Originally Posted 01-18-2012
Figuring Out Linear Algebra
One of my challenges this semester is implementing a linear algebra class with many new components. The considerations are these:
- I last taught a linear algebra class five years ago at and a different institution. Therefore, the audience is new to me.
- I am incorporating use of the open-source mathematical computing system Sage.
- I am using WeBWorK for “routine” homework assignments.
- I am using an open-source text which is still “in development.”
This is probably too much. But I am doing it anyway. Another thing which wouldn’t count for anyone else, but counts for me, is that I am trying to blend in an inquiry-based learning approach. This isn’t new to me, though for this material it is.
So far, I find that I haven’t carved out enough time to make the WeBWorK assignments work. This is a major goal of the next few days.
I ran a couple of Sage introductory workshops, one last night, that seemed to go pretty well. The first night went well, with lots of great questions, but was poorly attended. The second night I had a full room, but the crowd was not interested in conversation. One outcome is that I have at least made materials for running these in the future.
The biggest trouble is really that I find I haven’t hit the right stride in class, yet. I can’t seem to get an interactive environment and still include the computer. I am finding it difficult to make activities centered around the material, given that I am roughly following a text. By the way, the text takes the interesting approach that the students should learn all of the computational skills right away, so all of it is in chapter one. Applications come next, and then the theory starts in chapter three. I have already discussed matrix and vector algebra (minimally); the equivalence between solving matrix equations, solving systems of linear equations, looking for a realization of a vector as a linear combination of other vectors and the geometry of intersecting hyperplanes; Gaussian elimination. Next time we will cover rank and determinant, and maybe eigenvectors. Then we’ll have a quiz.
I’ll get there. I suspect that this will be a “muddling through” experience, and then next summer I will try to do something more serious. Maybe I should look at the AIBL grant cycle.
I have two other classes running this term, and they seem to be going well.
My dynamics class is going gangbusters. Almost. I have several students who have had classes from me before, and lots of people who are willing to give presentations and ask questions. I have two or three that I worry about because they have been very quiet. I’ll have to do a personal check on each of them.
Math in Decision Making
(My liberal arts class.) I think that this is going well. I have succeeded in making them confused about things, and then unconfused about some of it. Check!
I was a little aghast that they had no reaction to the weirdness of infinite sets. I mean, they just managed to prove that there is a bijection (we call it a ‘matching’ in class) between the natural numbers and the even natural numbers. I jumped up and down about how weird that is… They couldn’t really muster any emotion. Perhaps this is a bad indicator. At the very least, it means that they haven’t thought deeply about this issue (surprise!), at worst, it means they are just uncritically accepting whatever happens in a math class. I need to work on both of those items.
Other stuff from today
I mentioned in a department meeting that exactly zero people had volunteered to lead a summer research experience in math after my last call for proposals. This was a bit depressing. But I got responses from three colleagues right after the meeting. So, that is looking up.
Tonight, I am looking forward to a soccer game and a night out with friends (for free pie!) to help soothe the cares away.