My wife and I like to watch mystery shows together like Poirot, Midsomer Murders and Miss Marple. Unfortunately I have a slight problem: when watching television in a comfortable position, I tend to drift in and out of sleep, no matter how interesting the show might be. This can be quite disasterous for mystery shows, especially ones with major unexpected plot twists.
Just yesterday we were watching an episode of Marple called The Pale Horse and I woke up from a doze at the scene where everyone was gathered in the dining room to reveal the killer. And I had not the slightest clue what was going on.
Later I went back to see the bits I had missed and it turned out I had missed a total of about three minutes of viewing in small snippets, but these were precisely the key moments I needed to be able to follow that final revelation.
This morning it occurs to me that some students I have helped in the MLC have been in a similar position with their maths courses. A particularly common example is in Maths 1A too with the word “span”. It is mentioned in passing in one of the early Algebra lectures, with the discussion lasting for a total of about a minute, and it doesn’t seem related to the content of the course at the time. But then later it becomes one of the most important ideas and is talked about as if they already know what it is. If they “slept through” the first mention, they’d be most confused! It happens in our own bridging course too, with the idea of a “unit vector”. It’s mentioned on precisely two pages in our course materials, and is very easy to miss. Students almost always completely ignore the word in their assignment and then struggle to get what we are asking them to do. (This is one of the reasons we hope to rewrite the resources in future.)
As teachers, we need to remember that a maths course is not like a murder mystery. In a murder mystery it’s the fact that working out the case hinges on small details that makes it mysterious and fun. But maths courses don’t hinge upon small details, they hinge upon big ideas. We need to make sure that anything pivotal is mentioned several times and discussed deeply so that even if their attention wanders for a minute once, they can still pick it up again and still follow the story.