First off, this isn't about the ubiquitous question every math teacher faces: "When are we ever gonna use this?" (The answer: You may not use an individual skill from class. Then again, you might. Few of us end up doing exactly what we thought we would as kids. More importantly, while learning the skills, you're developing the problem-solving, critical-thinking part of your brain, and THAT you will always need.)
With that out of the way, here's what it is about. Sometimes math teachers or textbooks make us do things in an overly demanding way, or using arbitrary rules. It's not always the times students think. There are good reasons for doing things the long way before learning shortcuts.
Here's one example where I think we get away from the spirit of mathematics. "Put your answer in the form of a fraction unless there are decimals in the original problem." Um, okay. Why?
What if I have a problem involving money, using only whole numbers initially, but the answer isn't a whole number? It only makes sense to give that answer in a decimal. That's an obvious case, but what about regular bare-numbers equations? What's so wrong with saying 0.5 instead of 1/2? They're equivalent.
So I've gone for a rule that's a little tougher. It means I have to watch for multiple correct answers when I grade work, and it means students actually have to think a little extra. I want the exact answer, not approximations, except when (a) the instructions say to round to a specific place value or (b) the context dictates an approximation is the only way it makes sense.
The reason? That's how answers get used in the real world. You use the form of the number that makes the most sense for the situation.
Kids need to know how to think, how to reason, how to work something out. When they get used to memorizing arbitrary rules ("Do it this way because that's how the teacher said to do it"), they don't delve in for deeper understanding.
That's what I think, anyway. Are there other rules your math teachers made you follow that didn't seem necessary to you?
1 comment:
I have 2, and they were both in college and involved proofs:
You MUST use the mathematical notation the teacher uses. I would be a better student if I were completely fluent in *all* the mathematical notations, I'm sure, but sadly, I'm not. I've had several teachers who thought they used the only CORRECT mathematical notation and (confusing to me) they were different from my last teacher who thought that.
Related: You must spit back the proofs on the test exactly the way the prof put them on the board in class. Another failing of mine. Can't do it. I think in tinier steps than the profs do. I never seem to know which steps (especially algebraic) I can skip and not lose a "-", etc., so I put several lines to their one.
JohannaQ
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