As a student I was very careful with my calculations. I would hunt down every negative sign and make sure I didn't make any mistakes when doing homework and tests. As a teacher I started out trying to get my students to do the same thing. I would get crabby when noticing students trying to sneak in negative signs towards the end of a derivation instead of having them correct all along. I found, however, that I wasn't teaching well when I did this. This post is about how I teach now, specifically with those pesky negative signs.
For me, it's all about getting my students to trust their gut. I figure if it's not in their gut, they haven't learned it. So when I teach something with negative signs involved, I make a special effort to at least make sure the signs are in their gut, if not all the rest. Here's an example: when deriving the potential formula for charged particles, you first have to teach about fields (possible negative signs), then about potential energy (more signs: should I integrate from infinity, is it me doing the work, is it the field doing the work?), then about potential (even more signs). Now I just have students do the integral and separately teach about whether the result should be positive or negative. I can be heard saying "don't write any signs down, just do the calculation and then ask yourself whether it should be positive or negative."
Knowing that like charges hate each other is often enough to help students get their signs right (though admittedly this is easier for potential energy than potential). I've noticed that my students can get that concept pretty quickly but sometimes they'll still panic about how to go about doing a problem. When they do I'll ask something like "does this charge want to be here?" or "would you have to move that charge or would it move that way on its own" and it's funny how often their confused faces turn to confident statements.
Charged particles are just one place where I do it (and have done it this semester) but I do the same thing in many situations. I'd be interested to hear other's thoughts on this.
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Oooh. I like this. As one who can't keep his negative signs straight from beginning to end, this will make me look like less of a fool during derivations. And I just hate the empty silence while we stare at the board wondering what went wrong. Thanks for sharing!
ReplyDeleteBut now I just realized...what if the negative sign changes the algebra? In other words, if the negative sign is left out, two terms are added together, but if the negative is put in, then those same two terms would now be subtracted and yield a different answer.
ReplyDeletethat's a great point. If there's adding/subtracting involved then this 'gut' approach only works term by term. In other words you have to decide whether the term in questions should increase or decrease the answer.
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