Pedagogy as Struggle

[See also: On Giving Advice and Recognizing vs Generating]

So this quarter, I’ve been tutoring for an undergraduate computer science course, and one interesting thing that I’ve revised is how I think about teaching/learning.

Let me try to illustrate. Here’s a conversation that happened between some staff and the professor one day; it’s about what advice to give students when testing their code.

Tutor A: “I think that we should remind students to be very thorough about how they approach testing their code. Like, so far, I’ve been telling them that every line of code they write should have a test.”

Tutor B: “Hmmm, that might backfire. After all, lots of those lines of code are in functions, and we really just want them to make sure that their functions are working as intended. It’s not really feasible to test lines of code inside a function.”

Professor: “Actually…that seems like a fine outcome. We want students to be thinking about testing, and I’d actually be very excited if someone came up to me and asked how to test for what goes on inside a function…”

This was surprising to me because most discussions I’ve previously had about student learning had focused on how to reduce confusion for the students. But in this scenario, the professor was fine with it happening; if anything, they seemed pleased that the concepts, when taken to their extremes, incited more questions.

And this general concept, of giving students something that’s Not The Answer, in an effort to move them closer to The Answer seems to show up in several other areas.

For example, from my shallow understanding of how kōans work in Zen Buddhism, there’s a similar mechanic going on. The point of a kōan isn’t to develop a fully satisfactory answer to the question it asks, but to wrestle with the strangeness / paradoxical nature of the kōan. The auxiliary things that happen along the way, en route to the answer is really what the kōan is about.

To be clear, the thing I’m trying to point at isn’t just giving people practice problems, the way that we already do for math or physics.

Rather, I’m imagining things like people purposefully writing incorrect / confusing material, such that it prompts students to ask more questions. I guess there’s already a good amount of people in the rationality space who write abstrusely, but I wonder how many are doing so for pedagogical reasons? Seeing as noticing confusion is an oft-cited useful skill, I think that there’s more to do here, especially if you’re upfront about how some of the material is going to be incomplete, and maybe sometimes even wrong.

It seems like there’s a slew of related useful skills here. Several times, in math class, for example, I’ve had my instructor make an error while doing some proof. And now I’m confused about how we got from step N to step N+1. Sometimes I figure that they’re just wrong, and I write what I think is correct. And sometimes I get scared that I’m the one who doesn’t understand.

But this whole process raises good questions. What if I hadn’t noticed that something was wrong? What does that say about my understanding? When I do notice that something is wrong, how do I know if it’s me or the other person?

This all seems applicable outside of a pedagogical context.

2 comments

  1. If you do this, I think it’s very important, for students like myself, to be very clear that you are giving them *an* answer, but not *the* answer.

    This may seem obvious, but to me it emphatically would not be. I tend to accept answers from more experienced, knowledgeable and esteemed people as *the* answer to my questions.

    Call it an autistic trait, a lack of critical thinking, an overestimation of the extent to which we have *the* answer to any question at all, it doesn’t matter. The fact is that student-me would be likely to take your word for gospel, unless clearly qualified and that would not achieve the intended goal.

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  2. I was helping a student with a problem at office hours a few days ago which had a choice to either prove or disprove the statement. The answer was to disprove, but the student said he thought it was true, so I worked with him to try and prove it. Obviously this didn’t work, but through trying to prove it he saw why it didn’t work, and even better, he now had an exact formula for a counterexample!

    He later came up to me and told me how much he appreciated that method of explanation, and how he really enjoyed it. The reason why I think it was so satisfying because it is how I would have approached the problem myself, and hence feels more real and practical as a problem solving strategy. Had I made the same (incorrect) guess at the answer and tried to prove it, I would have found myself more confused, but once I dealt with the confusion I have more clarity than I did before I started. I’m guessing that increasing confusion is more representative of real life problems, and having to sort through them yourself rather than having confusion-free tests leads not only to more satisfaction, but better growth as well.

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