Units: Not Just Window Dressing

There are lots of things to try to get students to do with units.  High on the list tend to be:

• Write them down when recording data.  This one can be an epic fail: ever take a bunch of data in the lab, go home to try to analyze it, and have no idea if you measured A or mA?
• Write them down on answers.  Certainly, you won't go on a run with me if I tell you that we're going "30."  I could be a crazy ultramarathoner; who knows, if I don't give you a unit there?
• Write them down in the work leading up to that answer.

Now this last one is where the rubber meets the road.  The previous reasons are pretty straightforward, but this is a reason both subtle and deep.  There are a variety of advantages that keeping track of these units during the process give you:

• You don't *really* know what the units on your answer are if you haven't checked the cancellation of the units in the work leading up to it - you're just assuming that you won't end up with ftlb/weeksecond or some such hogwash
• Checking those units is just another chance for you to find your mistakes.  If your units aren't just silly (ftlb/week, for a problem about power), but instead wrong (ftlb/weeksecond for the same problem), then it's not worth your time getting out your calculator - it's wrong.  The converse isn't true (units working does not imply a correct answer), but this can catch quite a few mistakes.
• Paying attention to the units, and the answer's size in general, gives you a real leg up in terms of catching other kinds of mistakes; if you get 700 million meters per second for the speed of the car (or anything!), that's a pretty good hint that you did something wrong.  

A lot of these issues about carrying units around everywhere are geared towards mistakes.  If you're in a point-crazy lust for a correct answer, then there's real psychological incentive not to check your units!  Any sort of check that you do on your answer could reveal that it's wrong (*gasp*)!  This isn't a terribly rational motivator, because it gets in the way of you getting more correct answers, but for a kid afraid of math/science, it can be real.

All of this is predicated on the idea that finding mistakes is good, because it shows you where the work is needed.  That doesn't come automatically; it requires a lot of re-education of your kids.  We want to find their mistakes, because it shows us where there's a chance for improvement.  That's why the homework is so hard! :) 

If we have the proper incentives in place (no immutable points for initial quizzes, labs, HW, etc.) and a focus on a better goal (real understanding - knowing that it won't be complete right away, but that finding the issues will result in a better knowledge down the road), then maybe kids can buy into really using units, and not just write them because I told them to.