# Modeling the Mistake Game

I’ve been convinced for some time about the value of playing the mistake game, but I have been unable to get my students to successfully buy into it. Today we started graph stacks, where one of the three kinematic graphs (position vs. time, velocity vs. time, and acceleration vs. time) are given to students and they need to qualitatively sketch the other two. I wanted to use it as an opportunity to once again try the game.

First period I allowed students to work for a while on attempted the graphs, and then I assigned two groups the same problem. I asked one of the two groups to purposefully make a mistake and didn’t say anything to the other group.

While I liked the comparison, we ended up with 6 people in front of the room while all the conversation was focused on the three with the mistake. They rode it out and did a great job, but I still didn’t feel like kids knew what questions they should ask to back the group into a logical corner. So I decided to change it up 2nd period.

I again let students work for a while, and then I picked a problem and put it on the board with some mistakes embedded. The position vs. time graph is the original that was given, and the black on the v vs. t and a vs. t graphs is what I originally drew . The orange is the corrections we eventually made through questioning.

I told students that I was going to model a presentation where we play the mistake game. I then gave the presentation; “The position is decreasing and positive so the velocity was positive but decreasing as well.” Then I gave them a minute to talk to their partners about good questions to ask.

And they didn’t ask good questions.

But what happened was that I was able to stop the minute someone asked a great question. “What is the slope of the position graph at time zero?” We then had a conversation about how forcing someone into a logical corner doesn’t happen with one question; it happens with a series of questions. So once I know that the slope of the position graph is zero at time zero, that leads to the logical connection that the velocity has to be zero at time zero.

Still, I didn’t feel like it went that well. So I let them work for a while again, then I picked the next problem and modeled it again.

They forced me into a corner in less than 2 minutes.

They learned through the first modeling session that a good question is one about the specific of the graph, not about what the person was thinking. Starting a question with “Why did you….” often doesn’t help. Starting instead with “What is the slope…” or “Are the velocities positive, negative, or zero…” does.

3rd period I repeated the process of modeling the mistake game with exactly the same results; it was painful the first time, and quick the second. I think I’ve got a keeper. Tons of students asked questions; they really seemed to be into it. Monday we’ll be trying the game with students presenting and I’ll update this post with the results.

UPDATE: Anecdotally, I felt like the day students presented their graph stacks with purposeful mistakes was one of the best whiteboarding experiences I’ve had so far. For each and every problem students were explicitly evaluating and analyzing every aspect of each graph, as opposed to correct graphs where they seem to say ‘yep, looks right.’ The quiz results were impressive. Out of a 4 point scale, last year the average was 2.36 whereas this year’s was 3.21 (p<0.0001). I’m in for the mistake game as a regular part of class from now on!