The Common Core Standards came out, and they said "teach everything in Geometry by transformations" which just about no book does... I finished my second year of teaching 4 sections of geometry, 2 levels each year which used different books... Matt posted that he was tired of starting with undefined terms, he wants to jump straight into triangles... PCMI had a big focus on questioning this year... My department head starts geometry with patterns and conjectures...
This morning I took all of those ideas that have been rattling around my head, and I made a curriculum map. This is the first time that I've ever planned out an entire course. In the past I've just followed the textbook, maybe switching around a couple chapters when someone suggested it. Last year I invented the curriculum for a course, but I made it up as I went along because it was for severe special ed and I went into each topic having no idea what their prior knowledge would be. Having taught Geometry for 2 years, and to over 200 students, I finally have the knowledge to decide how I want this course to work. Obviously I don't expect this to go perfectly; I would love advice on the orders you've tried and had successes or challenges with. But it was great to be able to sit down and really have a sense of how everything connects, where students thrive and what activities work well. That will most definitely not be the case as I start teaching PreCalculus this year!
I will share the map below, but be warned that it's very much meant for me, so there are lots of obscure references. Quite a few of the activities are ones that I've blogged about, so if you're interested in learning more about something try the search bar or just leave a comment and I'll add in the details.
I'm also starting Standards Based Grading this year. The standards list is probably more accessible to the general public. I don't plan to give this to students since there is no way to write a standards list for Geometry that doesn't give away the surprises I want them to discover. I may even let them decide on some of the wording. I'm really happy that I ended up with 25 standards since it's such an awesome number. That said I may end up breaking some apart, adding things in (skills I assume they have from Algebra that are lacking?) or cutting some (trig for the fundamentals class).
Geo Standards List
If you want to further engage in the conversation about geometry, head over to our wiki or tweet with the hashtag #rethinkgeo. My next step is to come up with some sort of intro to each unit that gets students started asking questions (for the points and segments in triangles unit that question is: three cities are building an airport to share, what is the fairest location for the airport?). Then I want to start writing/sorting problems that assess each standard so I have a pile to pick from for quizzes, tests and reassessments. Geometry questions are particularly difficult to come up with off the top of your head since the diagrams can be seriously misleading if you don't think the whole thing through!