Fifth Week of Instruction (1/31, 2/2, 2/4)

Monday (1/31)We spent the entire class withstudents presenting problems. One volunteer came to the board and gave very elegant solution which took only four lines and was very clear and everyone appeared to get it. It had the essentials but was missing some points. I suggested that the class help him and a few ideas were given but in this fashion the class was not able to finish the problem and we left it there. Yet another student presented and all the elements are there but it is quite poorly expressed and this was confusing for many of the other students. I eventually made the suggestion to consider using induction or some equivalent form such as the well ordering principle, which some students did not understand so I explained it. At this point we still had a few minutes but no more eager volunteers. I acted surprised and said "Surely each of you has a problem you've done that you're proud of." This brought out a few responses and one more student presented and gave a very clever solution which illustrated the power of "going outside the box" and "look for an alternative representation."

Wednesday (2/2)Today I begin class by handing out "problems of the day" and this will be our method for the remainder of the course: I will bring a small, new set of problems to class each period on which we will work for that day. In this way we will avoid the possibility that thirteen students want to work on thirteen different problems and make it easier for groups to find consensus on choosing a problem to work on. Also, after handing out the problems we have a formal period of orientation: for five to ten minutes the students read the problems and ask themselves what is the given and what is to be determined or proved. Further, I want them to try and categorize what content resources (for example, number theory, combinatorics, logic, etc) and methods might be applicable. I then call on students to answer these questions for the different problems. After this we break into groups. There is lots of interaction and with the prompting from the orientation activity, I think, the work on the problems is more focused.

Friday (2/4)I again hand out a new short collection of problems and have an orientation period. During the period in which we share ideas about needed resources and techniques I try to get students different from the previous class involved. Again, in groups the work is more focused because the students have taken stock of the kind of mathematics that will be needed to do the problems.