12. Long-term Memory and Desirable Difficulties

Have you ever taught something one lesson, been pretty sure the students have understood it, and then returned the next day to find it was as if the previous day never even happened? I have had a Year 10 student swear blind to me that they had never seen ‘one of these weird wiggly graphs’ before, despite this being their third lesson on cumulative frequency diagrams.

Such experiences are soul-destroying for all involved, and occurred all too regularly during the first ten years of my career.

Most of the issues tackled so far in this book have been concerned with the early knowledge acquisition phase of learning. We can use the principles of Cognitive Load Theory to present material in the most effective way. We can break down processes using the principles of Deliberate Practice. We can intelligently choose and present our examples and practice questions to students. And we can help them develop the ability to solve problems via the careful batching of related problems, combined with the power of Purposeful Practice.

That is all well and good. But if students cannot retain that knowledge, then we are wasting our time.

In order to tackle this issue, we are going to look at explicitly and deliberately making the action of thinking difficult for students. We will see exactly what such difficulties entail, why they are likely to be beneficial for learning, and consider how best to apply the principles both in and out of our maths lessons.