I am going to start each class by asking you what questions you have about the material from the last class or the homework assignment. We will base the class discussion on these, so it is important that you spend some time thinking about questions before coming to class. In order to facilitate this, I am asking you to come up with (at least) two written questions each day. These can be about anything that you didn't understand, or about new ideas that you have thought of and want the class to consider.
To help encourage you to think about the material between classes, I am going to ask you (as a group) to write short (two or three paragraph) summaries of each class. We will be using an on-line conferencing system to facilitate this in the following way. I have set up a Math 53 Conference on the department's conferencing system (I'll give you instructions on how to use it soon). Each day, I will start a new topic for that day, and ask two or three of you to post short summaries of that class as the beginnings of new conversations. Others should feel free to add comments to these. The main comments should be posted by 10:00 the night before the next class (so everyone has a chance to read them), but you are welcome to post additional comments at any time.
I will be posting the homework questions (other than the hand-in ones) to the conference as well, and you should answer these or respond to other student's answers before the next class, as well.
Not everyone needs to comment on every class or every homework question, but I expect that by the end of the term, everyone will have made at least fifteen or so substantive comments along the way, will have asked at least eight questions in class, and will have summarized at least six classes (that's fewer than one a week).
The idea is to continue to think about the material after it has been presented in class. Your summaries should describe the major ideas, but should not simply repeat what we said in class. The summary should not be a simply laundry list of the ideas we discussed, but should pick out the important material, and should interpert that material, making connections to past parts of the course, or speculations about what is to come. Try to organize and codify that material. (This is a skill that you need to practice.) It is important for you to take time outside of class to think about the material, and these write-ups should help you focus your concentration.
The questions that you bring to class and ask on line will be what drive the course, so the insight and effort you put into these will have a big impact on the quality of your classroom experience this term.