At MathFest 2013 in Hartford, I got to participate in the Project NExT activities as a presenter and facilitator. This is a professional development program for new faculty in mathematics run through the Mathematical Association of America. I was a Project NExT fellow way back in 2007. That makes me a “Sun Dot,” because fellows all wear an extra colored dot on their badges at the annual meetings. It was fun to meet so many of the “brown 13 dots.”

My first responsibility was to run a quick discussion on using technology in college mathematics courses for a small group of fellows. This is something I have actually been thinking about a little bit lately! Regular readers (Hi, Mom!) know that I have participated in a project called UTMOST, and through that I have tried to incorporate Sage into my linear algebra course.

The first step in our conversation was to take a few minutes to write down some questions about teaching with technology to share with the group. I didn’t get the chance to share mine, but I was proud of them. I just found the note card I wrote them on, and I really should recycle it. Fortunately, I have a blog! Regular readers (Hi, Bret!) know that I just write whatever I damn well choose and I don’t care if they read it or not. (Please, keep reading.) So, here is my chance to shout into the aether and be proud of myself.

- How do we use technology to liberate class time for “meaningful work” with depth?
- How does technology enable orÂ
*require* new questions and activities?

I think it is important to teach the use of computing technology in a discipline-appropriate way. Otherwise, we are presenting a limited view of mathematical work to our students. But introducing the computer (whatever shape it takes) into a classroom has implications for the kind of work we ask our students to do. What are those implications?

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Hi TJ!

P.S. I love your use of the word “liberate.”

My idea about technology is similar: “Think of what you want to do pedagogically (assuming no limitations), then try to make it happen. If you can’t make it happen, see if there is any technology that will allow you to get around the roadblock.”

Pedagogy before technology. . .

And how! I find that perspective useful for dealing with classroom tech, by which I mean those things I use to manage class somehow: wikis, blogs, electronic grade books, email, web apps, etc.

I feel challenged by the ways in which technology *is* the curriculum, or might be. How do we think about teaching general purpose computing as a tool for mathematical work? I wasn’t taught this, but it feels important.

Classroom tech divides into two categories:

1. Is there ubiquitous technology that makes what I am making my students do by hand unnecessary. For example, we no longer expect students to come out of HS knowing how to compute a square root by hand. This, plus Wolfram Alpha, has deeply influenced the way I think about teaching Calculus.

2. Is there classroom technology that could allow me to ___ in less time overall? I am strongly considering using a clicker substitute to conduct exit questions for my beginning classes. This could take less time overall because I wouldn’t have to keep track of all those slips of paper and I would be able to read the comments quickly because I would not have to decipher students’ handwriting. The less time overall is very important because a lot of classroom tech is so buggy (Blackboard I am looking at you) that it takes more time to use the computer than just do the thing by hand.

TJ, I’m working on some aspects of this as my next blog post. But briefly, I am planning to take more photos and use one of the many tools to manage them (ThreeRing, most likely) as a way of freeing some of my classroom “sense” from taking notes during class to managing students.

I agree with Mariah that computing by hand is so much less important now than even 15 years ago, but a lot of our teaching has yet to catch up. To make an analogy, we spend little time (probably too little) teaching students how to estimate in their heads, in favor of computing on paper. With the ubiquity of computing tools, we need to de-emphasize paper in favor of teaching how to use a computing tool effectively.

Indeed. My first question is all about technologies that make our classroom experiences more manageable. I am experimenting with some things to run my Geometry course (blog for communication, Google drive form/spreadsheet/script for assessment). I would like to hear about how you use ThreeRing. My guess is that it is a tool for managing assessment. Am I right?

But the other question is more challenging to me. For example, how do I incorporate GeoGebra (or Geometer’s SketchPad) into my geometry course? How should I go about introducing students to the capabilities? In what way does it change the practice of a working mathematician who wants to prove theorems in classical planar geometry? How do I get students to understand the decision point about when to go to the computer and when not?

all of that remains for _general computing_ (say with Sage) in other courses.

I feel that there is great potential in Dubinsky’s idea of having students program to make mathematical things seem like “objects.” I am intrigued by APOS theory, but I have not made it central to my teaching plans.

I am going to have to look those up. Unless you care to drop helpful links.

I suppose I could give you some links:

http://www.math.kent.edu/~edd/ICMIPaper.pdf

http://www.amazon.com/Calculus-Concepts-Computers-Ed-Dubinsky/dp/007041033X/ref=sr_1_1?s=books&ie=UTF8&qid=1377449025&sr=1-1&keywords=dubinsky+calculus

http://mathforum.org/kb/thread.jspa?forumID=185&threadID=433456&messageID=1372408

I figure it is always useful to link to a webpage from 1997 in these instances.

Bret