There is an old quote of Confucius that I’ve been pondering recently: I hear and I forget. I see and I remember. I do and I understand.
I want to spend some time deconstructing how I read this quote, what it means to me, and it seems sensible to do so in the obvious three parts. I’m pondering how this quote relates to my teaching practice, both my mathematics teaching and my aikido teaching.
And so we start with the first part, I hear and I forget. The basic observation in this quote is one that we have other phrases for, most notably the one about things passing in one ear and out the other. We’ve all had the experience of being in a conversation and finding ourselves in that awkward moment when we realize the other party to the conversation is looking at us, having just said something, and all we have is the vague memory of the sound of their voice in our ear but not any of the words they actually said.
And yet, for most of our history, we have listened to each other. For most of our history, before we discovered writing, we would perhaps distill our experiences, the things we’ve learned, into stories that we would tell each other, sitting around a fire for warmth and protection from the beasts in the night.
Perhaps the issue lies in the difference between hearing and listening. Listening is an active thing. We watch the speaker, follow their gestures, becoming part of their story, rather than just passively letting the speaker’s voice interact with the mechanisms of our ears. But I’m not sure whether this is a distinction that Confucius would have been happy with.
But even when we’re actively listening, our bodies are passive. Perhaps we’re sitting, perhaps sitting comfortably, and our attention wanders, and we lose some of the story being told.
So how does this relate to teaching. We try and model our teaching to some extent on these fireside chats. We the teacher stand at the front of the room, perhaps with a few students or perhaps with many, into the hundreds, and we talk. Sometimes we accompany these talks with visual demonstrations, the working out of mathematical calculations or the proofs of theorems on the board, or an aikido technique.
I talk a lot when I’m at the front of the room. There are evidently now studies that show that students in lectures retain a remarkably small proportion, say 10%, of the material spoken by the teacher, the lecturer. Without knowing about these studies, I’ve tried to fight them by being entertaining, presenting the material in an interesting way, bad jokes, anything I can think of to keep the attention of those in the room.
But perhaps that’s not enough. Looking back, I’ve had experiences that I should have paid more attention to or extracted different meaning from.
There was the time when I was a graduate student, I was running a calculus tutorial. For the first half of the tutorial, I worked through questions asked by the students in the class. For the second half of the tutorial, the students had a quiz, working through a question from that week’s tutorial sheet. Someone asked the quiz question, and I worked through it in some detail on the board. But I forgot to erase the board before the quiz. And even though I’d worked through the question just minutes before, and even though the answer was still visible in all its glory on the board, almost half the students couldn’t get the answer to the quiz question.
And similar things have happened since, though not so blatantly. Students have written things in their solutions that indicate they weren’t paying attention when I was talking through some mathematical point. But up until now, I’ve always felt that the issue was that I wasn’t explaining some point sufficiently clearly, rather than explaining being the wrong thing to do.
This all gets back to my uncompleted project to keep you, gentle reader, in the loop on my thoughts about how I was going to reconstruct the teaching of my graph theory module for the current academic year, described here and here and here , a project that I didn’t complete but which is still very much on my mind. What can I do besides talking to my students. Besides talking at my students.
I have done what I discussed in those earlier posts. I have engaged in some flipping in my teaching, giving students written notes some days before each lecture and asking them to read them, and then talking around them during the lectures themselves. But I did miscalculate in one critical respect, taking as an example to work through in lectures an example that was too complicated to be useful. That caused me to backtrack a bit and go back to a more standard chalk and talk lecture style, and it’s on the list of things to fix for next year.
