Last week I posted a short video from a tutoring session I had with a kid. We were solving equations, and he had some interesting ideas, and it was nice to have those ideas and his mental workings become explicit.

Here’s another chunk of that video:

Comment on whatever you like, but here are some prompts:

  1. Help me understand his thinking. How did he devise his test for whether his solution is correct?
  2. What does this say about what he thinks about 2/0?

Or jump in with whatever you like in the comments.

Comment on anything that you like, but here are some prompts:

  • Do you like my questioning? (Because I didn’t. Notice that moment when I pause and try to unask my question?)
  • Describe, as best you can, the way that this kid thinks about the Distributive Property.
  • What would you say next, if you were me?
  • Does this video have implications about the way that you’d teach this topic? (And, come on, don’t give me that “they need lots of practice stuff.” Of course they do. But what else?)
  • Do you prefer having videos over images on this site? (Because I have about a half hour more footage from my work with this kid…)

Looking forward to a great bunch of comments here. Don’t let me down?


Here’s how I responded:

Clearly the kid doesn’t have a deep conceptual understanding of how to solve equations or simplify expressions. True, the kid probably learned some stuff proceduraly as opposed to conceptually. (Though, I can confirm, that in this classroom nobody ever said anything, like, “When you have an equation you need to add something to each side to isolate the x.” The balanced-scale model was used at first.)

There’s still two interesting, deeper questions, to consider. (Possibly more: bring it up in the comments.)

a) Would this kiddo always make this mistake, when presented with an expression to simplify?

b) If not, then what exactly is it about this problem that prompts the kid to employ a basic move from equations?