I have submitted responses for all the chapters, as well as the dimensional story, however I forgot to do a mid-semester reflection, so I'll try to make up for it with the following end of semester reflection.
Like in Plato's Allegory of the Cave, I now realize there is much more to our "reality" than I thought, and more than anything that is what made this course interesting. By learning about the fourth dimension through mathematics and geometrical analogies (like Flatland), I feel that I understand more about the mathematical process and discipline more so than in any other math class that I have thus far taken.
I really liked the loose framework for the course and how topics discussed were decided by class interest. I thought that the emphasis on the paperless classroom was a little too extreme. Some handouts now and then illustrating certain concepts gone over in class would have been helpful.
There are only a couple of rationales that I can think of that would justify the "paperless" classroom. The first is that not using paper would make the course more environmentally friendly. As we are already using a book made of paper as an integral source of information for the class, I don't see how turning in assignments electronically would significantly lessen the environmental impact of the course, plus paper can be recycled pretty effectively. The second rationale is one of organization. Handing assignments in over the web allows students to view each others' work (as well as your comments) and allows students to respond to each others ideas and saves time having to hand in and hand back assignments during class, Saving class time is a bonus, but a minor one, the real benefit of this type of paperless classroom should be in the ability of students to learn from each other, through the paperless forum of the web, I'll reflect on the efficacy of this later. The advantages of this type of approach is, of course, the ability of students to see what other people are doing, however a disadvantage of this approach is that at first not everyone knows how to do it. I think that the paperless classroom would work really well in an english class. I remember that when I used to be a member of Prodigy people would often post poetry and stories onto specific bulletin boards to receive crititcal reviews. As writing can be a highly collaborative process this type of electonic forum seemed ideal for that kind of a situation. I know the CS dept also hands its assignments in electroncially (how novel!) and that their assignments could be viewed and even executed by different people in the class or outside of the class.
I did not have much of a problem utilizing the basic technology to hand in assignments after some very helpful assistance from a Mr. Dave Stanke (Hi Dave!). I think an extra class period would have been helpful though in explaining the ins and outs of html. I have a friend who said that he made a web page without having to know html using some kind of a special word processing program, maybe that could be utilized the next time this course is taught. Also, those java applets were really amazing. I could not get them to work on my computer which was kind of frustrating after seeing them in class. David's applets rocked, especially the one that could rotate four dimensionally. Obviously, programming skills would also be helpful in a paperless course.
I really enjoyed reading what other people had to say in the course, especially their dimensional short stories. The weekly assignments were helpful in keeping me on track in my readings and your responses were informative. As for input and output to other peoples responses, I did not receive nor give much of. I think this has to do more with the nature of the assignments as responding to a response doesn't seem very productive, especially if your knowlege on the subject is limited to what everyone else has been reading for the class. I thoroughly enjoyed the final projects however and the presentations have been awesome!
As part of my final project team I illustrated a comic that explained geometrical concepts in the fourth dimension and how one goes about doing so in two dimensions by using shading. I used a comic book format so that it would be non-intimidating, visual, and informative for the grade school audience. I also helped Laura Lee scan her pictures in.
We didn't get to work a lot together but after some initial meetings we got some ideas together and pursued them individually, but in the end it all came together really nicely. Laura's story was perfect for an introduction, Keith and Alexis's opus provided an in depth look at fourth dimensional geometry, Kathy showed how higher dimensional geometry could be used in education, Scott gave a history of higher dimensional geometry, and I illustrated some interesting phenomenon that can happen in four space. It would have been better I think if the scope of our project were more focused, but I think it turned out alright.
Prof. Banchoff's response