Three months after the class was over, I conducted an interview with the class. During the interview, Alan brought up this class day in particular when I asked the students to describe a “typical class day”. Below I have a transcript of the portion of the interview surrounding this discussion. As it was three months after the class, none of the students had a clear memory of the day.

After the discussion of this day, the interview moved to having the students discuss whether the type of conversations we had in this class was unusual, and why they happened. Notice how John and Jim have very different perspectives on why the conversations happened. I think they are both somewhat right. Many of my classes have been filled with education students at the end of their university career, and seldom do I get a class with the sort of interactions that I had this term. This seems to argue that it is not the type of students that made the difference, but possibly these particular students. However, I also ran this class differently from any class I have run in the past. I spent a lot more time talking with the students about why I was teaching what I was teaching, and how I made the choice of what to present. Finally, the structure of the research projects this particular term encouraged a different kind of interaction in my office than frequently happens in classes, and I believe that interaction also contributed to the environment of the class.

Curtis Bennett (CB): So, if they asked you what did a class day look like, what would you tell them?

Alan: I think it depended on the specific task for that day. Some days we came in and we would work on groups on homework, but I felt like a lot of the time it was us kind of blindly of walking through this idea of "I think this is where we want to go" and your just kind of OK we'll let them go there and wait until they run into a wall, and when they're dizzy I can help them back to the uh… So that's what it felt like to me, like we as a class decided where to take, where to take the next step in terms of what was going to come up the next day, we kind of decided, OK this is where we think were going to go and sometimes you'd be like "OK, no don't go there cause it's going to take us a whole class period and it's really bad," and other times you would let us go that way and we learned a lot from that.

John: Can you give an example?

Alan: Can I give an example?

John: Yeah.

Alan: Yeah, the one time that, Now I can't remember the exact example but I know there was a time where we were doing… trying to solve something, I don't know what it was but Jill suggested one way and I suggested another,

Lyn: Wasn't it the root thing.

Alan: I think so, I think so, and mine went way off track or something and like, no why don't we try this way. I don't remember exactly what it was but there was cases and when sometimes there were things that I was like there is no way that can work and someone else suggested it and we ended up doing it. Maybe someone can help me with the one I am thinking of. The one I am thinking of is the one with the idea that … I think it was the idea that you could move a function to the other side. Maybe you could help me Dr. Bennett?

Lyn: Something with the square.

Alan: I had this notion that you couldn't subtract from the other side because it was… I don't know I don't remember, maybe if I saw it in front of me it would click what it was.

CB: Could it be the day of finding the polynomial that had a root?

Lyn and Alan (at the same time): I think that was what we were saying.

Lyn: I guess you were suggesting something about move it to one side then do it then move it back

Alan: I was like, "No you can't do it!"

CB: Was that typical of your other classes in math would you say?

Alan: No.

CB What made this one different that way?

Jill: There was more of us (Neal: Explored) exploring, I think one of the things that we all, I guess we can't say we all, but I really got out of it a way of teaching, you'd taught us a lot of new stuff but you also taught it in a way that it ingrained it into us more because when you would do something in class you would ask us a lot of questions and we had to participate in the class and it wasn't just sitting there and writing lecture notes. And writing out everything the professor says. It was being in a class that you had a say in learning.

Neal: In other words we did some of the talking, sometimes a lot of the talking, whereas when we're lecturing…

Alan: I think for me that was the biggest thing there was a lot of working as a group to going back and forth between our conjectures, we've been talking a lot about this in our TE class this idea of chucking back and forth between conjectures and the board and what we generally see in our class is "definition theorem proof" and in our class, in the 496 class it was very different from that a lot of times it was (Jill: Conjecture) it was like conjecture, start a proof, figure out it is not quite right, fix the conjecture, continue kind of stuff. So I think I got a better view of what math is. That math is more of that, this idea of exploring that it is not always about math doesn't come about in that definition, that what we see in math books is the finished form of a proof and not all of the 50 pages of scrap paper that you use to get there.

John: I think one of the things that altered the way, sort of the pedagogy of the class is that almost all of us were people who were very interested in and capable about talking about mathematics and talking through mathematics. I know in a lot of other math courses, where, I know in the math courses I teach, and also in the other math courses I have taken is the different group of kids, and I think it has a lot to do with people who are interested in math education as opposed to just mathematics I think those people are less comfortable with talking and with trying to work through those sort of ideas.

CB: Any thoughts on that - I guess - this is interesting.

Alan: I guess maybe I am confused about what you are saying, could you say it again?

John: Well, I think there were sort of two things. One of the reasons the class was structured the way it was and why it worked the way it did is because we were all very interested in and capable of participating, and particularly in verbally participating in class and being able to talk through a problem and saying well how bout this no that doesn't work, no that doesn't make sense, etc. Whereas I think with a different, if you had a pool of 20 students who were taking mathematics, even 20 math majors at the college level, who weren't math education majors, or maybe even more the particular math education majors this year, it would have been very different I don't think you would have gotten as much response. So in part, the structure of the class reflected that and was suited for that was suited for our capabilities, but I think in part it was kind of determined by that. I think the class could have very easily been you know discussion proof if we had let it become so. I mean that is not a knock on Dr. Bennett.

Jim: I don't even know if it was necessarily just the students or just this year. I mean I think Dr. Bennett had set it up in a way that we didn't feel uncomfortable saying something. We didn't feel like we were going to get shot down because the professor is that much smarter than us we all know he is smarter than us, but he didn't act that way, he didn't go up there "oh no, no that isn't right." It was a comfortable setting that we could talk like that. I think it could have happened in a lot of other math classes as well just because they had you, just because we felt comfortable speaking in it.

John: I guess maybe my reflection coming out of it is that I don't think Dr. Bennett engineered what happened in the class. I don't think he totally created the conditions. I don't' think … I think a lot of it is an interaction which is a good thing.

Alan: I think I agree with what you are saying, because I have tried some of things that we've done in our class, in the class that I teach, the 133 math calculus 2, and a lot of times I feel like I'm really pulling teeth to get anyone to say anything. And then I have this idea: " I only meet them an hour a week, so now I'm under a time constraint that if I just sit there and don't say anything, maybe someone will eventually speak up, but I don't have the time or the luxury to do that.

Jim: Also the difference between one hour a week and three times a week that we met. (AB: maybe) The classes that I've been in as a substitute teacher I taught a middle school class all 8th graders a math class there for a whole week, by the second day I had kids talking who never talked. (AB: right) I had kids doing their homework that never did their homework because they felt comfortable with me. I mean I was in there, I made them feel comfortable because I was telling them stories about myself, you know my family my friends, stuff that, personal things that let the kids relate to me, not necessarily as "you're not that much older than me, but you're a pretty cool guy, you know". And they were actually by the end of the time I left, they wanted me to be their full time teacher you know I mean it wasn't just a couple of them, it was like the whole class, "yeah yeah, Mr. Jim come back" I think if you set it up like Dr. Bennett set it up, where you feel comfortable with it, you'll get a lot of interaction even out of kids you wouldn't expect it from.