Monday, November 11, 2013

Proofs Pt 2

I am never sure how long it should take to teach something. Part of me says lets teach until everyone gets it, but that could mean I'd only teach geometric notation all year. Part of my says lets go as fast as we can so when there is something we need to slow down on we have extra time. All along though the big question for me continues to be, does another day make a difference, do I make a difference.

I set out to try and measure that impact with a difficult concept in geometry: Proofs.

My colleagues and I decided on a seven day unit on proofs with a test the seventh day. I agreed but told them I'm going to test on day two and day seven. I wanted to see if they improve. Really I wanted to see if what we do in the class is worth a damn. I don't think people are 'born' with math ability, but I do think some students walk into my class better at math then others. Proofs exemplifies that 10 fold. Those that give up easily, those that lack prior skills, and those that won't try, usually suck at proofs. So can I change that or is it a lost cause?

Day2: I tested and scored them. They were mostly terrible. Very few getting to that higher level proof completion. So instead of a score which may set students back, I gave them an X or a Y. X was for those students who barely knew how to start a proof and Y for those that made progress but didn't have it all together.

The next 5 days: We did things as a class and we did things as separate groups. We would work as a class on flash cards for the first 20 min, then the rest of the time X would work on page 10 and Y would work on page 11 (different pages symbolize varying degrees of differentiation). Nobody complained, nobody said "Why do we have a harder assignment?" and I even had X group people wanting to get done with page 10 to get into the Y group and work on page 11.

Students knew what was coming and that makes testing easier, maybe it doesn't make them smarter or better at proofs but I gave them a test that was closely mirrored to what the test was going to be like on day 7. They had a goal, not all set that goal for A level completion, but they all knew there was something on that test they could complete. So everyone tried, everyone tried to get better over the next 5 days. The question is did they get better?

Day 7: Punched them in the brain with a quick review and we tested, this test has three levels of proofs, C, B and A. C level is 3 steps, B level 4 steps, and A level 6 steps. They did better, but it closely mirror the day 2 results. Student improved but only slightly.

Meaning: I'm not sure yet, days after the end test we came back had another retest, chance for students to improve scores and it continued to get better. I don't have enough evidence, but I'm very close to saying we speed up our curriculum then monitor and adjust after.