There were two reasons that the class was a little different tonight. First was the snowstorm and because of it we had less than half of the class there. I had planned to talk about math for an hour or so and then go to the computer lab. We never made it to the computer lab.

When I walked into the room there was a discussion going on about a problem from the homework. It was number 15 on page 7 from the book in the section about induction. Namely prove that F_{2n} = F_n L_n. The first time I looked at this problem, took me a while to solve this one and I never did figure out why it seems so much harder than the other ones in this section. I came up with a very difficult solution to this problem. I know that there must be an easier way to prove it but I will provide you will half of my solution. The second half I left as an exercise to put in your journals. You may print out the following page and fill in the missing part of the proof. If you have a shorter explanation of this, please send it to me so that I can post it.

Next I showed off a letter that I had from the Ontario Lottery commission. Bruno Fullrone looked on the web site for the lottery and found the 1-800 number that you can call to get information about the lottery. He asked them for an explanation about how the probabilities for the lottery are calculated and they sent him a letter in the mail. I loved it. Their explanation for the lottery sucked and I suggest that we (as a class) write a new one that is well thought out, clear and short and send it back to them. Part of our discussion lead to the following short list of things that we will need to address in our solution:

- we will develop the discussion on the forum, the actual document will be done in pdf and I will maintain it at the web site while the rest of the class comments on the solution
- the final product must include a formula for people who prefer a recipe of computing the answer
- We must assume some mathematical facts but when we do we will make it perfectly clear what we are assuming and why
- The original explanation was 3 pages and we don't want to exceed that. Length is important because they won't take the explanation seriously if we don't.

Finally I returned the final exams. This is where they class became distressed. A lot of students who thought they were doing fine got back their exams and found a grade which was not what they were expecting. We then had a long discussion to try to address the problem with this. The exam was out of 100 but there were some really nice papers where I deducted 2-5 points on most of the problems and so it is graded on a scale. By the way, I MUST have your final exam back a week or two after I have given it to you. I am required to keep them in my files for several years.

Here are some points that came up.

- I tried to make very clear what my expectations for this exam
were before you sat down to write it and the grades were based on if
you met those expectations or not. I felt as though I got back
some exams where people did not understand the instructions. I
was looking for clear, complete and coincise solutions. I graded
only on
the first two of these constraints and I graded harshly because that
was the very
point.

- People in the class told me that my expectations were not clear
and that the level of detail that was expected was unreasonable given
that we have discussed problems like these before (e.g. "why do we have
to explain what the phrase 'choosing spots' means when we have
explained problems like this before?"...my answer is: not everyone did
problems like that before).

- The serious issue here was that this is your only grade for this class so far. I wanted you to have other grades at this point (namely the journal) but I haven't collected it so far due to logistical constraints. The journal is a collection of homework assignments that I can't possibly correct and grade. You need to be doing lots of problems and I can't read them every week. You also have the 'forum' but I have not evaluated that yet.
- I will be evaluating the journals and it was suggested that I should have an interview with each student about the journal. This was my intention anyway but I think that it is clearer. I want to start collecting the journals very soon.
- Another issue with the final is that it was an all or nothing. There were students who did not understand my expectations did not find out what they were until after the exam was returned. One way that we might resolve this problem is to give a grade where there is some sort of feedback earlier. To this end I would like to start asking a question a week towards the second part of the final exam.
- My expectations of this course have developed since the first day
I started teaching it. The material that we are covering in this
course is "number theory and combinatorics" but the skills that I
expect you to take away are much more general, that is, I want you to
be able to "read, write and explain mathematics." That is what
this exam was about.

- I will give you a first problem for part two of the exam
- I will evaluate the material on the forum
- I will discuss with you about having roughly 6 people handing in your journals to have them evaluated.
- After you get back your exams, I would like you to add to your journals rewrites of problems that you got less than 10/20 on.

-Mike