Mathematics Through Play in the Early Years

Books

Kate Tucker

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    About the Author

    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.

    Acknowledgements

    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.

    Foreword

    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 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.

    Dr SueRogers, Institute of Education, London
    References
    Donaldson, M. (1978) Children's Minds. London: Fontana.
    Edwards, C., Gandini, L. and Forman, G. (1998) The Hundred Languages of Children: The Reggio Emilia Approach,
    2nd Edition
    . London: Ablex Publishing.
    DfES (2007) Statutory Framework for the Early Years Foundation Stage. Nottingham: Department for Education and Skills.
    Rogers, S. and Evans, J. (2008) Inside Role Play in Early Childhood Education: Researching Children's Perspectives. London: Routledge.
    Rogers, S. and Rose, J. (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/10.1080/09575140601135130
  • Appendices

    Photocopiable 1: Independent play

    Photocopiable 2: Independent play in the outside play area

    Photocopiable 3: Observation sheet for Independent play

    Photocopiable 4: Record and assessment sheet for review time

    Glossary

    AlgorithmA step-by-step procedure for solving a specific problem, such as an addition, subtraction, multiplication or division problem.
    ArrayAn ordered collection of objects or numbers, often presented in rows or columns.
    CardinalThe number that indicates how many there are in a set.
    CDCreative development.
    CLLCommunication, language and literacy.
    Complementary additionThe mathematical operation that finds out how many more are needed to make a given number.
    ELGEarly Learning Goals.
    FSFoundation Stage
    ICTInformation and Communication Technology.
    IWBInteractive whiteboard
    KUWKnowledge and understanding of the world
    LitLiteracy
    OrdinalA number denoting the position in a sequence, such as 1st, 2nd, 3rd, etc.
    PartitionThe act of dividing a set of of objects into two subsets.
    PDPhysical development.
    PEPhysical Education.
    PictogramA visual representation of data pictures to denote the nature of the information it represents.
    PNSPrimary National Strategy.
    PSRNProblem solving, resoning and number.
    RReception.
    REReligious Education.
    RotationThe movement of an object about a fixed point.
    SchemaRepeated patterns of behaviour in young children.
    SequenceObjects, shapes or numbers arranged in a line, such as cow, sheep, pig. When this is repeated several times, it forms a repeating pattern.
    SukkotJewish 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.
    SymmetryA picture or object that has ‘sameness’ on two sides.
    TessellationFitting shapes together without leaving gaps.
    TranslationMovement along a straight line.
    Yl/2Year 1/2.

