A few weeks ago, I wrote an article for TheAtlantic.com describing some of the problems with how math is currently being taught. Specifically, some math programs strive to teach students to think like "little mathematicians" before giving them the analytic tools they need to actually solve problems.This may sound wildly off topic, but the struggle a third grader has "explaining" why two plus two equals four strikes me as being of a piece with the struggle basic writers have trouble writing a conclusion, especially a conclusion in a 5-paragraph essay, a highly compressed form that leaves you no room to "ask a rhetorical question" or "suggest future lines of inquiry" or "close with a quotation that captures your view" and the like.
Some of us had hoped the situation would improve this school year, as 45 states and the District Columbia adopted the new Common Core Standards. But here are two discouraging emails I received recently. The first was from a parent:
They implemented Common Core this year in our school system in Tennessee. I have a third grader who loved math and got A's in math until this year, where he struggles to get a C. He struggles with "explaining" how he got his answer after using "mental math." In fact, I had no idea how to explain it! It's math 2+2=4. I can't explain it, it just is.The second email came from a teacher in another state:
I am teaching the traditional algorithm this year to my third graders, but was told next year with Common Core I will not be allowed to. They should use mental math, and other strategies, to add. Crazy! I am so outraged that I have decided my child is NOT going to public schools until Common Core falls flat.
With the 5-paragraph essay, when you get to paragraph 5 you've said everything you were going to say (if you're lucky), but the teacher wants you to say something more.
One thing I always liked about William J. Kerrigan's X-1-2-3 approach is the fact that he didn't bother with introductions and conclusions. The introduction was 1 sentence - Sentence X - and the conclusion was 1 sentence, too. Kerrigan called the final sentence the "rounding off" sentence, as I recall. Really, that's all anyone should do in a very short paper; otherwise your introduction & conclusion - 2 paragraphs out of 5 - take up 40% of the essay.
I've had to abandon Kerrigan's one-sentence policy, though, since I'm pretty sure other instructors don't look kindly upon one-sentence introductions and conclusions, not that I've asked.
So my students, like the 3rd grader trying to explain 2+2, solve the problem they've been set and then struggle to say something else about the something they've just said.