ABSTRACT
Mathematics instruction at the college level, indeed at any level, has traditionally been synonymous with the lecture format. Of all the liberal arts disciplines, mathematics has been among the slowest to implement alternative, innovative teaching techniques. There are several reasons for this conservatism. Many college and university mathematics professors, although not all, consider themselves researchers first and teachers (a distant) second. Almost all were trained in mathematical research, not in teaching. After all, the Ph.D. is a research degree, not a pedagogical one. Thinking about changing the way we teach has not been a high priority. The majority of all college professors, of course, were trained to do research, so why should mathematics be any different from the other disciplines? Again, there are several reasons. First, most mathematics professors were trained by the traditional lecture method; it is our basic model of mathematical teaching. That traditional lecture method does not readily lend itself to classroom discussion or interaction. Some of us may be uncomfortable trying to lead a discussion. The symbolic nature of the language of mathematics also may inhibit verbal intercourse and discussion. In addition, mathematical research can, although it does not have to, be a relatively isolated pursuit. Teams of researchers, where they exist, often consist of a few mathematicians who are highly specialized in a particular area. While discussions about research with colleagues occur, this type of discussion is of little use in an undergraduate classroom.