    Resources

    Mrs Mopple's Washing LineHewett, Anita (1994) Red Fox
    Jasper's BeanstalkButterworth, Nick and Inkpen, Mick (1992) Hodder & Stoughton
    Bumpus Jumpus DinosaurumpusMitton, Tony and Parker-Rees, Guy (2002) Orchard
    Ladybird, LadybirdBrown, Ruth (1998) Andersen Press
    The GruffaloDonaldson, Julia and Scheffler, Axel (1999) Macmillan Children's Books
    Jamaica and BriannaHavill, Juanita and O'Brien, Anne Sibley (1994) Heinemann
    The Sand HorseTurnbull, Ann and Foreman, Michael (2002) Andersen Press
    The Enormous CrocodileDahl, Roald and Blake, Quentin (1978) Cape
    Rosie's WalkHutchins, Pat (1992) Random Century
    The Pet ShopAhlberg, Allan and Amstutz, Andre (1990) Heinemann
    A Bit More BertAhlberg, Allan and Briggs, Raymond (2002) Puffin
    The Mousehole CatBarber, Antonia and Bayley, Nicola (1990) Walker Books
    Handa's HenBrowne, Eileen (2002) Walker Books
    Honda's SurpriseBrowne, Eileen (1994) Walker Books
    The Story of Little Babaji, Bannerman, Helen and Marcellino, Fred (1997) Ragged Bears
    Numicon®, Numicon Limited, http://www.numicon.com
    Useful storybooks depicting counting, cardinal and ordinal number
    My Granny Went to Market: A Round the World Counting BookBlackstone, Stella (1995) Barefoot Books
    Mr MagnoliaBlake, Quentin (1999) Red Fox
    Handa's HenBrowne, Eileen (2002) Walker Books
    Engines, EnginesBruce, Lisa (2001) Trafalgar Square
    1, 2, 3, to the Zoo: A Counting BookCarle, Eric (1987) Hamish Hamilton
    Out for the CountCave, Kathryn (1991) Frances Lincoln Ltd
    Ten Green MonstersClarke, Gus (1993) Andersen Press
    One Green IslandHard, Charlotte (1996) Walker Books
    Emeka's GiftOneyefulu, Ifeoma (1995) Frances Lincoln Ltd
    Addition and Subtraction
    Five Little DucksBeck, Ian (1992) Orchard Books
    Ten SeedsBrown, Ruth (2001) Andersen Press
    Many Hands Counting BookGranstorm, Brita (1999) Walker Books
    Ten Red ApplesMiller, Virginia (2002) Walker Books
    Ten Terrible PiratesRogers, Paul and Emma (1994) David Bennett
    Two Little WitchesZiefert, Harriet (1996) Walker Books
    Using Money
    A Bargain for FrancesHoban, Russell (1992) Mammoth
    The Great Pet SaleInkpen, Mick (1998) Hodder Children's Books
    Small ChangeLewis, Rob (1992) Red Fox
    Bunny MoneyWells, Rosemary (1991) Picture Corgi
    Multiplication and Division
    The Doorbell RangHutchins, Pat (1986) Bodley Head
    One Is a Snail, Ten Is a CrabSayre, April Pulley et al. (2003) Walker Books
    Bridget Riley. Paintings from the 60s and 70s texts by Corrin, Lisa G., Kudielka, Robert and Spalding, Frances (1999) Serpentine Gallery
    African, Indian and Islamic Art, http://www.geomatrix.co.uk
    Andy Goldsworthy produced by Hollis, Jill and Cameron, Ian (1990) Viking
    Tom Thumb's Musical MathsMacGregor, Helen (1998) A & C Black
    Useful Storybooks Depicting Pattern
    What Goes Snap!Boyle, Alison and Gale, Cathy (1998) Walker Books
    The Very Hungry CaterpillarCarle, Eric (1970) Hamilton
    Kings of Another CountryFrench, Fiona (1992) Oxford University Press
    Nikos the FishermanFrench, Fiona (1995) Oxford University Press
    Mrs Mopple's Washing LineHewett, Anita (1994) Red Fox
    Ten Bright EyesHindley, Judy (1998) Leveinson
    Lucy and Tom's 1, 2, 3Hughes, Shirley (1989) Puffin
    Curious ClownfishMaddern, Eric (1990) Frances Lincoln
    Elmer McKee, David (1990) Red Fox
    My Mum and Dad Make Me LaughSharratt, Nick (1994) Walker Books
    The Big Concrete LorryHughes, Shirley (1989) Walker
    Snail TrailBrown, Ruth (2000) Andersen
    Traffic JamOwen, Annie (1990) Orchard Books
    Come Away From the Water, ShirleyBurningham, John (1977) Cape
    Jack's Fantastic VoyageForeman, Michael (1994) Red Fox
    Katie Morag and the Two GrandmothersHedderwick, Mairi (1985) Bodley Head Community Playthings, http://www.communityplaythings.com
    MondrianDeicher, Susanne (2001) Midpoint Press
    Barbara HepworthGale, Matthew and Stephens, Chris (2001) Tate Gallery Publishing
    Spy Shapes in ArtMicklethwait, Lucy (2004) Collins
    Useful Storybooks Showing Shape and Space
    Brown Rabbit's Shape BookBaker, Alan (1994) Kingfisher
    If At First You Do Not SeeBrown, Ruth (1982) Sparrow
    The Secret Birthday MessageCarle, Eric (1972) Hamish Hamilton
    Little CloudCarle, Eric (1998) Puffin
    The Shape of ThingsDodds Dale, Ann (1994) Walker
    The Wheeling and Whirling-Around BookHindley, Judy and Chamberlain, Margaret (1994) Walker
    Changes, ChangesHutchins, Pat (1994) Red Fox
    Grandfather Tang's StoryTompert, Ann (1991) MacRae
    The Shape GameBrowne, Anthony (2003) Doubleday
    Lasy®, Lasy® GmbH, info@lasy.com
    Useful Storybooks about Weight and Capacity
    Who Sank the Boat?Mien, Pamela (1982) Hamilton
    The Lighthouse Keeper's CatastropheArmitage, Ronda and David (1986) Deutsch
    Mr Gumpy's OutingBurningham, John (2001) Red Fox
    Honey BiscuitsHooper, Meredith (1997) Kingfisher
    Length, Distance and Height
    Rosie's WalkHutchins, Pat (1992) Random Century
    Six Feet Long and Three Feet WideBillington, Jeannie and Smee, Nicola (1999) Walker Books
    Jim and the BeanstalkBriggs, Raymond (1970) Hamilton
    Hue BoyMitchell, Rita Phillips (1992) Gollancz
    Time
    The Bad-Tempered LadybirdCarle, Eric (1997) Hamilton
    Tick-TockDunbar, James (1996) Franklin Watts
    Mr Wolf's WeekHawkins, Colin (1997) Picture Lions
    The StopwatchLloyd, David (1986) Walker Books
    The School Bus Comes at Eight O'clockMcKee, David (1993) Andersen Press
    2Simple Software, info@2simple.com
    Bear's AdventureBlathwayt, Benedict (1988) MacRae
    The Lighthouse Keeper's LunchArmitage, Rhonda and David (2007) Scholastic

