Does this make sense to you?
by John Pearson
One of my biggest frustrations as a teacher is the fact that it is so difficult to teach logic and sense. It's always an epic struggle to get my kids to look at their answers and ask themselves if they make sense.
For instance, I will peek over a student's shoulder at his paper and see that he has added 11 and 9 and arrived at 101. It's a simple enough (though aggravating) mistake – he put the 9 in the tens place instead of the ones place – but it should also be easily spotted. Instead, though, this student is happily working on the next problem, never having even glanced at his answer once he wrote it. If I ask the student if his answer makes sense, he can usually tell me that it doesn't, it's far too big, but that's only if I point it out to him.
When we do word problems in class, I always make sure that our final step is rereading the story and seeing if our answer makes sense. Usually, this is streamlined to, "Should our answer be bigger or smaller than what we started with?"
With me leading the discussion and talking the kids through it, there are rarely any hang-ups. "OK, Tommy had 30 marbles and he bought 20 more at the store. Does he have a BIGGER number of marbles now or a SMALLER number of marbles now?" Of course, all the kids scream, "BIGGER!" Though on their own, half of them subtracted the numbers and got 10.
I can enforce my rule of "show your work" because I can visually see whether or not they have drawn a picture, written an equation, and included a unit in their answer. But I haven't yet discovered a way to force them to see if their answer is reasonable.
All I can do is model it, every time we go over a problem in class. Make sure that we don't move on until we've completed that final step – Does our answer make sense or not?
When a child does finally understand the importance and can articulate why an answer makes sense, it's a monumental breakthrough. There have been times when I've almost cried when one of my students explains, "Carla has 15 crayons, and Gracie has 8, and they are asking how many more crayons Carla has. If you add, you get 23, but how could she have 23 MORE crayons when she only has 15?? The answer has to be smaller than 15!"
YES!! She truly gets it!
Of course, for every one student who gets it, I still have five students who rationalize their answer to that same problem by reasoning, "My answer of 23 crayons does make sense because I added 15 plus 8, and when you add, you have to get a bigger number."
Touché.
Then there are always the kids who aren't really interested in logically assessing their answer, they just want to be the first and loudest to respond to my question, right or wrong. If I ask, "If Kevin has 45 baseball cards, could he give 25 to Adam?" these kids shout, "NOOOOO!!” with an almost righteous anger, as if I had asked if they wanted brussels sprouts for dessert.
I continue to work with them on this extremely difficult topic, but for now the conclusion is an easy one.
My kids just don't make sense.
John Pearson is a third-grade math and science teacher in Dallas, Texas. He has degrees in mechanical engineering from Duke University and Texas A&M, so most consider his math abilities adequate enough to teach nine-year olds. He is also the author of Learn Me Good (Lulu, 2006), a funny, fictionalized account of his first year in education. Read more at learnmegood2.blogspot.com
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Other readers' comments on this article:
To quote Spock: "logical"
Posted by Heather Wolpert-Gawron on Apr 22, 2008 10:12 pm