Mathematics Through Play in the Early Years

Kate Tucker, Author

• Publisher: SAGE Publications Ltd
• Year: 2014
• Print ISBN: 9781446269770, 9781446269763
• eBook ISBN: 9781446297865
• Edition: 3
• Topic: Education
• Subtopic: Early Childhood Education

?The book is grounded in the latest research about how children become effective learners, particularly in relation to mathematics. Bringing together research and practice in an accessible way, Kate Tucker provides an essential resource for all those who work with young children. I strongly recommend it!? - Dr Sue Rogers, Head of Department of Early years and Primary Education, Institute of Education

Offering practical examples of focused, playful teaching this popular book is back for a third edition, with even more activities to use in your setting with children aged from 3 to 8.

Completely updated to include the revised Early Years Foundation Stage, this new edition covers all the hot topics in the field, and now includes:

• a new section on teaching mathematics in Forest School
• more coverage of using ICT to teach mathematics
• more coverage of children with Special Educational Needs (SEN)
• a key vocabulary section at the end of each chapter, and a detailed glossary
• expanded and updated suggestions for Further Reading
• even more activities to use in lessons, with some extended to include 7-8 year olds

With a user-friendly layout, this new edition is an ideal resource for practitioners wishing to enhance their mathematics teaching, and for students wishing to develop their knowledge and understanding of how to use play to teach mathematics.

Kate Tucker is an early years teacher, trainer and writer based in Devon.

1

Play and problem solving

This chapter covers:

• how some theories of play have influenced early years mathematics education

• how play is an appropriate context for problem solving

• creativity and mathematical development

• including all children and families in playful mathematical experiences

• the transition from Foundation Stage (at age 5 years) to KS 1 (5–7 years)

• implications for an appropriate early years mathematics pedagogy.

Why play?

Play is what young children are about, it is what preoccupies them and it can be considered both a mode of behaviour and a state of mind. We understand that play is a natural pursuit for young children, but what we seem less able to understand is how to harness appropriate play pedagogical processes and use them to support mathematical development.

In recent years, it has seemed that a playful approach to learning has been at odds with UK government directives. Teachers of mixed-age early years classes and those teaching Year 1 children (6-year-olds) are aware that the transition from the Early Years Foundation Stage, a distinct phase of play-based education and care from birth to the end of Reception (5-year-olds), to a more subject-specific Year 1 can be disjointed, bewildering and potentially detrimental (Ofsted, 2004). The Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools (DCSF, 2008), led by Sir Peter Williams, however, described play as a feature of effective early years pedagogy and stressed the importance of connection making, creative recording and mark making, along with appropriate transition from the Foundation Stage to Year 1. Two further reviews, the Independent Review of the Primary Curriculum: Final Report (Rose, 2009) and Towards a New Primary Curriculum: A Report from the Cambridge Primary Review, Part 2: The Future (Alexander, 2009), led by Professor Robin Alexander, also regard play as a significant feature of good early years practice. They argue that, far from being trivial, play is an effective and age-appropriate pedagogy and one which concerns itself with how children learn, and not merely with what they learn. Although play is complex to define, some theories of play have had a particular impact on the teaching of mathematics.

Piaget

Piaget’s constructivist theory states that active learning, first-hand experience and motivation are the catalysts for cognitive development. Learning develops through clearly defined ages and stages – a continuum from functional play, through symbolic play to play with rules. Piaget (1958) has not only influenced early years practitioners in their practice of allowing children self-choice, but his work has also been very influential in commercial maths schemes which assume a hierarchical view of mathematical development. This had the effect of advocating ‘pre-number’ activities, such as matching and sorting before a child could progress to counting and manipulating numbers.

Vygotsky

Vygotsky (1978), unlike Piaget, emphasizes the significance of social interaction, in particular the use of language, which assists learning and development. His social constructivist theory regards social interaction with peers and adults, through which children can make sense of their world and create meaning from shared experiences, as crucial. Learning occurs in the ‘zone of proximal development’, which represents the difference between what the child actually knows and what the child can learn with the assistance of a ‘more knowledgeable other’. Play with others can provide these ‘zones’ because of the meaningful and motivating social context in which they occur. His influence on mathematics has been to encourage mathematics teaching to be related to the child’s own experiences and to encourage talk about mathematics.

