SUMMARY TO QUESTION 1 OF THE SUPPLEMENTAL COURSE EVALUTION

Every student who turned in a supplemental evaluation indicated that they had achieved growth as a consequence of this course. For some the course was a confidence booster, others strategies for approaching problems, for yet others specific techniques, and for a few it reinforced knowledge and methods obtained in other classes. The responses follow.

"I learned how to break down more complicated problems into things that I can do. I also learned how to use the pigeon hole principle."

"Through math 30 I've learned to question math; the equations, problems, givens, solutions. I learned to look at problems from different views, to try to alter the way the problem is written in order to understand what or how the problem is asking. Contential (sic) I've been exposed to some number theory, proof by induction, some graph theory, invariance principle, and some pigeon hole principals."

"I think one of the main ways I grew mathematically is through confidence. As a woman, especially a non-math major women math classes are always very intimidating. But this class helped show me that I am good in math and can solve problems, even if at first they look too complicated. That is another thing I learned, to search for a way to solve a problem and try different strategies till one works."

"This class made a dramatic improvement in the way I approached a mathematical proof. Most of the concepts I had seen before but they had been addressed briefly and as a result I never knew how to use them. In this class, often we would work on a problem that when solved clarified principles such as Pascal's triangle and binomial expansion, recurrence relations, pigeon hole and others."

"I became more aware of numerical patterns, such as Fibonnaci numbers and Pascal's triangle. I became willing to try geometric problems (for instance all pts, in a plane are colored one of three colors prove there are two of the same color one unit apart)"

"Exposure to many different types of problems and learning various techniques to solve them. Many strategies had already been introduced to me in other classes." "I think I became more comfortable with proofs this quarter. In particular, I made sure to focus on my goal and possible ways to get there."

"Content knowledge that I learned included aspects of graph theory, number theory, and combinatorics. An essential strategy that I learned (or at least worked at; I don't think I'm quite there yet!): State clearly the problem before beginning, know where I'm at in the beginning, where I want to go and how I think to get there. I definitely feel that keeping in mind this one strategy has improved my ability to solve problems and do proofs. For example, I tried to use this strategy on the final exam. I also learned the extremal method for solving problems, and the importance of 'thinking outside the box.' The latter was very useful with spatial problems, though I didn't apply it consistently. Lastly, from all of these problems I attempted (and probably only half of which I turned in), I learned that discovery along the way is just as much fun as reaching the goal."

"I became much more acquainted with the pigeon hole principle. It seems that in upper division courses I've had its always been introduced, but rarely used. This course taught me especially how to categorize items in order to apply the principle."

"In this class I learned things like induction, modulo, pigeon hole principal, uses for Fibonacci sequence and Pascal's triangle, invariance, series and proofs. I also learned to change the way I was thinking and the way I solved problems like changing stragity changing the rules and I think most importantly to make math simple again. Example: When I was in geometry I understood it almost automatically it was because I was able to look at the problems simply. As math got harder I lost that but I got it back in this class."