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Pre-parative and Post-parative Play as Key Components of Mathematical Problem Solving

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Problem Solving in Mathematics Instruction and Teacher Professional Development

Part of the book series: Research in Mathematics Education ((RME))

Abstract

It is well known that educators such as Froebel, Dienes, and Gattegno recommend periods of free play with material objects before introducing mathematical questions designed to lead learners to encounter and articulate underlying mathematical relationships.

In this chapter, I challenge a proposed distinction between play and exploration (Panksepp, Affective neuroscience: The foundations of human and animal emotions. Oxford University Press, Oxford, 1998) in the context of mathematics, and I advance the conjecture that inviting learners to engage in a preliminary mental free play with the situation or context proposed in a word problem could serve to enrich learners’ awareness of the underlying mathematical relationships which are needed in order to resolve the specific problem. Also, after solving the initial problem, playing with a successful method and varying quantities in the problem can enrich the example space of solvable problems and increase the chance of similar actions becoming available when faced with similar problems in the future. When teachers act playfully with tasks that they are going to assign to learners, they may find pedagogical affordances opening up of which they were previously unaware.

In homage to the insight and design skills of my friend and colleague Malcolm Swan.

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Change history

  • 01 February 2020

    The published version of this book included multiple errors in code listings throughout the book. These code listings have now been corrected and text has been updated.

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Authors and Affiliations

  1. The Open University, Milton Keynes, UK

    John Mason

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  1. John Mason
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Correspondence to John Mason .

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Editors and Affiliations

  1. Departamento de Ingeniería Matemática, University of Chile, Santiago, Chile

    Patricio Felmer

  2. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Peter Liljedahl

  3. Department of Science Teaching, Weizmann Institute of Science, Rehovot, Israel

    Boris Koichu

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Mason, J. (2019). Pre-parative and Post-parative Play as Key Components of Mathematical Problem Solving. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-29215-7_5

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  • Online ISBN: 978-3-030-29215-7

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