by Derek Smith
Last quarter I had a video consultation through the TA Development Program on campus. Every new teaching assistant must sign up to have a section recorded. The consultation consisted of a one-on-one discussion, with the DVD used to move the conversation forward. I took away many ideas which I’d like to share. I ripped the DVD and edited out a representative problem, which is linked below. The class is Math 34A, Calculus for Social and Life Sciences, at UCSB. The students are mainly freshmen who need the class to progress through their major.
For reference, I will describe the course. All homework is completed online, with three assignments per week. The WebWork system randomizes numbers which appear in the problems to hinder direct copying (though group work is encouraged). I gave a quiz every section and iclickers are utilized in lecture. The professor has a very thorough portrait of student participation.
The consultant, Roger, mentioned that he liked my outline of problems at the beginning of class. I poll the audience and get a feel for which homework problems they’d like to discuss. Prior to recitation, I review the assignment so that I can adjust the suggestions on the fly. I can then judge the similarity of the problems and length of time required and come up with a plan for the 50-minutes right on the spot. I almost never guess which problems will be requested, but by the third section of the day I know what to expect.
In case you haven’t realized already, a successful recitation section requires preparation, preparation and more preparation. Although I spend an hour or two per week in preparation, Roger and I discussed methods for making more effective use of this work. It is inevitable that by the fourth section of the day, I have become somewhat automatic in my presentation. But by it is a simple exercise to turn around that practice for the benefit of the student. For instance, I could easily draw a diagram or graph on the board to visualize the problem. Alternatively, I could ask a student to perform the task. Turning the next step into a question is more instructive, a also prevents me from reciting from an internal script.
I still have trouble turning these questions into sign posts on the board. I’m more inclined to engage in a discussion on the idea of a problem, then moving into computations without much of a bridge. It’s definitely a goal of mine during this quarter to improve the organization and completeness of my board work.
This course consisted of almost 850 students in total. I ran four sections with ~25 students each. With numbers this large, it’s not surprising to see a wide range in mathematical ability. I strive to reach the middle half of the students, but find it difficult to know when I’ve reached this point. In the video I attempt to end the problem, but a question around the 8:15 mark reveals that the class is divided on how to convert from seconds to hours. Other students have more significant problems, which brings up another point: be familiar with on-campus tutoring resources. I take 10 minutes during the very first section of the quarter to describe this list in detail. For instance, at UCSB we have the MathLab run by graduate students as well as tutoring outside the department.
I’m currently experimenting with taking this process a little further. I’m requiring students to make a trip to my office to cross their name off a list before the first midterm. The intention is to have them at least figure out where the mathematics department is before the week before finals. I’ve heard another interesting variation on this: on the first or second quiz require the student to write down the name and email address of two classmates with the idea of encouraging group work.
During the opening portion of the video taped lecture (edited out from YouTube), Roger commented on my use of the few minutes before class began. In this particular instance, I was handing back quizzes and midterms. Apparently, the question of when to hand back graded material is a bit of a philosophical one. Do you risk loosing those who performed poorly right off the bat? Or do you slowly loose everyone as they anxiously await their results? I began class, as usual, with a weekly quiz (again, a controversial choice) and then opened the floor to questions about the returned material. My own opinion is that this time-saving measure is worth the anguish.
