Part 2 - Generative Learning and Mathematical Practice

What does it really mean to “learn” mathematics? There’s a difference between performance (short-term success) and learning (long-term retention and transfer) (1). A student may appear fluent today but be unable to recall or apply the knowledge a week later. Sound familiar?

This is where the concept of generative learning can be useful. Generative learning is a theory from educational psychology and cognitive science that emphasises that to learn students can’t just passively receive knowledge - they have to actively create meaning by doing something with the information they are presented with (2). Perhaps by connecting new information to what they already know, reorganising ideas, and using strategies that require doing something with the material.

So, in mathematics, instead of simply practicing procedures, learners might summarise a concept in their own words, draw a diagram to represent a problem, explain their reasoning to a peer, or even teach a new idea to someone else. Each of these strategies - organising, elaborating, retrieving - pushes learners to process content more deeply. And deep processing, as cognitive science shows, is what leads to durable, transferable understanding. Notice too, that retrieval is more than just recalling information because I’m asked to. In order to remember, I have to have a reason for remembering and that reason has to have some personal relevance.

So, as teachers, do we have to choose between fluency and meaning? Not at all. And the same is true of mathematical games. Effective mathematical practice can be both rigorous and deeply human. If you design games incredibly well, you get the best of both words - high doses of thoughtful curriculum practice plus enjoyment. - anchored in memory, connection, and personal agency. That's the kind of mathematics children will carry with them beyond just completing a level.

(1) Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In M. A. Gernsbacher, R. W. Pew, L. M. Hough, & J. R. Pomerantz (Eds.), Psychology and the real world: Essays illustrating fundamental contributions to society (pp. 56-64). Worth Publishers.

(2) L. M. Fiorella, L., & Mayer, R. E. (2015). Learning as a generative activity: Eight learning strategies that promote understanding. Cambridge University Press.