Mathematics for Liberal Arts Students

Abstract

I have been developing a course for liberal arts students for many years and it is time to report on these efforts. I found that the process of developing this course changed the way I teach in all courses but in ways that make teaching harder, not easier. And I have had some insights into the reasons why studying mathematics usually doesn't teach students to think. First some history. Near the end of the spring 1975 semester, a student who had taken finite math from me the semester before hailed me as I walked across the campus and asked, Hey Doc, guess what? What? I responded. He said, It's been a semester since I took the course and I haven't seen a Markov chain yet. The first thing that popped into my was, Yeah, kid, and I bet you never do. But I never shared that with him. Instead, I responded with some statements about how generally useful Markov chains were, and about how he would know what was being talked about if anyone who worked for him used them. I didn't give him any of the training the mind justifications because I knew him and I knew he would never buy that. He grudgingly accepted what I said and walked away, but I knew I had to change the course. I remembered the saying that your education was what was left after you threw away your notes and forgot everything you ever knew. In his case, what would be left? I couldn't find much. He and many other students had taken the course with utilitarian goals in mind. But except for some linear programming and the elementary algebra it required, I doubt they ever used anything in the course while they were undergraduates. And once they left? It seemed to me that the small number of people who might have contact with a small number of these topics at some distant time in no way justified all this effort by so many people. Groping for a solution to this dilemma, I used Mathematics, A Human Endeavor, by Harold R. Jacobs, in both semesters of the '75-'76 year. I began reading Polya's How to Solve It, Mathematics and Plausible Reasoning, and Mathematical Discovery, as well ,as Wayne Wickelgren's How to Solve Problems. I noticed that mathematicians often referred to each other as investigators, so in the spring semester I assigned a term paper, which was to be an of one of the questions on a list I handed out. This meant that if the student could not answer the question, then the investigation would be the partial results obtained. If the question could be answered, then any other questions that arose as a result also had to be pursued. This Written Investigation is an assignment I have made ever since. One student wrote a paper on, Is it possible to place 9 on a table in such a way that they form 10 lines with exactly 3 on each line? Interpreting chips and table, to be points and plane, respectively, he looked at a 3 by