# Rosie’s Round Table

A few weeks ago I gave the following problem to my students:

I had them find the answer to the logic puzzle and then write a convincing “proof” of why their answer was the correct one.  This was their first “proof” and the idea was to have them work in small groups to workshop their proof-writing skills. I put students in groups of 3 and had them read over each other’s proofs, talk about what worked well, what could be improved and then collaborate on a group write-up of the proof that incorporated the good things they were already doing with the suggestions they had made to each other. The whole activity went really well, if I do say so myself.

But this was my favorite part.

One student, Rosie, submitted this as her answer:

Her group members were adamant—that’s not what it means! It doesn’t work like that! One of them asked me to arbitrate. Who was RIGHT?

Well, as far as I know, there is no mathematically rigorous definition for the word “across”. So I said to him: “It looks like Rosie had a different assumption that you for what it means to be across the table. Is it that Rosie is wrong, or is it that the instructions aren’t clear enough?”

A thoughtful expression crossed the student’s face. “You’ve got me this time, Bree.”

I checked in with the group a few minutes later. They’d decided to define “across” as meaning along the diameter of the circular table[1]. Everyone was okay with this definition. More importantly no one felt like Rosie’s idea was inferior or that she wasn’t smart to have decided on a different definition earlier. They just needed to make a decision so that they were able to communicate effectively. And so they did.

[1] I think the basis for deciding this way was along the lines of “majority rules”. Not the most mathematically based reason, but oh well. I would have loved a discussion about how using the diameter limits the options for who is “across” from whom, but you can’t have everything.