Reflections on maths, learning and the Maths Learning Centre, by David K Butler

Too many presents

Once upon a time when my daughter was very young, she was given a lot of presents – it was a birthday or Christmas but I can’t remember which. What I do remember is that she played with just one present all day long, leaving all the others untouched.

I think we sometimes do the same thing to our students that friends and family did to Charlotte: we give them too many presents and then get upset when they don’t play with them all.

Let me explain.

Playing with it is one of the main ways to get a deep understanding of concepts and to get fluency with procedures. You ask yourself, “What would happen if…?” and say to yourself, “I wonder…”, and you try things out in different combinations. It’s awesome when it happens and you feel all sorts of positive feelings like curiosity and joy and satisfaction. Even teachers who don’t consciously subscribe to a play-based approach are usually happy when they see this sort of thing happenning. Many of the people who become university lecturers had similar experiences when they were students and assume their students also play with the ideas in their courses.

And the students actually do. It’s amazing how often even the struggling students are trying to explore. And the students who were engaged with the content long before they joined your course are sometimes aching for chances to explore that aren’t being given to them. But there’s a big problem: there’s just not enough time.

A university course has multiple new concepts and procedures every week, and there’s just too many of them to play with all of them. Yet the assignment questions tend to assume a level of familiarity with every single thing in the course that only comes with a decent amount of playing with every one. There’s just too many things in the course to be able to give all of them the time they need. And if a student gets nerdsniped and goes on a deep dive on one thing, they are forced to sacrifice play time with the other things.

I see it most clearly in two places.

First, in a course like Nursing where students are expected to be fluent in all the various ways to do calculations with multiplication and division quickly without a calculator. This fluency comes to most people through years of play: trying new problems, seeing how others do them, noticing strategies worth trying, and noticing when they’re not worth trying, storing away relationships between numbers. But in a first-year Nursing course with students who have past traumatic experiences with maths, there is literally not enough time for this kind of play, even if a student realised that the play was the thing that helped them be better at getting the answer, because they also have to play with how to listen to patients and what all the drugs do and any number of other things that go into becoming a nursing professional.

Second, in a pure maths course for students who chose a pure maths degree because they were interested in pure maths. These students deeply want to play, but there are so many concepts coming at them, there is just not enough time to play with them all, and they feel overwhelmed. Especially when their lecturer assumes unconsciously they have already done the play just because they’ve got previous experience with maths.

My great hope is actually to give students less to play with, so they have time to play with each of them as they go. But failing that, we need to at least not get upset when they don’t play with everything, and definitely not assume that they are lazy or uninterested or ungrateful. They’re just toddlers with too many presents.

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