After a couple weeks of p, q logic proofs, we started proofs “for reals” in Geometry this week. First, we did algebraic proofs. The kids were not happy that they had to show all of their steps. “But I can do this in my head!” Yeah, right. At least it was a pretty easy introduction to proofs. Anywho…
After learning all about segment and angle addition postulates, we started beginning baby proofs. The first day went really well. I took a page from the amazing Fawn’s book and modeled my first proof lesson after her problem solving lessons. After all, proofs are just giant problems you have to figure out. I gave them a proof. We wrote down our “given” and marked up our diagram. Then, I had them “think” silently for a few minutes. I encouraged them to write what they were thinking or to take notes, but they didn’t have to do any “work”. I just wanted them to think about what they knew.
After those few minutes, I gave them a few minutes to talk to their group about their observations and what they were thinking. I walked around and heard amazing things. “Could we just add these up?”, “Aren’t these equal?” and “I think we could use the segment addition postulate here.” Then, we pulled it all together. I let the students tell me (and each other) what I should do next. The students explained their thinking to their peers and I also jumped in occasionally when needed.
Learning how to “do” proofs (how to prove something) is problem solving. This takes time and effort. This takes a person looking at something on their own and really trying to figure it out. You can give a student strategies, but I don’t think you can “teach” someone how to do a proof. They need time to figure it out on their own. The time spent in class “thinking” and “talking” to each other before actually doing this together as a class was well worth the time. First of all, I have freshmen, so a few of them are not doing their homework as consistently as I would like. This means that the in-class time is the only dedicated time they will get. Also, many of my students get frustrated on homework at home and will just quit. I wanted them to have support when they were starting out.
The best part was when we worked as a class. Since I gave them time to think silenty and work together, some of my students “figured” out the approach they would take. They were excited to explain it to their peers. Their peers are much tougher on them than I am! Students often had to explain their reasoning in a couple of different ways. The listeners wanted to know how and WHY their classmates are doing a certain step. And voila, there are the proof “reasons”.
I was worried about teaching proofs, but it has been amazing so far!
Day 2 – Proof Stations!