Tuesday, October 4, 2011

Let me tell you about units...

Sometimes students think that units are for me.  I get all excited about them writing down and checking their units.  "It's a chance to catch your mistakes," I say.  "It's a chance to really know what the units in the answer are," I say. "It can tell you how to do the problem!" I exclaim.  "Come out to the coast, we'll get together, have a few laughs," I say (wait, that wasn't me).

Anyway, the students that see it, buy it, or try it... succeed.  Those that refuse... generally struggle (certainly, they struggle more than they need to).

I get that you might (should?) need more than my word to buy into something.  That's where the logical argument and all of the times that we've seen it work in HW and class should come in.  If that didn't do it for you, then how about this?

On our first assessment covering amplitude of oscillations, I asked this question, after showing a video of a lab cart oscillating with the help of two horizontal springs.  They had already determined the amplitude at my request, and had stopwatches available.

     "How far would the cart travel in a year, if its amplitude remained constant?"

Yes, it's not terribly 'real world,' because the cart certainly won't go that long, with all of those juicy damping forces around.  That's OK - we're just stretching our legs a bit.

What I like about this is that it connects period/frequency and amplitude.  That, and we'd never done anything like it before.  There's always something new on a physics test, but you can apply old concepts to figure it out.  That's just... how physics works.  If you're waiting for me to list all of the "types of problems," then you'll be waiting a long time.  The concepts that we apply to this multitude?  Well, you can list that pretty easily (it's the list of standards for the term!).

Anyway, here's where the units hit the road.  Folks that have taken my advice and really gotten into checking their units had a real advantage:

     Not only did unit-checkers get all of the more familiar applications of T, f, and A correct, they also all got this entirely new question correct!

Yeah, all of them.  Here's a chart showing how folks that check their units did on the question, as opposed to those that didn't:
I'm not really sure how to say it more clearly than that.


  1. I like the problem. I also like the data, but I worry about correlation vs. causation here.

    I can easily see how students who understand these concepts well enough to solve complex problems are also the students who can see and interpret these quantities in terms of their units (and use units as a check on their work). I am weary of any interpretation of this data to mean that the students who don't understand the concepts or who can't solve problems should start focusing all their efforts on understanding units.

    To me the data points to a question, not an answer. So I guess, I'm curious: what it is that you are saying is clearly said by the data.

  2. I find the same correlation when students draw a velocity time graph, motion map, free body diagram, etc. to solve a problem. I wonder about which causes which: kids who can draw the diagram can thus do the problem, or kids that can do the problem are able to draw the diagram.

  3. I wouldn't say that checking the units would be the only skill necessary to get a problem like this correct.

    However, it's close to the only skill that you need to figure out if your answer is wrong (in a problem like this).

    My main message here to kids is that some fraction of the students that were in the "check units, correct answer" column were originally in the "check units, incorrect answer" column, but the act of checking was the signal that they had more work to do.

    Whether it's units or special cases or variable dependencies, having signals to tell you that there's more work to be done is half the battle.

    It's not that experienced, skillful problem solvers never make mistakes - it's that those mistakes were private, because they caught them before showing that answer to anyone.

    There's probably also a fraction here that actually used the units to determine the correct way to combine the data (rather than intuiting and checking); that's a good message, too, though it's confined to a relatively slim class of relatively shallow problems.


    What you say here about the nature of expertise is profound, and I thank you for sharing what you see in that data and what you tell your kids about it. I usually take this one step farther and say that those who have learned to make more mistakes privately have had lots of prior opportunities to make those same mistakes publicly.