It depresses the hell out of me to think about how cool math is. Because I wish my students could see that. Because I can't do enough to make them see that. Because I make math boring. Because these kids will never see the beauty in that.
After school today I saw a senior, the brother of one of my algebra I students. I asked him why I was not seeing his name on the superintendent's list, and he proceded to tell me about his different classes, the trouble that he had been having in his calculus class before his new teacher arrived. I asked him what they were doing now, and he gave me a reasonable explanation of finding maximum area of boxes that had polynomials as their sides. Damn the boxes though, the mathematics itself is beautiful.
But in a five minute walk down the hall, I explained anti-derivatives to the kid. Just taking a derivative backwards. He told me the antiderivative of 2x was x^2. Good, but what is the derivative of x^2 + 1? 2x. So what is the anti-derivative of 2x? It could be two x squared plus any number.
Just that small leap of inference was beautiful. I would kill to teach that calculus class. But it also kills me to think of these kids trying to find the maxima and minima of functions. Even if you had just a cubic function, taking the derivative is easy. But setting the resulting quadratic to zero and solving it? In eight grade, I ate solving quadratics problems. Bam, boom, negativebplusorminusthesquarerootofbsquaredminusfouracallovertwoa. Give me another. I just feel terrible, like I am not preparoing my kids for this at all. KW could do it in three years, maybe even two. But the rest of them? If QR ever cared about anything. Maybe CH. And maybe MR. But almost all of them are smart enough to be able to do it. With the exception of, perhaps, 3 students, all of my students are at a level of intelligence equal to or above my high school calc class. If they were born in the berkshires, about half of my kids would take calculus.
Math has always seemed easy to me. This hsa been, certainly, an impediment to teaching it. When I get out of here, it might be really nice to have the opportunity to teach kids for whom math is easy. I know, at that point, that I wouldn't really be making a difference, but it would be fun. I'd love to take the top fifth and sixth graders, take them through a program that would get them from algebra I through calc in ninth grade. That is so possible for so many kids. Right now, I could take KW from algebra I through calc by the end of her junior year. But I hope she leaves. She needs to be at the math and science academy. Just like most of my kids, she needs to be anywhere but here.
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2 comments:
Hi there,
I found your blog somewhat randomly by googling "you never can tell with bees" because the phrase has some personal meaning to me. I was pleasantly surprised to find your most recent post on math. Random never fails to disappoint me :)
When I was in high school I was in an AP math program. I quite enjoyed it for a while and then I started to lose the passion for it as it got more difficult. I probably would have given it up earlier if not for the wonderful math teacher I had. I will never forget Mr. Hatfield and his passion for parabolas.
Today I work in the advertising industry where there isn't much use for derivatives. Still, I am always sad to hear people around me say, "ugh, math, I can't do it. That's why I'm a writer/designer". It's no excuse! You can be creative and love math too!
I wrote a creative blog post last year about my relationship with math, which you can read here. I would love to play around with derivatives again; I'd love to *remember* how to play around with derivatives again. I miss math. I think I'd like to study it again just for a fun break from words.
I'm not sure if any of this makes you feel any better, but trust me, your passion for math will resonate with a student if it hasn't already. Math *is* beautiful and it's with us for life.
You're welcome, Michael. I realized afterward though that you and I live in very different worlds. I grew up in a relatively wealthy neighbourhood that afforded me the luxury of being able to lose myself in a math lesson every day. I didn't have to try to pay attention to my teacher when I was really worried about all the things that come with growing up in the hood. You sound like a very caring person who goes above and beyond the duties of a teacher. I wish you well.
"You never can tell with bees" was a reference to a friend of mine who introduced me to the Winnie the Pooh stories this past summer. I was thinking of him as I wrote the post although it also applies to a few other relationships I have. I don't think he'll ever read that post, but I guess I just felt better putting it out there.
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