Final Reflections

Lisa Eckstein

1) How has your view of yourself in relationship to mathematics changed over the course of the semester?

I never thought math could be this fun! In fact, I still don't necessarily believe math is fun, because I almost refuse to accept that this class was actually about math. When I tell people about Math 8, I feel compelled to explain "It's not really math".

Seriously, this class opened up my mind to the world of math as more than just sets of equations which students have to solve, even though someone else has already figured out the answers. I was glad that in Math 8, we were asked to report on our thoughts and ideas, not to provide solutions to already answered questions. I don't think I realized before that math can be creative, or that math has so many applications in the arts and in everyday life.

I hope that I will use this new knowledge. I would like to try to incorporate math and dimensionality into my own artwork. I want to look at the world and see math, without being frightened by such thoughts. I wish that more math classes would teach real applications of math. While calculus and algebra are perhaps not used in art as frequently as geometry and dimensions, and classes in these areas may not have time to look at math from the perspectives of many disciplines, all math teachers should share with their students the beauty of math, which the teachers must appreciate if they have devoted their careers to mathematics.

2) For you, what are the most positive and the most negative aspects of the course? Would you suggest any major changes in structure or emphasis?

This is one of the few classes for which I have consistently enjoyed attending lectures. Professor Banchoff is an incredible and passionate teacher. I liked the fact that often students were asked to make suggestions for the day's lecture topics. The extensive use of visual aids--models, movies, Web images--really brought the material to life. The explanations and 2-dimensional illustrations in the textbook frequently left me wishing to hear the subject explained in more detail or to see a 3-dimensional model. Then I would go to class, and my wishes would come true! Perhaps future editions of Beyond the Third Dimension can come with a tiny Banchoff clone?

This class was also, for the most part, relaxing and not stressful. Although we usually didn't cover in class all we had planned to, we didn't need to feel rushed, because even if we never returned to the material, there was no need to worry "Oh no, now I won't understand well enough and I'll do poorly on the test!" This was by no means a gut course, but it was definitely a refreshing break for an overworked junior.

There were very few negative aspects to the class. I guess the main one was that there wasn't as much dialogue between students as was planned. Even though we had the technology available for a lot of discussion of ideas, the technology was not put to full use. I'll get back to this in a later question. Other than the occasional technology problems (not unexpected since this was the first time these methods were used), I can't think of anything that really needs to be changed.

3) Comment at length on the concept of the paperless course. What are the advantages or disadvantages of this approach? In what ways could such an approach work in other courses?

I actually had another paperless course this semester, but unlike Math 8, this class can't be conducted on paper. The class is a hypertext fiction workshop, and hypertext must be written and read in some sort of computer environment. We used a program called Storyspace to write our fiction and stored the writing on a server. Other class members could read our work from the server and make comments in a Web-based newsgroup.

I think that many classes could make the move to the Web, at least partially if not completely. Once every dorm is networked, this will be a much more attractive option than it currently is, since right now a great number of students are at a disadvantage when it comes to doing classwork that requires convenient Net access. (As a side note, I expect that networking more dorms will eliminate some of the overload at the public clusters, since many students have their own computers but use the cluster computers for email and the like.) I think that most computer science classes have copies of all handouts and homework assignments on the Web--perhaps in the near future professors will stop distributing paper copies, which is a drain on the environment. Many classes, CS and otherwise, have newsgroups, which are a great way to transmit information and ask questions about material, assignments, and deadlines. I would love to be able to email my papers to my professors, or even turn them in on disk, rather than wait in line for a printer. (Again, this change would benefit students and the university--there is talk of charging money for laser printing because such a high volume of paper and toner gets used.)

A paperless course has definite ecological and financial benefits, but it also enhances the academic quality of a class. In Math 8, I got to read other students' papers, which is something I haven't had a chance to do in other classes. Reading other people's ideas caused me to think about aspects of the material I hadn't considered before. This improved my knowledge of the subjects and led me to new ideas of my own. Since Math 8 is a somewhat large class with mainly a lecture format, there isn't much time in class for students to exchange ideas; the Web site was a valuable forum. I can't think of any disadvantages with a class that operates in this manner, provided students are able to use the technology (there was understandably some trouble with that this year).

4) Comment on your experiences with the technology used in the course. What can be done to make things easier in the future?

Definitely the main problem with the Web site was that people didn't know how to use it. A mini-course in HTML at the beginning of the semester is definitely in order. My other major gripe is that the Web page was not entirely user-friendly. It was very aggravating to have to click on every name to find out whether or not there was a paper in that slot. Hopefully there will be a better format available next time this class is offered.

The discussion forums were also poorly structured--it should have been possible for each user to find out if there were any new articles, just like in a regular newsgroup. My hypertext class uses a Web-based newsgroup which keeps track of read and unread messages; each student uses a password to log in. This program, which is called WebCrossing and is on the Modern Culture and Media server, also allows for the use of HTML within messages, something else the Math 8 forums do not do.

On a more minor note, I wish the home page had been more attractive, since I looked at it so frequently. Oh, and I wish the server hadn't been down so often!

5) Describe your experience with the weekly assignments and the "response from Prof. B." feature. Comment on the public nature of these interchanges, and the possibility of linkings among student work and communication with the other class members. To what extent did you read the submissions of other students (and/or the professor's responses)?

For the most part, I read everyone else's work, and I read Professor Banchoff's response to their paper if it was present at that time. I occasionally linked my papers to other students' assignments, and I was glad that other people did the same. I heard a lecture about the Web in which the speaker commented on the time factor of the Web (she used a nice phrase, but I can't remember it): Pages are generally linked to pages which were previously created, so older pages don't link to newer ones unless they are updated. I can't remember the exact point she is making, but it is an interesting observation. Class members should be encouraged to make changes and add links to other students' papers even after they have initially turned in their assignments.

I wish the discussion forums had been used more. I imagine the lack of discussion was due to both the problems with the forums and the fact that people often don't do things which aren't specifically assigned. I hope that switching to an easier-to-use discussion format (a different Web-based one like I described above or a regular newsgroup) would increase exchange of ideas.

I definitely enjoyed seeing Prof. B's comments on my own work. I am always happy when teachers take the time to respond to an assignment instead of just giving it a grade.

6) Describe in some detail your activities as part of your final project team.

Our group met frequently to discuss ideas and decide on topics, but we each wrote a separate section of the project. We chose our topics from a wider range of ideas to find subjects that complemented each other and provided an overview of the important aspects of cosmology. I did the section on Shapes of Space. I'm afraid there aren't any other details I can provide.

7) In the old days, the final project was mostly an individual effort, on the order of a ten-page paper. How would you characterize the experience of working on a team, and how did that affect your effort in the final project?

In general, I don't like working in groups very much because often the team doesn't work well together, or one or two people end up doing all the work. I wasn't that thrilled by the idea of doing our final math projects in groups, but contrary to my expectations, our group project was a big success. I think that part of the reason, from my point of view at least, is that each of us essentially did an individual project. But working as part of a group was a great help to writing my report. It was easier to focus on a specific topic in a group format because it wasn't necessary to include a lot of background information--we could make a link to another person's section which dealt with the subject. Also, meeting with the group from time to time, and just talking informally with other group members, helped me generate ideas and receive suggestions.

Prof. Banchoff's response