by Conrad Hengesbach, Mathematics
Teaching Effectiveness Award Essay, 2012
The past two summers, when I taught second-semester calculus at UC Berkeley, brought the same two challenges. The first one was the far more diverse student body of the summer session: apart from the seasoned Berkeley undergraduates, there were external students as well as entering freshmen about to take their first college-level class. The variety of the students’ backgrounds meant that everybody brought different prerequisites to the table, especially when it came to their training in first-semester calculus. The second challenge was a more obvious one, namely having to deliver what is usually a fifteen-week course during the regular semester in only eight weeks. This latter challenge made the former more pronounced: the fast-moving pace of the course allowed for very little in-class review time. Given this constraint, I needed a mechanism to ensure that towards the end of the first week everybody was on the same boat, and that nobody would be lost from the beginning. I set two personal goals for the first week: first, I wanted to make it very clear what students should expect from the course. Secondly, I wanted to find out as much as possible about the mathematical background and interests of each student so as to be able to help everyone accordingly.
On the first day of class, aside from reviewing and discussing course logistics, I spent a good amount of time giving an overview of the topics we would cover in the weeks to come. I also handed out a questionnaire that asked about previous math classes, which topics the students had enjoyed in particular and also about their interests outside of mathematics. This questionnaire was to be turned in during my first office hours. On day two, I had my students take a short quiz based on the previous day’s review. This quiz had been announced one week prior to the start of classes, and I made it clear that it would not count towards their final grade. The following day, I held my first office hours. When each student came in to drop off the questionnaire, I was able to return the quizzes individually, give instant feedback, and in some cases work through some of the problems on the blackboard.
The upshot of this method was that by the end of day three, my students were perfectly aware of what to expect from the class, what to expect from me, and also what was expected from them. They also now knew where and when to find me outside of the classroom. Furthermore, I had had the opportunity to personally speak with each one of my 36 students. I had gained a fairly good understanding of their mathematical strengths and weaknesses, and I was able to signal that I was there to help fill any potential gaps in their mathematical knowledge. Finally, thanks to the responses from the questionnaire, I was able to tailor parts of the course to my students’ personal interests. This led to more variety in our discussions later on in the class, for instance about differential equations and car suspension models, or integral estimates and the Gulf Coast oil spill.
I would evaluate the success of my method in two ways. As far as course statistics are concerned, nobody dropped out after the first week either summer, nobody failed the course, and the final grade averages were high. More important to me, however, is that the students seemed enthusiastic about the material, the fact that nobody was afraid to ask questions and that nobody would hesitate to seek help from me or from classmates throughout the term. Many students expressed an interest in taking more math classes in the future, and two have since become math majors (which is rare for students in this particular course). I feel that setting the right tone in the first few days helped to make this course an enjoyable experience for the students, and also for the teacher.