first!

I had an idea this morning. I was plotting out a calendar for the course I'm teaching this summer (the namesake for this blog, in fact) and also reading an article about teaching creativity—instead of just rote knowledge—that I had clicked on via someone's Facebook post or something long ago and had left open. (No, I wasn't performing these activities simultaneously.) I realized that I frequently have ideas about teaching, and math, and teaching math, that I'd like to remember for myself to use in the future or that I'd like to share with others, or both. Voilà! This blog was born.

I'll use this space as a way to keep track of my teaching of 21-127 Concepts of Mathematics at Carnegie Mellon University during this summer's second session, through July and part of August. I'll post some interesting ideas I hear about or have myself, I'll share how the course is going, I'll pontificate about things that incite passion in me, and so on. Who knows, really, how this will turn out? At the very least, it will make for an interesting "public diary" about my teaching experiences. Maybe I'll keep writing during the fall semester, but I'll make no promises on that at the moment.

For now, here is a link to that article I was reading today. I don't know anything about the experimental schools the author listed, nor do I feel particularly motivated to completely revamp school curricula. I am interested, however, in the idea of training students to be creative and ingenious, to not only answer questions but to ask them. These sorts of skills are always on the objectives list for this course I am teaching—we want our students to not just memorize mathematical "facts" but to understand why they're true and to even gain an appreciation for why we care about them in the first place!—but they seem to be the least stressed during the actual teaching of the course, and the main ones of which the students might not realize the benefits. This might be because these skills are hard to assess accurately, of course, but that's a cop out. All we need is a little ingenuity, ourselves, on the instructors' side.

I've been mulling over several innoventions on the homework/quiz/exam front for this course, and I'm hoping to implement them during this session and assess their effectiveness, so this has already been on my mind. Certainly, though, this article has reminded me that creativity is a skill we can address every day in the classroom, and even just a little emphasis can go a long away. If I find myself describing a difficult proof of an important theorem, I should stop and try to describe how someone came up with such an argument, or why they were thinking about it in a particular way. I think that by simply addressing the creative underpinnings of the daily content, students will benefit, at the end of the course. This doesn't take a lot of effort, just a little bit more talking in class, and maybe a pause for some questions for the students. I will try to keep this in mind every day and see how it effects the students! If I can convey any sense for the beauty and ingenuity that permeates mathematics, I will consider my endeavors a smashing success.