It wasn’t exactly where I had anticipated directing the discussion yesterday. And as it turns out, that was not only a moment of revelation, it was a glimpse into good things that can happen to mathematical discussions.

Have you seen a problem that is something like this one?

*31 students are going on a field trip. They travel in cars holding 4 students and a driver. How many cars will they need?*

With second language learners, I expected that we would have a discussion about what should be done with the remaining students. We never actually got to that.

At the Summary point in our lesson, I asked volunteers to explain their thinking and computation for the problem. Three student volunteers stepped up to the document camera and explained their thinking: student one divided 31 by 3; student two divided by 4 and student three divided by 5. Which one was correct?

The rest of the students kept turning around to me to see which of the three students had the right – as in which student had the **one correct** solution. I’ve been working on this area of my teaching for a while now, and fortunately I did not take the bait.

Because had I stepped into the discussion as “teacher as the holder of all things correct” , I would have missed one of the all-time great moments of teaching — the time when the students follow all those discussion norms we’ve worked on and have a debate about which student had the most logical interpretation of this word problem. I wish I had filmed it!

What did these fourth grade mathematicians decide? Although student one’s interpretation made sense to him, there was general agreement “4 students and a driver” did not mean divide by 3. Student two pointed out that bus drivers don’t go inside on field trips, so neither would car drivers; if the students were fourth graders, divide by 4. And student three? Student three is steadfastly holding the position that if the students were high school aged, one of them *might* be able to drive; therefore, divide by five.

And my question – what to do with the remaining students? Well, we’ll work on that one on another day.