Sixth Week of Instruction (2/7, 2/9, 2/11)

Monday (2/7)There is now a regularity to the class. I give out a short collection of problems which draw from several of the types that we have now discussed and leave open to the students to choose what approach to take. We also have an orientation period in which we discuss these things as a whole class. The balance of class had the students in groups. There is lively discussion. Today I make a point of paying specific attention to the male/female interaction in the groups to see if there is the usual dynamic of males trying to act superior and take over the group and see if they hold their own. What I see is that most of the women are quite articulate and don't hesitate to speak up and express their views, even flatly say that fellow (male) students are wrong or offer challenges such as "well then prove it". The discussions are getting more advanced at least from the kind of vocabulary I hear used. Among the terms circulating are: modulo, congruent, symmetry, relatively prime, iinvariance. The students are also learning to depend on each other rather than me: when one student didn't know the meaning of relatively prime their question was directed to the other persons in his/her group.

Wednesday (2/9)I begin by distributing the new problems of the day and we take our orientation time. Then into the groups. There is lots of brainstorming on the problems and there is even consulting between groups and swapping of ideas. Among the terms used are: combination, remainder, modulus, the method of ordering, cardinality, one-to-one correspondence, enumerate, though the degree differs with the relative standing of the groups, those with fewer courses relying, sometimes with considerable success, on ideas and more general approaches, the more mature students often trying to recall theorems (of course, this can be a legitimate heuristic: "try to relate to a similar problem").

Friday (2/11)Distribution of new problems and orientation. Then into groups. Today there is lots of quiet at first as all the groups appear to have chosen problems that involve some investigation at first and rather than work out cases together the students within the groups do it individually and only then begin to compare results. Even with the data, the groups appear stuck and this could perhaps be due to lack of familiarity with number patterns, i.e. perfect squares. Ultimately this is overcome when they use the calculator and find that the numbers they are generating are very close to perfect squares and then realize that they are each one less than a perfect square. Now, of course they have to prove this in general and they again encounter some difficulty because of they have to get their hands dirty and actually multiply expressions, get polynomials. The other problem worked on in the groups also involves investigation and pattern recognition but that seems to be more straightforward and successful