Kathleen Davidson, Math 8

0) Have you submitted responses for weeks 5 through 13? (This is the minimum requirement for satisfactory completion of the course. Folders should be complete by Sunday May 5 at midnight.)

yep. If they are not in my folder, they are in Envall's or Caroline's. We completed some of the homeworks as a team - it was funner this way to discuss the chapters. If we did not understand something individually, one of the others usually got it...

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

I have started seeing dimensions everywhere. By this I mean, the idea of going from one dimension to another was a really interesting and powerful one for me. Studying dimensions in math, and having the luxury of relating math to other topics, has been great. I feel I automatically look for mathematical connections to something that I would not ordinarily associate math with. I mean hey, if we successfully studied the Victorians in math class, or discuss dimensionality in literature, then there have to be other connections between math and non-math subjects. In this way I think the class was great, and I am backed up by the really cool "Dimensionality in Literature" final project. They made a lot of connections that I bet they would not have been so aware of before this class. I also feel like I more greatly value visual teaching aids in geometry education - this is what I researched for my final project - and the models Banchoff brought in to class also usually helped me understand what we were talking about a little better.

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?

I feel like the "all-rows-face-forward" lecture-format of the classroom squashed a lot of possiblities for discussion. I also really enjoyed the days where we split up into mini-groups to solve quick exercises, and was disappointed that this happened so infrequently. If this class is going to implement technology so majorly, I feel there should be a play-in-the-lab day, or maybe 1 week, where everyone is in the lab together designing html pages, learning how to use the web to find math information, maybe learning some simple math/geometry visualization packages too! Then the participation electronically would probably be a lot higher.

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 think that there could be an easier way to view submitted documents. I felt it was too easy to hand in a document and (if you are not a web-surfer, which I am not) never have time to come back and check the response, or read other's responses. Perhaps each week there could be a different team of students who would collect responses, watchdog to make sure they were all submitted, and then format them and read them for interesting connections, and link them together. That would be fun to see how a group of students interpret connections between what everyone writes. Then at the end of the week there would be one "coherent and uniform" unit of responses to read.

Another possiblity along these lines would be for everyone to hand in their questions in one week, then the next week be responsible for going in and adding links to others' documents, and to outside-Brown documents! This way, students would not be distracted from what is ultimately important in the resposnses thought and content. But, there would also be opportunity to take advantage of hypertext and web resources.

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

I feel like I only recently started enjoying the potential of html to format and display nice documents. In this I am really psyched, cause html is a good thing to know. But I feel like there were a lot of rough edges in the lectures - everything seemed to crash or be broken when we went to look at it, and we spent an awful lot of time looking at Banchoff's home page! Perhaps one whole TA allocated toward tech crises would help. I think as I mentioned earlier, mandatory lab days where everyone is together working on very simple tutorials would help. That way, even if there are different levels of understanding, you can learn from someone in the lab next to you. You can also meet people in the class this way - that is one of the best parts of a class when you get to work with some one and trade ideas with them.

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)?

I was thrilled that Banchoff cared enough to give such incredible, thoughtful responses to everyone's work. I haven't really had many teachers who are willing to keep a dialogue going on an assignment whose due date has already passed. When I read other people's papers it was very interesting then to read Banchoff's response. In this way the technology of the web provided an excellent forum for finding out what everyone else in the class felt about the material. However, I felt in a way that I was doing something prying or nosy, like looking through a folder of graded papers that were waiting to be handed back. I guess this is because we as students are not used to, say, finding out what the "secret comments" in red on our peers' papers are. The teacher's response to student work is traditionally kept private...It takes some getting used to, the fact that it's okay to read the teachers' comments!

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

I illustrated postulates and theorems, and also researched a topic of my own interest - geometry education. I like art a lot and believe that visual aids really can solidify murky understanding of a topic. I was glad to put this philosophy to work in both parts of the final project! It gave me great pleasure to work so hard on the illustrations and then see that most of the information I read about geometry education, especially for young kids, advocated visual aids, and art as a means of teaching and developing appreciation for geometry.

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?

I think working in a group is so much more beneficial to a very complete, many-sided understanding of a topic. Group work seems very complementary to the community feeling of the web, where everyone can be connected to each other, use each other's understanding to complement and extend their own. I wanted my talents and interests in the final project to highlight the mathematical work and creative work that was being done by other members. I feel like this goal was acheived in our project, and I feel like my research and illustrations also helped the others make their points with their work.

Prof. Banchoff's response