This course has been an experiment itself. Upper division math courses tend to be technology free, while present day mathematics in practice when done by mathematically trained people is often aided by computer algebra system calculations or other mathematics software. Our textbook surveys various topics that you have encountered at some level as a math major and tries to motivate each topic with an ambitious application that gives a peak at the power of computer algebra calculations in aiding our mathematical thinking, while keeping the exercises to a more modest level of difficulty and providing almost template-like examples leading up to them to explore the use of technology in some context, not just doing "pure" math for its own sake. It is a good example of a self-study guide in which you learn by doing, not to cover any particular content, or achieve any math-specific goals, but to open your eyes to the possibilities that technology can offer even in areas where you have not been led to expect its use.

I have kept the performance pressure low and minimized the role of grading, hoping that your interest in mathematics would be your motivator, while giving you guidance along the way. However, the limited feedback I have gotten from your worksheets is not enough for me to know how much benefit you have had from working through the textbook. The goal I had stated and hoped to get you to pick up on was improving your mathematical reporting skill that could best be revealed in the end of chapter problems where you were to try to give a complete mathematical statement of the problem and its resolution as opposed to simply following instructions and putting in a few comments. We may have fallen short there. Attention to this aspect is particularly important in the final project, which, though not a long term project, is a last chance to do this well, but there is also the risk of just responding to the instructions instead of trying to explain well every aspect of your response and do a little extra that was not specifically requested. Keep this in mind as you develop your worksheets for that project.

Many of the course evaluation questions are not quite relevant to this freestyle kind of course, so it would help me to give more appropriate feedback about how this course might be improved if it were offered again. Has it helped you in any way or has it been a waste of time? Be honest. Are there ways in which more outside worksheet work could have been encouraged? How many hours a week roughly did you actually spend on worksheets outside of class time? Would you have preferred less emphasis covering the whole book and instead spending more of the semester on a longer term project in some area of interest of your choosing? Or would you have preferred to spend more time on the end of chapter problems? None of you worked with a partner before the project even though this was advertised as an option. Should a partnering system have been enforced to help you learn from each other by working together or would that have had a negative effect by chaining you to your partner in getting work done? Would a consulting partnership have been better, each student doing his own worksheets, but teamed with another student to help each other out? Could I have provided more of my own worksheet examples to suggest how you might respond better as a math reporter?

Please send me an email (you may wait until you receive your course grade if you wish) with a thoughtful reflection about the course from your point of view. Constructive suggestions are particularly important as well as letting me know if this alternative exposure to "almost self-learning" had any value in how you think about learning new mathematics or finding a use for mathematics you have already seen a bit of. You will certainly be called upon to learn new things if you have a job using your mathematics degree but there will be no classroom to help you do it (short-term high-pressure workshops perhaps). Senior coworkers will be your only resource somewhat like a professor, but the comparison is a stretch. This course tries to give you a little experience in guided self-learning. Has it been useful or not? Specific feedback on the topics in the book would also be helpful. Which chapter (or chapters) did you find most interesting? Which least interesting? Was there any particular problem within any of those chapters that made the light bulb flash in your head, ie, drove home some point or made a connection in your mind that previously was not there? Could I have played a more active role than I have done, or was it useful to try to struggle through problems with hints from the book complemented by consulting advise from me when you were stuck, together with my discussion of some general points that every one might suffer some memory loss from?

I've raised a lot of questions to help stimulate your reflection. Once you have a quiet moment, in particular after your exams are complete and you have received your final grades, please help me with your feedback. Thanks for offering me this opportunity to see how you function in this kind of environment. I hope you will remember the experience as a positive one.

bob jantzen April 27, 2004