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.