180-x=The Talmud
One of the kids I tutor goes to yeshiva. She studies all the regular subjects, plus a full curriculum in Jewish history, law and scripture. Her dad is Israeli and she applies the pleasant iron will I associate with Israelis to her learning of SAT math. When I tell her f(x)=y, she says, “Why? Who says that? What makes that true?” I find myself having to prove the fundamental assumptions of algebra to her, rarely to her satisfaction. It’s gotten us into some interesting discussions about math being just another language. This seems to placate her, since she is bilingual in English and Hebrew. Every time she argues with me that f(x) doesn’t have to equal y, I ask her to translate an English word into Hebrew for me and then pester her, asking “Why? Why does that mean ‘book’?” Why? Who says?” until she admits that in a language, a certain symbol and sound gets associated with a certain object or idea, and that’s just the way it is. In trying to explain to this kid why f(x)=y, I finally understood Saussure, this French linguistic theorist who made me cry in college. Sometimes it just needs to percolate for a while.
Working with a kid who actually speaks, reads and writes Hebrew, as opposed to reads it phonetically in order to get through her Torah portion, pass Mazel Tov and collect $15,000 in bar mitzvah gifts has provided me with an interesting anaology for how math is taught versus how it should be taught. Math is currently taught to most kids the same way Hebrew is currently taught to most Jewish kids–as a language to learn by rote and use to participate in a kind of rehearsed call-and-response. Only the very religious actually learn to understand the Hebrew they are reading and only the very nerdy actually learn to understand the math they are doing. It doesn’t have to be this way. Learning Hebrew or math by rote in order to jump through hoops, be they educational or religious, is a waste of time. Why are we teaching kids languages, ancient languages of sacred truth at that, without teaching them the meanings of any of the words and symbols?
Tonight, I saw a case in point of what can happen when a kid does understand the languages she’s speaking. We were working out the notoriously hard last question of the math section together. I was trying not to give away the secret of the problem, which was that if 180-x=a and 180-x=b+c, then a=b+c. I was quite excited about this secret and was waiting with some suspense to see whether the kid would see this or not. I guess this is how I am able to maintain my interest in my job. When I start to lose interest in my job, I will start gambling on whether the kid will see the secret to the last problem in the math section. That’s why they call it, “making it interesting.”
The kid was frowning and muttering in that advanced stage of math-problem determination and I was rooting for her. “Don’t tell me,” she kept saying, so I kept my mouth shut.
Eventually she figured it out and triumphantly circled “(E).”
“Very good,” I said. “You got that if two different quantities are equal to the same thing, they are equal to each other.” She even knew that it’s called the transitive property, which most kids don’t know.
“Well,” she shrugged, “We’re studying the Gemara in school. It’s like, part of the Talmud. And it has all these laws, and they are the same as other laws, so you have to see that if one thing is the same as another thing, and another thing is the same, then they are all the same. So I raised my hand and said, ‘Isn’t that the transitive property from math?’ I guess that’s kind of dumb.”
“Are you kidding?” I nearly shrieked. “That’s not dumb. That’s using math to understand religious law. That makes perfect sense–law is logic and logic is math.”
I thought of my friend Josh, who was always messing with his computer in his basement and went to MIT and keeps getting degrees in things like computer science and engineering and artificial intelligence. We used to have big arguments about whether poetry had any value in the world. He always said math was the only thing that was real. After he went to MIT he had some nice things to say about math, like “Math is a way of saying what is true.” I told the kid this and we agreed that religious texts tell us what is true according to the laws of one particular system, and math tells is what is true according to the laws of another system, and these truths are both articulated according to a language and system of meaning that helps us to convey the truth.
You see what happens when kids understand what they are reading and doing? They learn how to articulate the truth. I understand better than ever why schools spend thirteen or even seventeen years teaching kids to regurgitate lies instead of discover and speak the truth. Regurgitation is a lot safer than revelation.