I recently got an email from someone who saw some of my many posts on geometry (you can see all my posts about geometry by clicking here). I realized I never shared them formally and everything is a bit scattered. So I’m going to try to include a few resources here. But the real joy is in all the blogposts, honestly.

I taught Advanced Geometry at my school for two years (2014-2016), and I wrote the curriculum with a good friend and dear colleague. We both hadn’t taught geometry before and decided we’d do a super deep dive and come up with a sequencing that made sense to us, and that prioritized conjecturing and noticing. In fact, we were so excited by this process that we shared our thinking both about how we built up the curriculum but also how we collaborated at a conference. Below are our slides, but you can also click here and go to the slideshow and read some of our presenter notes for each slide for more detail.

We were super intentional about everything. We carefully thought through how we wanted to motivate everything, and we didn’t want to give anything away throughout the course. In other words, we wanted kids to do all the heavy lifting and to be the mathematicians that we knew they could be.

Below is a word document with all our skills/topics (you can download the .docx file here: All Topic Lists Combined). The order might seem a little strange (we end, for example, the year with triangle congruence), but it worked for us! Everything was done on purpose (in this case, congruence is just a special case of similarity… so that came beforehand, along with trig which is all about exploiting similarity!). We eschewed two-column proofs for different forms (paragraph proofs, flowchart proofs, and anything else that showed logical reasoning).

Oh wait! For some reason our work on Area and Volume didn’t have a topic list. And I just looked and my core packet for Area and Volume derivations (where kids just figure things out on their own) has handdrawn images in it, but I didn’t scan a PDF of those. Well, at some point in the future if I remember, I’ll try to write a post to share that. (We did it after kids learned trigonometry, so they had a lot of flexibility. For example, I think kids came up with like 6 different methods to find the area of a trapezoid when they were asked to create a formula and justify it!)

I hope this is helpful for anyone trying to think through geometry. As I said before, the best thing might be to just read the blogposts, but this is a bit of an overview.

What the distinction between advanced and regular geometry?

Great Q. I think there might be a difference in course content (advanced might cover more but I don’t totally remember… this was a few years ago and I don’t have a great memory). But in advanced, we had a lot more depth/abstractness and the pace was significantly quicker (less review, and I think less scaffolding).

Thanks that leads me to a followup: how did students pick which version they took?

Hihi- at my school (an independent school) many students were in our middle school. So their 8th grade teachers made the determination. Students joining the high school from a different middle school took a placement exam. Over the years, the exam changed (from one we had for ages, to one we created ourselves which incorporated problem solving, to one that is electronic whose name I forgot but seems to give us reliable results). Students don’t really have a “choice.”