This month’s Launchings column by David Bressoud identifies the lecture format as “The Worst Way to Teach” calculus. Amen, I say. Eighteen years ago, when I decided to use a guided discovery model for my abstract algebra course, I felt as if I needed to justify my move away from the norm, especially since the course is required for the major. (My colleague Mike Olinick had already been using the Moore method for years in his topology course, but that’s an elective, so students could choose not to participate.) Why, I wondered, don’t we ask instructors to justify lecture-based teaching?
There is a lot of new vocabulary for my algebra students as they take the leap to a higher level of abstraction. As in a language class, they need to practice using that vocabulary and that abstract thinking with each other and with me. It would help them much less if all they did in class was listen to me show and tell. I’ve found that we don’t “cover” as much material as I did when I lectured, but I’m convinced that my students now learn more deeply and are more ready to learn independently. Further, when students talk more and I listen more, I have a much better idea on any given day of where each student is. I can identify and address misconceptions sooner. I can also see who is catching on quickly and is ready for more challenging problems.
The last two times I’ve taught linear algebra, I’ve chosen not to use a textbook. (Thanks, Frank, for helping me believe it’s possible.) Again, there are raised eyebrows at this deviant behavior (though not from my department colleagues), and I mutter something about how expensive textbooks have become and how it keeps me honest to set my own agenda. The truth is, though, that I want to get away from a system where homework is simply for practice and reinforcement of ideas introduced in class or the text. Instead, I try to choose homework questions that invite experimentation and anticipate coming attractions. In this way “going over homework” isn’t a necessary evil that threatens to eat up the class and bore half of the students, but rather a chance for students to hear each other’s ideas and for me to put them into a larger context.
Now for the confession: in calculus classes, I still use a big fat heavy textbook and spend too much time talking. It’s a more interactive picture than it used to be, but it’s too easy to slip back into old habits. The justification, if I dare call it that, is that we as a department have a common understanding of what our calculus courses should cover, and it’s already hard to fit it into our twelve-week semesters. (Midd faculty at large: can we please get rid of Winter Term once and for all?) If I were to move further toward a student-centered model, then I’d have to give up some topics that are generally considered essential. But I’m not comfortable with the status quo. A more active learning model should not be reserved for the mathematics majors. Bressoud’s article describes a study of a physics class using clickers and peer instruction, but he’s not endorsing them as the only alternative to lecture; he promises that “(n)ext month I will write about other ways we can shut up and teach.” I look forward to reading that column.