Digging out the proof that is stuck in the pudding May 24, 2012Posted by mareserinitatis in education, gifted, homeschooling, math, older son, teaching.
Tags: CLEP, economics, geometry, math, older son, proofs
Since the older boy was kicked out of school, I’d say he’s been doing more academically than before when he was in school. After he passed his GED in March, I asked him what he wanted to do until summer. He had the choice of getting a job or studying for a CLEP exam. He usually spends a good chunk of the summer with relatives, so he decided to wait on looking for a job and instead aimed to finish another CLEP. He chose to study macroeconomics. To do this, he got up nearly every morning and spent 3 hours at the university library (where he has no internet access), read through the entire textbook, and worked through the study guide. He passed the test on Monday, and we’re all very proud of him for his hard work. (He, however, was disappointed that he didn’t get a higher score and now wants to spend some time going through the text again to figure out the parts he got wrong.)
In addition, we began talking about college things, and I told him that he should take the PSAT in the fall because doing so would automatically enter him into the National Merit Scholarship Program. This is a scary topic because it requires that he go back and do something he hates: math. However, he keeps telling me he really wants to go to college, so he was willing to go back and do some. Of course, saying it and doing it are two different things.
He’d finished algebra 1 two years ago and last year, he’d made an attempt to jump into college algebra. He made it a good chunk of the way and then started having some real difficulties. Therefore, I decided to take a step back and see if he could get geometry done before summer. It turns out that he was better off than I thought because he did the initial evaluation and tested out of about 2/3 of the topics. In the past month, he finished off all the rest except for a handful, all of which had to do with proofs. (Apparently, he is serious about the PSAT.)
I have to admit that this is different than when I took geometry. My geometry class was entirely proofs. It was one of my favorite classes because, to me, doing a proof is a completely different animal than solving an open-ended problem. You know where you’re starting and finishing. All you have to do is find the path between here and there. Usually it was extremely obvious, so I was able to write out my proofs for class and often have time left over to read. I remember being very confused why other people thought the class was hard. Later on, when I took physics in high school, it felt like the same thing. You’re trying to find out a quantity using a bunch of other quantities and formulas. Easy peasy…
I sat down to help the older boy yesterday, and I have to admit I got frustrated pretty quickly. I read the problem, saw what was supposed to happen, and knew immediately the steps in the proof.
Problem was the older boy didn’t.
This really threw me for a loop. I mean, the kid’s obviously smarter than me (and just as obviously less wise and experienced). It really stunned me that there were a couple points where he was struggling to figure out what to do next. He was getting frustrated, though, so I walked him through a few of them, explained the reasoning, and tried to talk to him about how I viewed the problem (which is hard to do when you think in terms of vague notions of going places on diagrams).
It got me wondering, though, if this is why he doesn’t like math. Is it that hard for him to see the end goal? Is the process of finding logical steps difficult? And why is it so easy for me to formulate these things and difficult to him? Do our brains work differently? The whole thing left me with a lot of questions, and I’m still very perplexed.
By the end of the session, he seemed to have it down and was making good progress. I was able to back off and just let him work, and he even found some of his errors when he got things wrong. The best part was, however, at the end when he turned to look at me, grinned, and said that it was actually kind of fun. Mission accomplished.