The Things We Find Interesting

There’s a good debate going on right now on Dan Meyer’s blog about the nature of “interesting:” what makes for an interesting question, and what are the types of curiosity/perplexity that we want to inspire in our students?
We all have our own thoughts on that. Dan’s stuff --- and the prompts that others post on his site, --- uses a photograph or short video clip to elicit some question: How many gumballs are in the jar?, or Based on this satellite image, how many people attended Burning Man? They’re short and sweet, and foster good opportunities for problem solving. In this sense, they’re certainly interesting and I like them very much.
At the same time, there’s another kind of interesting: a kind that causes you to sit back and scratch your head and think, “I never thought about it like that before.” This is the outcome we’re striving for at this particular IP address, and our lessons tend to revolve around questions like:
Have video game consoles followed Moore’s Law...and are we building the Matrix?
What are the odds of finding life on other planets...and is the Drake Equation an example of anthropomorphic bias?
(We have other, less heady ones like, Do people with small feet pay too much for shoes and should Nike charge by weight? but these are the first that came to mind.)
The reason I became a math teacher was to challenge my students to think about the world differently. I wanted them to leave my class not just better at math but better at life. Perhaps that sounds paternalistic --- who am I to define “better at life?” (and if you knew me, you’d ask twice) --- but I think there are certain things that we as a society agree make for this: kindness; curiosity; fairness; an understanding of the world works and how the gears are turning beneath the surface. I think math lessons in particular can inspire this, and many of the conversations that motivate us at Mathalicious sound something like:

How many possible shoes can you design on Nike iD...
...and at what point does this result in paralysis by analysis?


How does your enjoyment change as you eat more candy on Halloween...
...and what is the relationship between income and happiness?

The debate on Dan’s site revolves around the teacher’s role in posing questions. If a student comes up with a question that’s more obvious but less rich than the one the teacher had in mind, can the teacher trump? (It’s actually a bit more nuanced than this and gets to the proper delivery of Socratic questions, but it’s the gist.)
For the most part, 101qs is motivated by, No, the process works best when questions come from students themselves. There is truth to this and works very well in certain situations.
At the same time, it's unlikely that a 13 year-old is going to come up with the question, Based on behavioral economics, how much is $1 really worth? That’s where the teacher comes in and says, You may not have thought of this, but I did. And now I’d like you to explore it and see where it takes you.
Asking which version is more interesting is a bit like asking which is better: hip-hop or jazz. (And I’m sure anyone reading this will agree that multiple choice tests, while easy to grade, are a bit silly.)
Still, everyone has a preference and I’m no different. I started Mathalicious because I find myself inspired by these types of questions and would like to live in a world where middle school students can have them, too. I think this is important not only for intellectual reasons but also social ones. We live in a country that seems less and less able to have a conversation with itself --- that tears itself apart over healthcare reform and seems more interested in talking points than talking --- and I believe that math lessons, intentionally crafted, can help change that. That they can put teachers in a position to not only teach calculus in eighth grade (as in the case of the candy lesson) but also to provide their students a more holistic way of viewing the world:
How much is $1 worth? It depends on how many you have.
This awareness starts with a question, too. Even if this question can’t be encapsulated in a photograph, I still think it’s interesting. Even when the question isn't obvious to an eighth grader --- perhaps especially when it's not obvious --- I still think it’s worth asking.

Because at the end of the day, I'm more interested in the content of the video than I am in how long it'll take to upload. Does this mean I think my version of "interesting" is better than the type presented on No. If I were still teaching, I'd incorporate both because I think they're both valuable.
And I suspect Dan does, too.

3 thoughts on “The Things We Find Interesting”

  1. Inserting pertinent Einstein quote here: "The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new problems, to regard old problems from a new angle, requires creative imagination and marks real advances in science."

    The deeper you go down the mathematical rabbit hole, I've found, the more important it is to be able to formulate "good" questions. One of the best ways to ensure students will not be able to formulate good questions is to teach math as a series of distantly related algorithms to solve poorly motivated problems. I agree with you; I think questions coming from both students and teachers is essential to fostering a natural curiosity and an intuition for what questions are worth pursuing. It's not always the case that students will be able to come up with the most perplexing question, or the question that will lead to the most interesting mathematics. But teachers overlook things too, and the most obvious or immediately interesting question to a student may be one a teacher has overlooked.

  2. I thought there was a lot to what you and I both heard Ed Burger say at NCTM. I may get part of it wrong, but the gist was that the art of teaching is to get students to ask the very question you want them to try to answer.

  3. I think you're right on the money. I've been using Dan's 3 Act problems in my classes and I have just recently subscribed to your lessons and tried my first of them (Family Tree exponential problem). I love both types. They will both fit nicely into my Algebra based courses. I do appreciate your questions "leading" us to a particular conceptual situation for which I have planned (and have decided is important to our common core requirements), and I also really like the teacher support materials that you provide along with the student activities.

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