The Coolness of Being Educated: Where Geometry and English Collide

What does math class and English class have in common? This is a trick question, right? It’s apples and oranges, as the saying goes. Or maybe not.

Two math teachers share my free period in the staff lounge, and we’ve had some interesting conversations on the topic this week. In geometry, which some of my 10th graders take, they are emphasizing that an idea in math requires the same proof that an idea in science or English does. I’d just taught my English students about the rhetorical fallacy of a hasty generalization (made by a character in the novel we were reading), and in writing our current paper, I told them that when gathering support for a point, three is sort of a magic number: 

• One is only one. (Not only is it a hasty generalization, but also you can twist one quote to mean just about anything. I once had a student who claimed that God was afraid of people learning things. He used a Bible passage to support it--Proverbs 1:7, “The fear of the Lord is the beginning of knowledge.”) 
• Two a coincidence. 
• Three starts to look like a pattern, like proof.

Just yesterday these two math colleagues were talking about teaching students the logic term “antecedent.” I perked up. “That’s a grammar term, too!” I interjected. We had a discussion of the similarities of use in logic and in grammar.

Here’s my Mac’s desktop dictionary’s many definitions:

a thing or event that existed before or logically precedes another: some antecedents to the African novel might exist in Africa's oral traditions.

• (antecedents) a person's ancestors or family and social background: her early life and antecedents have been traced.

• Grammar a word, phrase, clause, or sentence to which another word (esp. a following relative pronoun) refers.

• Logic the statement contained in the “if” clause of a conditional proposition.

• Mathematics the first term in a ratio.

I feel a short lesson on the prefix “ante-” and the root “cede” coming on. Especially since we start on a new vocabulary list next week. And since we’ll be revising a paper next week and editing it the following week, I’ll also design a few exercises on pronouns and antecedents:

• not using “it” with no clear antecedent (“In the book it says...” Just be concise and write, “The book says...”) 
• the problem of English not having a 3rd person singular non-gendered pronoun (“When a student doesn’t understand this, he makes many mistakes” implies this never happens to girls, but “When a student doesn’t understand this, they make many mistakes” shows lack of awareness of the need for pronoun/antecedent agreement.)

At the end of our discussion yesterday, one of the teachers expressed concern about possible confusion where the logic of math and humanities diverges: In math, one counter-example is all it takes to disprove an assertion, but in other disciplines, an exception proves the rule. Interesting thought. I have never had a student make that much connection between math and English. But if one ever does, I will throw a small party, and then think about how to answer.

One of the delights of teaching is introducing students to “the coolness of being educated,” as Nanci Smith told our staff a couple of years ago--the place where you find knowledge in one field enriching knowledge in another. 

Another delight is conspiring to help students learn.