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

## 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.

## Keywords

Problem solving Free play Enactivism Phenomenological Preparation Post-paration Exploration Three worlds## References

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