Dan Meyer busted out a new #anyqs video the other day. If you haven’t already, watch it before you read further.
In the spirit of #anyqs, I replied with my first question, together with some others (via Twitter)…
FIRST? Which is it? Top or bottom? SECOND? Why 10 seconds of outro? THIRD? What thinking is behind the wrong answer?
…and then I did a little work and noticed that they were both wrong answers.
So now we have an interesting question of task design. If we take seriously the framework of five practices for creating productive mathematical discussions in classrooms, then my third and fourth questions aren’t just throwaways, they’re really important.
Dan has anticipated and selected two student ideas for the first act of his lesson. On what basis did he choose them, and how might he have chosen differently (either to better or worse effect)?
Here are three arguments that occur to me.
1. These are the best choices
Students are likely to hold one of two conceptions. (i) Light travels instantaneously and (ii) Light takes time to travel across the solar system. Both of the possibilities presented in the video call (i) into question. Students who hold (ii) are likely to identify with the bottom scenario in the video.
Thus discussion is generated by the absence of conception (i) as a choice. Kids will introduce that one, and many students will gravitate to (ii). Perhaps these students recall that light takes eight minutes to get here from the sun, and they know the moon is closer to us, so the bottom choice looks appealing.
And even those rare students who know that light takes time to move, but who think the moon must be much, much closer than suggested by the bottom choice will choose the top answer. And that top answer is also wrong, which they will discover in the process of justifying their work.
2. these choices are not ideal
Maybe there need to be more choices.
Or maybe the instantaneous transmission of light conception should be one of the two choices (instead of the top one).
Or maybe we have missed some important student conceptions about light that should be represented among the choices.
In any case, being explicit about what we anticipate students will think about this scenario makes it possible to make purposeful choices of which ones to present in act one.
3. there should be no choices
The discussion so far has assumed that the two choices exist to provoke student discussion. But they also serve up the question. Without those choices, there’s just some guy shining his flashlight into the sky. Without those choices, I’m never gonna wonder how long the light takes to get to the moon.
Maybe we need a different way to get at that question-a way that offers students a wider array of entry points.
We can all get a lot better at designing tasks (for curriculum or our own classrooms) by thinking through technical and challenging questions of this nature. As always, I’m thankful for Dan serving up such rich food for thought.