An alternate title for this might be “what a difference a room makes.” Last semester I taught our general linear algebra course for majors (which is a linear algebra and proof course) in a room with arm desks and a seating capacity that was close to the number of students in the section; this semester I’m teaching the same course in a room with tables and space.

The room I was teaching in last semester is shown in the picture to the right; the room this semester is like that shown in the right-most picture in the header of this site. What’s the difference? What I’m trying to do in the class hasn’t changed; both semesters I talk(ed) a little and students work(ed) on “games” (worksheets) a lot. The worksheets themselves have been ported almost directly between semesters. The classes are almost exactly the same size, and both consist, or consisted, of good students who work hard. So all of that is basically the same.

The differences are really two: this semester I’m teaching three times a week for 80 minutes, while last semester I was teaching four times a week for 50 minutes; and this semester I’m teaching in a room that is set up for students to work together. Both of these are really significant changes, but here I want to focus on the latter. What difference does the room make?

I think there are two differences. One is perceptual: what do we expect to do in the room? And the other is functional: how well do things we do there work?

What does the room tell us about what happens in a class held there? A room with tables at which students sit and look at each other is telling us—my students and me—that their interaction is important. And that’s key to how we want to do things: research says (e.g., Laursen, et al.) that the pieces of instruction that matter for learning are the degree of students’ engagement and their interaction with each other. I’ve been teaching for a while now, and I like to think that I can get students to engage and interact (even) in a sub-optimal room (e.g., one like that I was in last semester), but if we all walk in and know what’s going to be happening in the room… well, I’ll use the word that is all but banned in our proofs: “clearly,” this is better.

Then we’re in class. How well do things work? At some level this is impossible to say—are my students learning better this semester? I certainly can’t say that’s true (both last and this semester my classes were and are about 25 students, the exams are different, the students are different…). But I think that it’s been easier for students to work together, which is the majority of our time in class. The fact that the room is slightly larger and I can easily get to every table is indisputable. I don’t think students always work with more than one neighbor, but I think they do so more when they’re at these tables than they did when they had to figure out how to wrestle their arm desks about. Clearly, these are good things.

On the last day of class for this term I walked into class armed with both a worksheet and, because it was a review day, a short lecture on how the material we were finishing the course with brought together the various central ideas in the course. I started by asking if students would like the lecture summary, or if we should just go into the worksheet. I didn’t take a scientific poll, but all of the people that said something (that I heard) voted for the worksheet. The small egotistical part of me shrieked in protest—this was a **good** summary!—and a larger part of me thought, well, maybe that’s a sign that things are going the way we want. Would their answer have been same in a different room? This I don’t know, of course. But hopefully those who know about these things will say their response indicates that the classroom was one in which we were making a difference.