the things we know and how we know them

Years ago now, I went to an internal university course of being a better lecturer and the person presenting, whose name I don’t remember, started with an exercise. List, he said, as fast as you can, the months of the year.

This is something we can all do incredibly quickly, as long as they’re the months we grew up with. (Not like the calendar in an episode of the Simpson’s that contained a thirteenth month.).

Now, he said, with a twinkle in his eye, list the months of the year in alphabetical order. And needless to say, we crashed and burned. Some of us did what we thought was the reasonable, logical thing, namely going through the months time and again, looking for the alphabetical first, then the alphabetical second; getting lost on which one we were looking for since we were trying to hold too much in our heads all at once, thereby running into a different notion from psychology that I love, namely cognitive strain.

But it took us a lot lot longer to generate the alphabetical list. And ever since, I’ve loved this little exercise, because it is an invaluable lesson that we as teachers need to remember. Namely, just because people might know something (for instance the months of the year), they know it in a particular context.

And that context is important. It’s like the months of the year are olives in an olive loaf, and the loaf is the chronological context. (Perhaps a bad analogy, but it’s close to dinner time and I’m getting hungry.). We can’t ignore the context and use the information as freely as we want to. And neither can our students, who won’t even have practiced manipulating the information in the same ways that we have.

It’s an infinitely flexible exercise too, since we can change the list of things and the manipulation of context. A good one is to say the numbers from 1 to 20, alphabetized by their spelling, because here the context is particularly strong.

Why is this exercise fresh in my mind today? Because I start teaching my graph theory class in a month (yikes) and I’m starting my preparations, and I’ve been teaching the class for a few years now.

I can sense how my own understanding of some of the topics has changed from when I first taught the class, and I need to be mindful that I don’t make assumptions about how my students will be able to use the facts we will be working through, since they’ll be seeing for the first time things that I’ve have seen multiple times and will have worked through multiple times.

We’ll also have new students in the University of Southampton Aikido Club, and I’ll need to maintain the same awareness with them as with my graph theory students. And there, the issue will be a stronger issue for me. I’ve been doing aikido for 21 years just about, and so my internal context and internal language for my aikido is deep at this point.

And what makes this an especially interesting challenge and imposes a duty on me as an instructor, is that the language of aikido is a language of movement, as opposed to the logical definitional language of mathematics. Translating the lessons from one type of teaching to the other is an interesting challenge, and one that I enjoy.

~ by Jim Anderson on 19 August 2018.

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