SUMMARY OF QUESTION 3 OF THE SUPPLEMENTAL COURSE EVALUATION

Perhaps the course was least successful in affecting any change in student beliefs about doing mathematics. What I meant here by beliefs are what Professor Schoenfeld of University of California, Berkeley refers to as the "tacit rules of the game", the conventions of the mathematics community which are used to judge whether a mathematical proof is correct and complete. It could be that different responses were given according as these students were more or less mature mathematically though I have no way of knowing since they were turned in anonymously. In some fashion beliefs were changed, at least for a few students. For these students the process of working on problems made mathematics active and therefore an enjoyable process, though not all students who remarked on this were as positive. For at least one student this approach made mathematics less enjoyable.

"My feelings about math have not changed but it was fun doing math in small groups."

"My beliefs about the psychology of math have changed. I can really see a difference between going into a problem thinking its impossible Vs. thinking it is possible."

"Yes, I always thought that there was a right and wrong way to do a problem but this class showed me that there are many ways to do the same problem and you have to find the way that is easiest for you to do."

"The problems brought fun back into math. I was beginning to get bored with some of the strictly computational courses. By making the problems difficult but fun, I was more interested in what I was working on and I therefore was inspired to learn more about the problem and the principles used to solve them."

"A bit. First it helped make math fun once again. Second, I had gotten to the point that the trick to most of the proofs I did just came to me. This class had many problems where it took me days of finding little steps to find a proof. I think this is probably what math will be more like in the future."

"I think my tolerance for math went down in the sense that I am less motivated to continue taking math for fun. I still like/enjoy doing math but the type of math we were doing in this class is not most pleasing to me."

"Not really, I mean math was always fun and I always liked problems since I was little and I made up my own problems."

"It confirmed my belief that math is not science and that it is also fun."

"I don't feel that my fundamental beliefs about mathematics and what it means to do mathematics have changed. But I do feel that I've added concrete meaning to my belief that mathematics is the language by which the universe can tell us about itself (its truths and laws). I can see how mathematics is very much like any other language in that greater acquaintance with its grammar, syntax, etc. facilitates one's ability to grasp concepts and also communicate clearly. The former is akin to the anthropological hypothesis that habitual expression of a language guides thinking."