February 14, 2013, 7:45 am
One of the projects I was taking on with my teaching this semester was a revamped linear algebra course built around peer instruction and the use of Learning Catalytics, a web-based classroom response platform. I probably owe you a quick update now that it’s nearly mid-semester (what?).
Linear algebra is a strange course in some ways. There are a lot of mechanical skills one has to learn, like multiplying matrices and performing the Row Reduction Algorithm. If you come into linear algebra straight out of calculus with a purely instrumental viewpoint on mathematics, you will almost certainly think that these mechanical skills are the point of linear algebra. But you’d be wrong! It’s the conceptual content of the subject that really matters. Like I tell my students, you can answer almost any question in linear algebra by forming a matrix and getting it to reduced row echelon form….
December 18, 2012, 4:17 pm
I’m excited and happy to be teaching linear algebra again next semester. Linear algebra has it all — there’s computation that you can do by hand if you like that sort of thing, but also a strong incentive to use computers regularly and prominently. (How big is an incidence matrix that represents, say, Facebook?) There’s theory that motivates the computation. There’s computation that uncovers the theory. There’s something for everybody, and in the words of one of my colleagues, if you don’t like linear algebra then you probably shouldn’t study math at all.
Linear algebra is also an excellent place to use Peer Instruction, possibly moreso than any other sophomore-level mathematics course. Linear algebra is loaded with big ideas that all connect around a central question (whether or not a matrix is invertible). The computation is not the hard part of linear algebra — it…
June 29, 2012, 2:23 pm
So, the six-week Calculus 2 class is over with — that didn’t take long — and there’s beginning to be enough distance between me and the course that I can begin to evaluate how it all went. Summer classes for me are a time when I like to experiment with things, and I wanted to comment on the outcomes of one experiment I tried this time, which is using a bring-your-own-device setup for clicker questions.
I’ve been using TurningPoint clickers ever since I started doing peer instruction, and I recommend these devices highly. They have a lot going for them in terms of classroom technology: They are small and unobtrusive, relatively cheap ($35), exceedingly simple to use, rely on no pre-existing infrastructure (for example, whether or not you have decent wifi in the room), and are nearly indestructible. They are about as simple, dependable, and inexpensive as a radio-operated garage door…
May 8, 2012, 12:52 pm
I blog a lot about peer instruction, but I think this screenshot from this morning’s Calculus 2 class is worth 1000 of my blog posts about just how effective a teaching technique PI can be. It’s from a question about average value of a function. Just before this question was a short lecture about average value in which I derived the formula and did an example with a graph of data (not as geometrically regular as the one you see below). I used Learning Catalytics to set up the question as Numerical, which means that student see the text and the picture on their devices along with a text box in which to enter what they think is the right answer. (I.e. it’s not multiple choice.) Here are the results of two rounds of voting (click to enlarge):
After the first round of voting, there were 12 different numerical answers for 23 students! (Some of these would be the same answer if students …
May 7, 2012, 8:58 pm
Today we started the spring term, 6-week Calculus 2 class that I’ve been writing about for the last few days. We had a good time today, getting comfortable with each other and doing some review of the basics of the definite integral. Before we get too far into the term, I wanted to outline the technology infrastructure of the course.
For a long time, I’d used the learning management system (LMS) of my institution as the basic technology for the course, and everything else kind of fit around the LMS. At GVSU the default LMS is Blackboard. But I decided after used Blackboard this past year that we have irreconcilable differences. I don’t ask much from my LMS; I mainly use it to archive files, provide a link to a central calendar, post grades, and to make announcements. I don’t need all the dozens of other features Blackboard offers, and the profusion of features in Blackboard tends to…