Bruner

Like Vygotsky, Bruner (1991) shares social constructivist theories which highlight the significance of interaction with others. Play serves as a vehicle for socialization and its contexts enable children to learn about rules, roles and friendships. The practitioner is proactive in creating interesting and challenging environments and in providing quality interactions, which act as a ‘scaffold’ for children’s learning. He advocates a ‘spiral curriculum’ where children revisit play materials and activities over time, using them differently at each encounter as their increased development dictates. The structure of the National Numeracy Strategy (DfEE, 1999), with its repeated visits to specific learning objectives each half term, reflected the need for children to revisit ideas and consolidate their learning before moving on to the next stage.

Smilansky and Shefatya

Smilansky and Shefatya (1990) define socio-dramatic play as requiring interaction, communication and cooperation, which allow children to test out ideas and concepts, unlike dramatic play, where the child may play alone. Smilansky and Shefatya suggest that enriched learning comes from the adult working alongside children in their play, or ‘play tutoring’. Through play, children can assimilate information and prepare for new situations. By selecting different role-play areas, practitioners can give access to different and appropriate areas of learning. This is a common approach in many early years settings, where the practitioner might establish a cafe or shop in the role-play area to provide a context for developing an understanding of specific mathematical concepts, often those involving the use of money.

Bruce (1991) argues that ‘free-flow play’ is the purest form of play where play is freely chosen by the child and without the confines of external expectation. During this ‘pure’ play, children will:

• initiate the activity in a meaningful context

• have control and ownership of the activity by imagining, making decisions and predictions

• experiment with strategies and take risks in this ‘safe’ context

• show curiosity

• repeat, rehearse and refine observed social behaviours and skills

• seek pleasure from the essence of the activity.

All of these processes, integral to play, are also essential for mathematical thinking and problem solving. Play and mathematics, therefore, seem natural partners, and their combination will allow the child to:

• gain an understanding of the cultural role of mathematics

• have a heightened awareness that mathematics can be useful in the real world

• recognize that mathematical activity can be both sociable and cooperative

• perceive mathematical activity to be enjoyable and purposeful.

In order to fully support mathematical development, playful activity requires adult involvement at some level. Early years curricula in the UK (DfE, 2012; SE, 2007; WAG, 2008) advocate that play which best supports learning is that in which there is a mix of child-initiated and adult-supported play. Indeed, a balance of practitioner-led, practitioner-initiated and child-initiated activity is desirable (Fisher, 2010; Pound, 2008). While practitioner-led activity can ensure the systematic teaching of skills, child-initiated learning, without adult control and dominance, can enable children to become self-regulated learners.

Creativity

There is growing evidence that it is how and not what a child learns that has greatest impact on their school achievement (Bronson, 2000). The revised EYFS emphasizes how children learn by the inclusion of the ‘characteristics of effective learning’, although it is Dame Tickell’s Independent Report on the Early Years Foundation Stage to Her Majesty’s Government (Tickell, 2011) that provides a more robust discussion about their inclusion. The inclusion of these characteristics – play and exploring, active learning and creating and critical thinking – promote key learning dispositions in the young child such as engagement, motivation and thinking, all of which are necessary for self-regulated learning and also vital for real mathematical enquiry. Arguably, creativity is at the heart of all young children’s learning and although difficult to define, can be regarded as comprising of four main aspects: imagination, purpose, originality and value (NACCCE, 1999). When young children are being creative, they:

• are captivated and curious

• will be driven by this curiosity to achieve their goal

• make links in their learning in order to make sense of their activity, refine their thinking and thus give rise to new thinking

• evaluate the process they are engaged in so that they might adapt or refine their task in order to be satisfied with their activity.

Creativity can be encouraged in mathematical play by:

• using open-ended questions and ensuring sustained shared thinking (see ‘Prompts and questions for problem solving’ below)

• providing open-ended resources (see Chapter 2)

• ensuring time and space for children to explore and extend their enquiry

• allowing children to leave out resources such as wooden blocks, model-making materials, etc., so they can revisit them the following day and develop their thinking further

• ensuring that children have the opportunity to review their work and talk about their thinking using appropriate vocabulary (see ‘Review time’ below)

• encouraging children to make links between maths an...

Table of contents

• Cover Page
• Halftitle
• Advertisement
• Title
• Copyright
• Contents
• About the author
• Acknowledgements
• How to use this book
• 1 Play and problem solving
• 2 Creating and using a mathematical environment
• 3 Creative recording and mathematical graphics
• 4 Counting and using number
• 5 Pattern
• 6 Shape and space
• 7 Measurement
• 8 Planning, organizing and assessing independent play
• 9 Parents as partners: involving parents in mathematics and play
• Appendices
• Resources
• References
• Index