Tuesday, November 12, 2013

Things That I Found Interesting Today

[This is a very, very tentative post. You should consider this a formal invitation to rip it apart in the comments, but, yeah, I want to put a little bit of distance between Future Michael and this thing.]

Here is a partial list of questions that I found myself thinking about today:

  • Had I gotten any emails or tweets after I turned my computer off?
  • What's the best way to understand conjugacy classes?
  • What sorts of things do we find interesting? What sorts of things do people get curious about?
  • What would my students do if I gave them a period of free-choice math?
  • What do the people look like in the subway car running parallel to mine?
  • What's the song that's coming out of that classroom?
  • When it snows, why does it harder to see the tops of tall buildings than the middles?
  • What was my wife's day like?

Dan Meyer has been thinking about what makes pure math tasks interesting, likable or enjoyable. I think that this is going to push him to a general theory of engagement, and he's asking folks to describe what makes their most likable pure math tasks so interesting and enjoyable.

This is worthwhile, but I think that reflecting on what interests our students will only take us so far. The problem is that we have so little access to what our students find interesting. It's hard for us to get into their heads.

On the other hand, it's really easy for us to get into our heads. Here's what I suggest: carry around a pencil and paper with you for the next few days, and every time you find yourself curious about something, mark it down. Then, after a few days, try to understand what sorts of things you find interesting. These can be math things, or they can be non-math things.

Based on the sorts of things I found myself curious about today, I'll toss out a couple early conjectures:
  • I almost always find myself curious about questions that I'm actually able to answer. I almost never find myself really curious about a matter that there is a low chance of me figuring out. 
  • I find myself most interested in questions whose answers are rare or uncommon. I suspect that this is the reason why I don't find easy questions interesting; it's because I perceive their answers to be common, cheap and readily available to others.
  • You can usually predict how interesting I'll find a question by asking two further questions: (a) How difficult will it be for me to figure this out? (b) How valuable is the answer of this question to me? (This value often comes in the form of other people being impressed with me.)
I'm not especially confident in my tentative ideas, but we'll see if they hold up as I pay closer to attention to the things that I find interesting.


  1. In the face of your challenge and Dan's current developing conversation, I find myself trying to reimagine the me that fell in love with school around 10th grade. What motivated me? I know it's foolish to think that this answer will unlock the mystery of motivating my current students, but at least it will give me some kind of insight. At least that it my hope.

    Sorry my claws were not out to tear into this, Michael.

  2. Not a direct comment, but perhaps related thinking that might be relevant, FWIW: I had a conversation today about the difference between introducing content with a "hook" - an exercise or connection intended to coerce students into being interested, which is often superficial, such as calculating the max height of a basketball even though nobody ever really wants to do that - a "puzzle" - a genuinely interesting question that piques curiosity, such as whether a basketball will go in the hoop and what information we might need to find that out (clearly stealing this example) - or a "rationale for learning" - beyond the test or the college or the career and something that compels me that I'm missing out on majorly important life stuff if I don't learn it (not sure what that might be in this example; my science colleague talked about the cure for cancer as a rationale for learning about cell organelles, and in this quadratics example, I wonder whether it's something about how linear and nonlinear models influence the decisions policymakers/medical professionals/scientists/companies make that affect my life).

    The "hook" feels like a cheap shot, the last resort of overworked teachers who also don't know why factoring is an essential life skill for 14-year olds (I have been this teacher, many times). The "puzzle" gets students interested in content for content's sake, not as an instrumental pitstop en route to college or obstacle to surmount. The "rationale" is my best case, as a teacher, for why I need you to know this to be the informed and educated citizen and human being that I know you can be and that our world needs you to be.

    Slightly different direction from what I think you're talking about here, but perhaps an application once you've got it all figured out?

  3. "This is worthwhile, but I think that reflecting on what interests our students will only take us so far."

    FWIW I'm not asking you to try to scan your students' heads (though that's kind of a fun exercise) I'm asking you to report on a task you yourself enjoy.

    1. I thought that by "likable" you meant "your students like" or "people tend to like it."

      But now I've got it. And I certainly agree.