5-30-10, Student-Centered Teaching, Geometry, and Number Strings

Does that title sound like a lot? It should. There are a lot of ideas I've had swirling around my head for the last month or so.

In August I was fortunate enough to be able to attend TMC NYC 16, hosted by New Visions. While I'd come across the phrase "number strings" before through browsing on MTBoS, it wasn't until I saw Michael Pershan demonstrate it that I really understood what number strings really are. It's like a really good problem set designed to get students to discover a concept on their own. And it reminded me of Bowen Kerin's style of problem sets (Important Stuff, Neat Stuff, Tough Stuff) which I got to experience first-hand at MfA's Chancellor's Day Workshop in June. And for a while now I've had this nagging voice in my head telling me to talk less in class. Find a way for the students to take over the talking. And I really want to do this. But how?

Number strings make perfect sense to me on an elementary or middle school level. Important Stuff, Neat Stuff, Tough Stuff makes perfect sense to me for an upper-level mathematics topic. But how do I make this work for Common Core Regents courses, with their mile-wide, inch-deep curricula. (Don't even try to tell me that the new curriculum has fewer topics than the old one so there should be time for more in-depth study. Don't even.)

These days I'm specifically thinking about CC Geometry, because I'm teaching it (for real) and developing this new curriculum for myself for the first time. The stars have aligned, and I have the opportunity to write it the way I want it on the first shot! I want to get it right (or as close to right as one can hope for) this year, so I don't need to make major revisions next year.

The challenge I face in Geometry is that students don't come to the class with much background knowledge. They think they know what a square is, for example. But they don't. How can I get students to define these shapes without me telling them myself? Is this even possible? Is this even the right goal?

So far this year, we've established the most basic vocabulary and we've reviewed geometric transformations. We're standing at the doorstep of the good stuff: angles and triangles. What should be my objective?