    References

    Athey, C. (1990) Extending Thought in Your Children: A Parent-Teacher Partnership. London: Paul Chapman Publishing.
    Atkinson, S. (ed.) (1992) Mathematics with Reason. The Emergent Approach to Primary Maths. London: Hodder & Stoughton.
    Bennett. N., Wood, L. and Rogers, S. (1997) Teaching Through Play: Teacher's Thinking and Classroom Practice. Buckingham: Open University Press.
    Bilton, H. (1998) Outdoor Play in the Early Years: Management and Innovation. London: David Fulton Publishers.
    Bruce, T. (1991) Time to Play in Early Childhood Education. London: Hodder & Stoughton.
    Bruner, J. (1991) ‘The nature and uses of immaturity’, in M.Woodhead. R.Carr and R.Light (eds) Becoming a Person. London: Routledge/Open University Press, pp. 247–72.
    Burke, S., Slaughter, C. and Tynemouth, A. (eds) (2002) Play Maths!Devon: Devon Curriculum Services.
    Carruthers, E. and Worthington, M. (2006) Children's Mathematics: Making Marks, Making Meaning,
    2nd edition.
    London: Sage Publications.
    DCSF (2007) The Children's Plan: Building Brighter Futures. 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).
    Desforges, C. (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.
    Donaldson, M. (1978) Children's Minds. Glasgow: Fontana.
    Fawcett, M. (2002) A non-paginated discussion paper ‘Creativity in the early years: children as “authors and inventors”’, Early Education (38), autumn.
    Fisher, J. (2002) Starting from the Child. Buckingham: Open University Press.
    Gersten, N., Jordan, C. and Flojo, J.R. (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
    Gifford, S. (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,
    2nd edition.
    Berkshire: Open University Press, pp. 217–26.
    Griffiths, R. (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. London: Paul Chapman Publishing.
    Haylock, D. and Cockburn, A. (2003) Understanding Mathematics in the Lower Primary Years. London: Paul Chapman Publishing.
    Hughes, M. (1986) Children and Number. Oxford: Basil Blackwell.
    Kitson, N. (1994) ‘“Please Miss Alexander: will you be the robber?” Fantasy Play: a case for adult intervention’, in J.R.Moyles (ed.) The Excellence of Play. Buckingham: Open University Press, pp. 88–98.
    Lindon, J. (2001) Understanding Children's Play. Cheltenham: Nelson Thornes.
    Montague-Smith, A. (2002) Mathematics in Nursery Education. London: David Fulton Publishers.
    Moyles, J.R. (ed.) (1994) The Excellence of Play. Buckingham: Open University Press.
    National Advisory Committee on Creativity and Cultural Education (NACCCE) (1999) All Our Futures: Creativity, Culture and Education. Department for Education and Employment/Department for Culture, Media and Sport.
    Ofsted (2004) Transition for the Reception Year to Year 1: An Evaluation by HMI. London: Officer for Standards in Education.
    Ouvry, M. (2003) Exercising Muscles and Minds: Outdoor Play and the Early Years Curriculum. London: National Children's Bureau.
    Pound, L. (1999) Supporting Mathematical Development in the Early Years. Buckingham: Open University Press.
    Qualifications and Curriculum Authority (QCA) (2000) Curriculum Guidance for the Foundation Stage. London: Qualifications and Curriculum Authority.
    Rhydderch-Evans, Z. (1993) Mathematics in the School Grounds. Devon: Southgate Publishers.
    Rogers, S. and Evans, J. (2008) Inside Role Play in Early Childhood Education. London: Routledge.
    Rogers, S. and Tucker, K. (2003) ‘Mind travel’, Primary Geography51 (April): 13–14.
    Rose, J. (2009) Independent Review of the Primary Curriculum: Final Report. Publications. http://www.teachernet.gov.uk/eOrderingDownload/Primary_curriculum_Report.pdf (accessed May 2009).
    SE (2007) A curriculum for excellence: Building the curriculum 2. Active Learning in the Early Years. http://www.ltscotland.org.uk/lmages/Building%20the%20Curriculum%202tcm4-408069.pdf (accessed May 2009).
    Siraj-Blatchford, I., Silva, K., Mutlock, S., Gilden, R. and Bell, D. (2002) Researching Effective Pedagogy in the Early Years (Research Report 356). London: Department for Education and Skills.
    Tucker, K. (2001a) ‘An interactive approach to learn about maths’, Early Years Educator3(7), November, 15–17.
    Tucker, K. (2001b) ‘Jumping on to a good idea to teach maths’, Early Years Educator3(3), July, 18–20.
    Tucker, K. (2002a) ‘You can count on drama to teach maths skills’, Early Years Educator3(9), January, 13–18.
    Tucker, K. (2002b) ‘Stretch children's imagination a little bit further’, Early Years Educator4(7), November, 32–5.
    Tucker, K. (2003) ‘Mathematical development in the early years’, Early Years Educator4(10), February, ii-viii.
    Vygotsky, L.S. (1978) Mind in Society, translated and edited by M.Cole, V.John-Steiner, S.Scribner and E.Souberman. Cambridge, MA: Harvard University Press.
    WAG (2008) Framework for Children's Learning for 3- to 7-year-olds in Wales. Cardiff: Welsh Assembly Government.
    Whalley, M (2007) Involving Parents in their Children's Learning,
    2nd edition.
    London: Paul Chapman Publishing.
    Worthington, M. and Carruthers, E. (2003) Children's Mathematics: Making Marks, Making Meaning. London: Paul Chapman Publishing.

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