I recently had the pleasure of participating in an on-site review team for the SACS Commission on Colleges. The experience was a good one; I learned a lot about the reaffirmation process and worked with a very talented group of peer-reviewers. But the most important take-away for me was much more than that.
It was interesting (to me) to learn that my colleagues on my team found it very interesting that I work on a campus with dormitories and food service. They thought it was weird that we had so few on-line courses. They were surprised that I hadn’t taught anything on-line yet. It really opened my eyes to the true world of higher education where schools such as UMW are, in fact, sort of the minority. This might not be true in terms of the number of students who engage in “our” experience, but it certainly seems to be true about the number of schools in our region (just over 800). Wow, maybe we need to get with the times?
As I work through the readings for the DOOO faculty initiative, I keep coming back to the idea of teaching mathematics content. This time, I’ve been thinking more about an on-line version of a course I have been teaching for many years. That course covers more advanced topics in discrete mathematics (graph theory and enumeration, mostly). I have trouble wrapping my head around how I would teach this content in an on-line environment. But as I’ve been thinking, I keep coming back to another idea that’s been stewing in my head ever since I attended a COPLAC meeting about 3 years ago.
At that meeting, I learned of a course taught at UNC Asheville titled “Reality Math.” The speaker told us about the various (not on-line) modules that she developed for the course covering topics ranging from a cost analysis of electric cars, to a careful understanding of interest and debt, to an analysis of nutritional content of soft drinks. All of this was handled in a very ‘quantitative’ manner. So, basically, she took contemporary topics of interest to students (and, probably, the general population), and looked at them from a purely numerical standpoint. In other words, what do the numbers say? Does this thing I’ve been doing over and over again for years make any sense when I look at “the numbers”? I feel like I’m getting somewhere with this idea. I’m hoping to sit down with one of my colleagues in DTLT sometime soon and pound out ideas on how to implement this on-line.
One of the many reasons I decided to participate in the Faculty Initiative of Domain of One’s Own was to try to determine how technology can best be used in the teaching of mathematics. Of course, mathematicians have been using technology in the classroom for decades. Maple and Mathematica have transformed the teaching of calculus, graphing calculators have brought useful visualizations of functions all the way down to the middle school level, and dynamic geometry software such as The Geometer’s Sketchpad or Geogebra make the discovery process for mathematical results come alive (especially with Euclidean Geometry). I’ve been using these tools since I was a graduate student at the University of Delaware in the 90s.
But the Faculty Initiative of DOOO is not really about using content based software. I view it as being more about using the open web to build connections, share information, and synthesize materials by using the Internet as a medium to advance our body of knowledge on a subject. I’m struggling to figure out how to do this in content driven mathematics courses. My first-year seminar course on Cryptology may be a good place to introduce some of these tools I’m learning. But that course is much more process driven.
I still do not see how content driven courses that are linear building — such as calculus or linear algebra — could benefit from an approach that uses these tools. I suspect the sciences will have similar struggles.