Seventh Week of Instruction (2/14, 2/16, 2/18)

The students now know the pattern of class: I hand out new problems each day (2/14, 2/16, 2/18), there is the orientation period. We then have a common full class discussion about the problems followed by breaking into groups for collaborative work. Sometimes questions are directed to me and I try to hand them off to someone else in their group. Usually this is successful. Also, the groups are sometimes fluid which is all right with me. I originally formed the groups so that the clustering of students would be comfortable and so that they would not obviously be dominated by any one student. As the students have all come to know one another and develop some trust this no longer appears to be necessary. In fact, on Wednesday, two of the groups merged because they were working on the same problem.

Part of Friday is devoted to presentations. The first presentation was completed with help from the students. I think that the fact that students are willing to present ideas, partial work, the outcome of investigations rather than only presenting when they have complete and polished work is evidence that a intellectually safe environment exists in the class and the students are willing to takes risks. The second problem illustrated this even more with the student really reporting on "things that he noticed." Though I have been good about letting students find their own way I do make some suggestions. The rest of the period is devoted to work in the groups though there is hardly time for more than orientation.

I am asked about the project, which I haven't thought about in over a week. Can I really have them do projects? The course is taking an enormous amount of time with my commitment to giving written responses to every problem they submit. I do mention some problems: the problem of derangements, that is, how many ways are there to put n letters in n addressed envelopes so that no letter is in the correct envelope (equivalently, how may permutations are there with no fixed points)? I also mention Buffon's needle problem, the Steiner 3-pt problem and the isoperimetric problem. I am not sure these problems (results) are really right, probably more appropriate for senior seminar since the students will not be doing the proofs themselves but rather researching a proof in the literature. I will think about this over the long weekend.