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Random Thoughts on Apparently Silly Ways to Do Math

Mar 20, 2014   [permalink]

I just noticed on facebook another rant about wacky ways of doing math and parental frustration that kids get marked down for getting right answers but not "the right way" (whereas other kids get full credit for getting wrong answers but having tried "the right way").

I've no kids and never seen these wacky math methods before -- and, full disclosure, am a math/computer science Ph.D. / professor sort of person -- but I do understand why one could be graded on whether you understood the process and not just if you got the right answer.

In the real world, you get to decide which tools to use to solve a problem. But first, somebody has to teach all the different tools you can use.

A non-math example would be in real life, you get to choose between hammering nails to hold two boards together vs. using a screwdriver and screws vs. glue, etc. But someone has to first teach you the pros and cons of nails vs. screws vs. glue.

If someone is teaching you how to properly hammer a nail, and as "homework" says "nail these two boards together," and you come back having glued them, you may be failing to learn how to use the hammer correctly.

Or, another example might be, your car won't start. You can (a) realize it's not a blown engine but just a dead battery and get a jump start from a friendly passerby or (b) have your car towed to a dealership where you buy a new car because you ignorantly think yours is completely broken and let the nice car dealers talk you into a purchase. :) If you skipped the "lessons" in life about knowing when your battery is dead and what to do about it, you might make a very costly decision to buy a new car when you didn't need to. In that case, getting the "right answer" (i.e. driving home in a car) isn't the only thing that matters; understanding the method (how to jump start a car) does matter.

The purpose of a given math homework problem might be to understand a certain way of doing something, so that later in life you can decide to use that tool (or a different one).

I do think getting the right answer is also extremely important, and that needs to be stressed too. My hunch is teachers and kids don't necessarily understand that learning how to use a certain tool is sometimes the point of certain homework. (And sometimes getting the right answer using any tool is the goal of the homework.) I never learned this "number line" thing that this facebook post was about, part of something called the "common core", which I know nothing about. (No kids, remember?) :)

In analyzing this "number line" thingie, I can see how it works, and it turns out it's one way I've done math in my head for years. I use various methods in my head to do math, depending which I think will get me the answer the easiest. (I'm still slow at simple math. I probably should have tried harder in school to learn the methods.) :)

Maybe the homework/etc. needs to say, "The purpose of this question is to practice and understand the XYZ method" or "The purpose of this question is to get the right answer, use any method you want." Then both kid and parent would understand the motivation behind the question.

(There may also be a third purpose: Learning how to think. Learning the whole process of analyzing a problem, analyzing what tools you have to use, figuring out which approach best alone or in combination, etc.)

Getting the right answer is usually what matters in real life, but if you don't understand all the different tools at your disposal, and know how to reason things out, you may go through life trying to hit everything with a hammer. :)

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