Things have gone much better the past two days with the trig proofs. Much much better.
Yesterday, I asked for volunteers to put up the solutions. Not every problem was done correctly (most were though). Having the students explain their thinking as they were presenting helped. They did a nice job asking questions of one another. I also stressed multiple methods so we saw different ways of doing things. Some were a bit convoluted, but they worked.
Today was more of the same, except this time I called on the, uhm, hesitant students. I told them they could use a lifeline if they got stuck. One girl clapped and cheered when she did it correctly on the board. One student initially said no. I told him it was his choice. So, of course he then got up and did it.
We have a quiz tomorrow. We talked about how to study for math. I’m still surprised by the number of students whose plan is to “look at” the problems. I suggested to take out a new piece of paper and do the same problems again. Then compare results. I shared that I’ve done the same problems over and over until I understood them.
We’ll see what tomorrows brings in terms of quiz results, but I’m really happy with the way classes have gone the past two days. The students have been doing the math, explaining the math, and asking questions of each other. Yay!
Good for you. We did proofs a few weeks ago, and it was ugly. I’m not sure there is a better way tahn just slogging through them.
I haven’t taught trig identity proofs in a few years, but I recall my experiences being similar to yours: not knowing where to start, getting flustered with the multiple methods, and usually giving up halfway through. It’s good to hear that you’ve helped your students make some progress! Fortunately for me, the IB Math SL syllabus only requires the students to use the double angle identities and the basic pythagorean identity; no proofs for us!
I also run into the studying-by-reading issue. I try to stress to students that math is not a spectator sport. You need to work through fresh problems on paper. I mean, didn’t practice by watching himself/herself on tape…
Yep, the classes went better after the initial struggle. I’m about to start grading the quizzes. We’ll see how it goes. *crossing fingers*
I occasionally give one of the problems in advance to ensure that the kids study by actually DOING the math.
Yep. I told them some of the problems on the quiz would come directly from the homework sets. And I followed through. And those who DID the homework/studied did well on the quiz. Shocking how that works isn’t it?
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I wish I had a better experience with proofs in my high school past. It was my one downfall. I actually bought a book a couple of years ago that promised to help me learn. The lessons seems to go on forever (I thought it was the whole fall semester) back then. I’m so happy for your clapping student. She deserves a big round of applause.
Thanks. She’s been struggling for a while now. It was nice to see her experience success (and be excited about it).