Mathematics education has long wrestled with the question: how do children best learn to become fluent, confident mathematicians? The answer isn’t simple - it depends what we mean by “success.” Do we mean preparing students to do well on the next test? Or do we mean helping them grow into lifelong mathematical thinkers who can use ideas flexibly and with confidence?

Most of us would probably say, both! But that prompts more questions. Are those goals always compatible? Can short-term test preparation and long-term mathematical growth live happily side by side, or do they sometimes pull in different directions?

Our priorities shape the choices we make in the classroom. And while there isn’t one “right” approach, educational theory and research in cognitive science and psychology give us valuable insights into how children learn mathematics - especially around how play and generative learning strategies can influence really good mathematical practice.

So with this short blog series, we’ll unpack these ideas in a bit more depth:

Part 1 (this post): Playful learning and mathematical practice

Part 2: Generative learning and mathematical practice

Part 3: ‘Put your hands together…’

Playful learning and mathematical practice

Let’s get clear about what we mean when we say ‘play’. Play is an activity, a pedagogy, a fundamental human instinct and so much more. So when we make assumptions that we’re all using it to mean exactly the same thing at the same time, it’s no wonder we can run into difficulties. Especially when the connection between play and learning (more on this in part 2!) aren’t always tangible, observable or simple.

A comprehensive look at the definitions of play is given by Dr Alison James in her 2022 study (1), several of which make us think of connections to learning; It's immersive, sometimes involves surprise, is serious and challenging, can be open ended and unpredictable, is freeing (either through the removal of constraints or through the acceptance of rules and limits that create a form of freedom), it provides a safe place to ‘have a go’ and then ‘have another go’ if we need to. When we say play, we mean experiences that embody any or all of these ideas, with a healthy dose of learner choice and agency thrown in.

These characteristics resonate strongly with mathematics. Consider children choosing between relationships to help them find a fact they don’t know yet, such as 7 + 8 can be thought of as 7 + 7 + 1 or even 7 + 10 - 2. As they consider and choose which relationship to use, especially if they compare to find the cleverest, they are playing. This kind of play can transform dry symbols into lived experiences. Educational theories stretching back to Piaget’s ‘schemas’, Vygotsky’s ‘more knowledgeable other’ and Bruner’s ‘modes of representation’ argue that children actively construct meaning in relation to their own previous experiences and interactions with others. Play is often the arena where this meaning-making happens most naturally.

This makes a strong case for playful approaches to mathematical learning, but what are your experiences? How can these theories work in practice? What are the tensions and barriers that we come up against in the classroom? And how do they influence what the children actually experience as ‘maths’...?

(1) James, A. (2022). The use and value of play in HE: A study. Independent scholarship supported by the Imagination Lab Foundation. Retrieved August 23, 2022, from https://engagingimagination.com