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.