Proofs (and writing) are difficult

The moment I started to have success helping student really learn how to write proof in geometry was the moment I realized that”The Proof” is nothing more than a persuasive essay converted to math class. It’s disciplinary literacy. And thinking of them as mathy-style essays can help us isolate some of the reasons the students struggle with proof in general. My experience leads me to think that many of the struggles are the same the ones the students experience with writing outside of math class. They don’t understand the structure, they don’t appreciate the value of honoring their target audience, and they don’t understand the content well enough.

Luckily for us, the ELA department has often hit those three points really hard. As math teachers, we just need to help the students bridge the gap.

What’s the structure to an essay? Thesis, supporting paragraphs, conclusion. Or, in math, “Given angle a is congruent to b, I’ll prove that segment a is congruent to segment b. Here’s the evidence I’m using to support my claim. And here’s what I just proved.”

Who’s the target audience? In math, it’s often either someone who doesn’t understand or someone who disagrees with you. That explains why you need to back up each statement with theorem, definition, or previously proven statement. Take nothing for granted or you’ll lose your reader.

And as for content? Well, have you ever read an essay from someone who plain ol’ doesn’t know what they are talking about? The best structure in the world isn’t going to save them if they can’t define the words they are trying to use.

So, when it comes to proof-writing, I think we math teachers need to appreciate that “writing” really is at the core of it, and the better we make that connection explicit to our proof-learning students, the more likely they are to be successful. And perhaps there’s a role for some meaning collaboration between high school math and ELA departments.

And with that, enjoy the latest “Instructional Tech in Under 3 Minutes” discussing, of all things, writing.

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