubledayLasy®, Lasy® GmbH, email@example.comUseful Storybooks about Weight and CapacityWho Sank the Boat? (1982) HamiltonThe Lighthouse Keeper's Catastrophe and (1986) DeutschMr Gumpy's Outing (2001) Red FoxHoney Biscuits (1997) Kingfisher[Page 159]Length, Distance and HeightRosie's Walk (1992) Random CenturySix Feet Long and Three Feet Wide and (1999) Walker BooksJim and the Beanstalk (1970) HamiltonHue Boy (1992) GollanczTimeThe Bad-Tempered Ladybird (1997) HamiltonTick-Tock (1996) Franklin WattsMr Wolf's Week (1997) Picture LionsThe Stopwatch (1986) Walker BooksThe School Bus Comes at Eight O'clock (1993) Andersen Press2Simple Software, firstname.lastname@example.orgBear's Adventure (1988) MacRaeThe Lighthouse Keeper's Lunch and (2007) ScholasticUseful Websites for Curriculum, Planning and Assessment
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Norwich: Her Majestry's Stationery Office.DCSF (2008) The Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools. http://www.publications.teachers.gov.uk/eOrderingDownload/Williams%20Mathematics.pdf (accessed June 2008).2003) The Impact of Parental Involvement, Parental Support and Family Education on Pupil Achievement and Adjustment. (Research Report 433). London: Department for Education and Schools.(DfEE (1999) The National Numeracy Strategy. London: Department for Education and Employment.DfES (2002) Birth to Three Matters: A Framework to Support Children in their Earliest Years. London: Department for Education and Skills.DfES (2006) Primary Framework for Literacy and Mathematics. Norwich: Department for Education and Skills.DfES (2007a) Statutory Framework for the Early Years Foundation Stage. Nottingham: Department for Education and Skills.DfES (2007b) Practice Guidance for the Early Years Foundation Stage. Nottingham: Department for Education and Skills.1978) Children's Minds. Glasgow: Fontana.(2002) A non-paginated discussion paper ‘Creativity in the early years: children as “authors and inventors”’, Early Education (38), autumn.(2002) Starting from the Child. Buckingham: Open University Press.(2005) ‘Early identification and interventions for students with mathematics difficulties’, Journal of Learning Disabilities, 38(4): 293–304. http://dx.doi.org/10.1177/00222194050380040301, and (2008) ‘“How do you teach nursery children mathematics?” In search of a mathematics pedagogy for the early years’, in I.Thompson (ed.) Teaching and Learning Early Number,([Page 161]2nd edition.Berkshire: Open University Press, pp. 217–26.1994) ‘Mathematics and Play’, in J.R.Moyles (ed.) The Excellence of Play. Buckingham: Open University Press, pp. 145–47.(Gura, R. (ed.) (1992) Exploring Learning: Young Children and Blockplay. 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