Can we talk?

With all the thought I've put into designing writing assignments and writing-intensive courses over the past few years, it's nice to know that I still have a lot to learn. Every now and then I'll trip over one of my own assignments and realize that there's always room for self-improvement.

The past few iterations of my MATH 280 course have included a number of "dialogue" homework exercises, in which I ask each student to construct a dialogue between herself and a putative member of the class who's having trouble understanding whatever key concept that particular homework set is meant to address. I feel that the dialogue format offers students a number of challenges and opportunities, including

1. the chance (and challenge!) to explore high-level logical or mathematical concepts using everyday language,

2. the opportunity to assume the role of the expert by taking the lead in the fictitious dialogue, and

3. the chance to break free of conventional mathematical writing and experiment (in a relatively low-stakes setting) with a novel discourse that meshes well with a number of students' learning styles.

I don't intend to do away with the dialogue exercises any time soon (students often comment that these exercises are among their favorite and I feel that they are truly effective activities for the above reasons), but in light of my students' performance on the most recent run (graded yesterday), I realize that I'm going to have to be a bit more intentional about this sort of assignment.

What went on?

Several students' submissions were superb (I'll say more about this in a bit): not only did they construct a dialogue (and not a monologue, as some of their colleagues submitted), but they made effective use of the dialogue format to truly engage their befuddled interlocutor. While the "friend" in the weaker dialogues would say little more than "oh, I see" or "I don't really get this," the best students' conversation partners actively pushed the dialogue forward, asking probing questions that highlighted subtle difficulties in the concept and offered a window onto gradually improving understanding.

On the other hand, the weakest student responses didn't even offer dialogues at all, but merely gave a brief paraphrasing of the relevant concepts (universal and existential quantifiers). Ultimately I don't think these students understood exactly what a "dialogue" was supposed to look like.

And whose fault is this? How often have they been asked to construct "dialogues" in the past, and how often in math or science classes?

Yeah, I shouldn't have assumed that they knew what to do. It's on me to lay out a bit more clearly the expectations I have for that particular exercise. Especially as it's not a genre frequently encountered in a mathematics course, it was incumbent upon me to explain more clearly the powers and the limitations with which the genre comes.

Oops.

What to do? Recovery begins tomorrow: I've TeXed up the two dialogues I felt were exceptionally good (there were about five or six more who earned 10 points out of 10; I felt these two warranted a couple of points extra). Besides distributing the TeXed copies of these dialogues as models to the other students, I figure we'll spend about ten minutes in class discussing what it is about these dialogues that makes them so strong.

For now, the Super Bowl calls. More later, I'm sure. I'll try to check in tomorrow and let you know how the in-class discussion went.