I have submitted all of weeks 5 to 13.
I feel like I have learned some interesting things about mathematics; most especially that I like explaining mathematics to others. I wish that I could have had a few more chances to do that. It makes me more comfortable with the idea of becoming a high school math teacher for a few years after I graduate.
I was most intrigued and most frustrated by the idea of an open, paperless class. I really like the idea of being able to read each other's work, but there are so many of us that it was hard to get a sense of what was going on in each others' heads. I think the idea of an open-work class, like this one, is great, but would probably work better in a smaller class, or one where the students were more on similar levels. I am thinking of my linguistics classes, for example, where the class size is under twenty (usually far under, around eight). In a class like that, the open-class concept where we can all read each others' work, is a great idea. With a class as large as ours, with levels of approach as different as ours, it's problematic: there are so many approaches to read, and the answers vary so widely across the different levels of approach. The wide range of topics broached and the diversity of student starting-points meant that we often addressed hugely different subjects, despited reading the same material, and I think we often lost each other. I know there were several weeks when I didn't bother to read everyone else's material.
The paperless course is a wonderful idea. Its primary advantage is the accessibility of all students' work to all students, and its disadvantages, of course, include an inordinate amount of time staring at a computer screen, the obligation to read everyone else's work, and the hassle it takes to get the entire class (nearly half a semester) up to speed.
The advantage of having everyone read everyone else's work didn't seem to really pay off in this class. I think it was mostly because it was such a large class. I know it's unrealistic as things stand, but this kind of technology would be amazingly useful in small classes, like eight or ten people. Then the class meetings could be only a physical chance to extend and elaborate on the kinds of work and thoughts going on outside of class. My fantasy is that the class be a seminar rather than a lecture and the web-postings be the homework assignments. As a lecture class, I find that it's hard to make the web-postings anything but a response to the professor, which makes the accessibility of the communicative mode moot. In addition, with the class as big as ours, it was hard to start a dialogue. Who can respond to everything thirty people have to say?
Although the problems of class size and lecture format may be hard to remedy (with the number of interested students, lecture may be the only option), we can perhaps cope best with the problem of student unpreparedness. I suggest that a paperless class should assume a student's knowledge of HTML and have a section outside of regular class meetings to learn it, for those students that need it. One of the hangups that was the most frustrating was that it was awfully hard to start a paperless dialogue with classmates who wouldn't or couldn't respond; another alternative, of course, is to have some basic (cs 2?) requirement to the class....
Besides the comments above (about the difficulty of reading everyone's response), I also had technical trouble reading prof. B.'s responses. I am afraid that my links to prof. B.'s response was not to the right place; I was never told where to link to. I understand that Prof. B was inserting links in other people's work, but mine (with links built in) weren't going to the right places. Oh well... I suggest a template for the weekly comments so that the instructor's comments would go to the right place for sure.
We all helped to come up with a general plan for the project (a general structure, that is, for the page itself). I served as something of a coordinator for the entire project, helping to make sure all the pieces got written. I wrote, with Alison, the slicing section, which was subsequently re-written by Alison and then Mike. I later wrote the section on duality, and Alison and I assembled the pieces into a more unified whole. All four of us chewed on bits of that code (Mike added lots of pictures and re-wrote some sections; Dave helped on some of the re-write and added the awesome applets. Too bad they can't be seen on most machines.)
I am getting used to working in groups (I have been doing it for my psychology class as well). My particular hang-up about working in a group is that I tend to turn into an autocrat--I take over and either do all the work or run the whole project or both. I think I managed to do neither, but still carry my weight; the ideal compromise. It was a good experience, though I wish I had had a chance to work with more than one person who I haven't known for the last six years. (it was nice to get to know Alison; I like Dave and Mike too but I have known them for a long time...).
Prof. Banchoff's response