Learning Goals for Linear Algebra: Content and Process

As part of my reworking of linear algebra, I have been reconsidering the course goals. I went back and read some of what I have written before about the mathematics to be discussed and the working habits on which we will focus. There is also this post from early in last semester. I think I only have small tweaks to make on these counts.

Well, I am a long way from having a fully developed set of Student Learning Objectives and a Student Outcomes Assessment set-up. (The SLO/SOA regime is the language used to sound official at UNI.) I have got a reasonable set-up for the department level technology SLO/SOA. At some point, I should get such an explicit set-up for my course. Maybe next summer I will work on that? Uh, sure, next summer.

Changes to Content Coverage

Last semester, the class got just within shouting distance of the three act content plan I wrote in the post linked above. Our discussion of determinants was superficial, and we just didn’t talk about the finite dimensional spectral theorem. Given that we basically wasted the first two weeks, I think those things can be addressed easily.

I would like to add just the smallest thing. Given all of the things listed here, and the focus I give to treating a matrix as a function, it would be great to add a discussion of the singular value decomposition.

Oh! Also, I didn’t talk about the cross product in Euclidean 3-space at all. I am comfortable with this.

Changes to the Meta-mathematical, process goals

I still see these as primary working habits that students must gain proficiency with to succeed:

  • make and explore examples
  • gain experience with abstraction
  • engage in more careful use of language

I will have to address these goals by writing my course so that students are forced to grapple with them, and also by being explicit with my students that this is expected of them.

And I still have these goals to deal with:

  • learn to use technology in an appropriate way
  • learn to read a textbook for understanding

I have a plan for the technology part. I have to work out something reasonable to help students with reading for understanding. Again, I have to be explicit about expectations and give focused instruction. (Somewhere in the back of my mind I have an evil plan to implement some sort of analog of a grad school foreign language reading exam.)