For the past seven years, since I started teaching, I have been teaching calculus. When I started, I had 8 students in my class. Now I have 36 students. I’ve had to shift how I’ve thought about the course tremendously, and I’ve undergone a dramatic transformation in the content I teach (it is non-AP) and in the style in which I teach it. Seven years with a class is both a blessing and a curse. And honestly right now, I’ve reached the end of my usefulness for the course. I’m spinning my wheels. The only way I would be able to do a better job with it is to leave it for a few years and come back to it with a fresh pair of eyes.
And luckily, I have the opportunity to try something new. Next year, I will be giving up Calculus to teach an Advanced Geometry course for the first time. In fact, it’s the first time I’ll have ever taught geometry at all.
When I first began teaching, I was scared of geometry. Partly because as a student in high school, I found geometry to be uninteresting. It certainly didn’t have the elegance of algebra, at least the way I was taught it. Partly because I realized in that course — more than any other course — you as a teacher really have to focus on hard things. If you want kids to be able to do a proof of any kind (two-column or not), you are really teaching intuition building and connection making. Which is tough, and daunting for any new teacher, and this is why I recoiled at the thought. Now, years later, I see this as such an exciting challenge.
Right now, I am not anywhere about how to teach this course. And in fact, I’m only teaching one section and the other teacher is teaching three sections. But he’s very open to really revitalizing the course. So now we’re in exciting territory. Before I go bananas on scouring everything out there, I thought I’d crowdsource.
For any of you geometry teachers out there, if you have time to answer one or two (or all!) of these questions in the comments, I’d be ever so grateful!
1) What are your favorite geometry teaching resources — both online and offline? I’m talking books, websites, applets, manipulatives, whaever?
2) What are your favorite math teacher blogs that focus on geometry?
3) Is there a lesson you absolutely could not imagine teaching Geometry without?
4) Do you teach the course with a connective thread? Like: We are studying space and the properties inherent in space as we build space? Or: We are studying exactitude –and in particular, how we define mathematical entities so they yield uniquely understandable creatures? Or: We are studying “measurement” (in the vein of Paul Lockhart’s book).
5) I’m concerned that our kids lose a lot of their Algebra I skills when they take geometry. The other teacher and I have talked about putting coordinate geometry front and center from the beginning to help with this. Do y’all do anything else that helps keep their algebraic skills sharp, and maybe even push them forward?
6) Anything else? Problem solving? Sangakus? Geogebra use? Things you throw out because you feel strongly it’s only taught because it’s always been taught? Incorporation of Euclid’s Elements or math history? Graphic-design-y projects? Math art?
UPDATE: WOW, everyone, thank you so much for your resources and advice and for taking the time to type out so much great stuff. Now I’m genuinely THRILLED and CHOMPING AT THE BIT to get started re-learning geometry (and then teaching it). I am going to sort through things this summer!