Dear Math 5020 students.
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.
During this discussion we also talked about the news story that said
that 40,000 Ontario students are failing high school because they
cannot cope with the new math curriculum. I had several questions
and people seemed to have lots of comments and opinions.
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.
Some things that I want to happen next week:
- 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.
We discussed this because I felt that these exams did not meet my
expectations and I needed your input on how to fix this.
-Mike