The First Time I Thought About Problems On Twitter

At this point of things I was (apparently) thinking of “engaging” as a stable property of a problem. In practice, that meant that I spent a lot of time searching for and trying to create great problems.

These days I don’t think of “engaging” as a stable property. The degree to which a problem is engaging depends on everything else — the preceding lesson, whether I launch a problem in a way that draws connections to things that kids already know, if I have hints/feedback ready in advance of the lesson for some common issues, if I selected a task that has a clear goal and that relates to math that my students are working on. This means that I spend more time worrying about what my kids know and what math my students might learn from an activity than I used to.

How did this development happen? I’m wondering whether my twitter archives might have part of the answer.

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3 thoughts on “The First Time I Thought About Problems On Twitter

  1. How does an “engaging” problem fit in with the pop-psychology idea of flow?

    Isn’t the appropriate amount of challenge important in determining engaging?
    I’m also not entirely with you on the idea that the engaging problem has to relate to the math that you’re currently learning in class.
    I do see your point on how an engaging problem greatly depends on the individual.

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    1. I have no idea how this relates to “flow.”

      For a problem to lead to learning I wouldn’t say that a problem has to relate to math that we’re currently working on, but it should relate to math that we’re working on. By “working on” all I’m trying to ensure is that the math is (1) valuable (2) unmastered (3) a focus.

      Of course, there are lots of reasons to work on problems that have nothing to do with learning math. (Fun, mostly.)

      I do see your point on how an engaging problem greatly depends on the individual.

      Yes! But not just the individual student. The individual unit. The individual teacher. The individual class. The individual course. There is no such thing as a stable definition of engaging. Come to think of it, there’s are lots of things that aren’t stable in teaching: properties of good feedback, whether a problem has multiple solution pathways accessible. But nearly all discourse surrounding teaching assumes that instruction has stable properties that are just waiting to be unearthed.

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