I teach geometry. This is my sixth time teaching it. I think I'm the only person in my department that hasn't changed what they've taught for the past six years. The perks: overall, less planning! The downside: more planning? trying to reinvent the same material so it doesn't seem like the same old thang, while still keeping it effective and relevant for the students.
I always push for questioning in my class. I do stand in front of the class and explain some things, but their questioning fills in some of the holes and also covers the curriculum. In the past, I've followed the set curriculum I helped to write a few years back. Just like any other typical class, I started at unit one and plowed through to unit 13 or 14, following the lessons in the order they appeared. I thought I would try something new this year: let the students decide.
My plan is to start with unit 1, the basics of geometry (terms, notation, polygons) and go from there. I have a paper that I made up with all kinds of lines on it and I provided three or four angle measures. With this, I'll let the students calculate as many angles as they can and find as many polygons as possible in 5 or 10 minutes. From there, they can share what they've discovered and we'll discuss in great detail everything they bring up. For example, if a student give me an angle measure, we'll talk about whether or not its correct and why its calculated that way and how it will lead to other answers. If someone points out a polygon first, say a kite, then we will explore every aspect of kites (angles, segments, symmetry, area, etc.) before we move on. Theoretically, the entire beginning of the course will be based upon this one worksheet. Unfortunately, I don't think I'll be able to give them complete freedom and follow wherever they lead me (not sure its physically possible to be that planned out) (now that I think of it, in order for my students to 'run' the curriculum, you would think it wouldn't require much planning since I'm not doing the work, turns out it might require more, hmmm...).
The downside is that my two geometry classes will potentially be at different points in the curriculum all the time. Its probably going to be tough to keep track of what I taught and what I didn't. The upside is, the students are thinking, their guiding themselves, we're working together, they're engaged. Now, as I type this a question arises, how do I handle assessment? I'll need to provide a certain amount of structure for this to work so it doesn't turn into complete chaos. Do I still keep the unit in the same order so as tests/projects can be used consistently between classes? I realize the exams should not be the motivation for such a decision, but how else would I handle it? If I let the units get criss-crossed and the previous order changes, do I allow it and move to project based assessment instead of exams? Or, do I simply evaluate when enough material is enough and write up new assessments, different for each class?
I probably should've thought this through a little more before the second week of school. Oops.