It's not about the answer!

I grade assignments regularly... but really, I just look and slap a number on.  What matters to students and me isn't the grade, but whether the student used the correct method.  And if they didn't use the correct method, they need to redo the problem the right way.

Last week I assigned the classic elevator problem: A 50 kg person stands on a scale in an elevator, moving up and slowing down with an acceleration of 2 m/s/s.  What's the reading in a scale?

How I ask students to solve: 
1. Draw the free body, which includes the force of the scale Fs up, the force of the earth mg down.
2. Acceleration is downward (slowing down, acceleration opposite of motion), so write mg - Fs = ma
3. Solve algebraically for Fs to get 400 N.

How a bunch of my students solved:
1. Draw the free body, which includes the force of the scale Fs up, the force of the earth mg down.
2. N2L says a = Fnet/m.  So (2) = Fnet / (50), making Fnet = 100 N.*
3. Now 500 N - 100 N = 400 N.

* Well, as you'd expect, half the class just said "Fnet = 100."  Sigh.

That's the right answer!  And the method couldn't have been much wronger.

No, Greg, it's totally correct to subtract the net force from the weight here to find the force of the scale!  And I got the right answer!  How dare you count that "wrong!"  Show me the mistake!  Don't take off points because I used an alternate approach!

Um, back off there, student who's been in physics class all of a month, or parent or colleague who is suddenly an expert in physics pedagogy.  We are NOT going to talk about points, we are going to be sure that each student has communicated an understanding of the problem.

Yes, you must use the methods taught in class.  In English class, if you're given instructions about how to write a new style of essay, and you decide you will write something completely different from the assignment... that's okay now?  So why is it okay here in physics class?  Physics is not about getting the answer, it's about communicating an understanding of how the natural world works. 

I brought in the students who had solved using the "wrong" method.  I made them do the problem again using the correct approach.

Think I'm being too harsh?  Here's what I discovered.  I mean, I already knew these things, but they were exposed to the students in the process of redoing this problem the right way:

* Most of the students thought they were solving for mg, not the force of the scale.  When they wrote "500 N - 100 N = 400 N," they meant that the scale reading minus the net force was equal to the "new weight".

* Most had no clue why they were subtracting 500 N - 100 N.  Once I made them redo this problem the right way, I had them do the next problem as well... where the elevator was moving downward and speeding up with 2 m/s/s of acceleration.  For this problem, these folks had added 500 N + 100 N!  Now they found out for themselves that their incorrect method had actually obtained an incorrect answer - the acceleration is still downward here, so the solution should be exactly the same as in the previous problem! 

* Turns out, as I suspected: One of the students who had taken physics at a different school, and sounds smart and assertive, had told the group how to solve.  Most of the class had blindly followed.  No worries, collaboration like this is an important part of physics learning.  And, learning that the smart kid isn't always right, that it's important to argue with the smart kid, is an even more important part of physics learning.*

* For the smart kid, the most important part is finding out that even they have to communicate carefully using the methods taught in class.

Today's moral: When you're "grading" assignments, don't just look for the answer - look for one component of the correct method.  In this case, I looked for a correct free body and "mg - Fs = ma".  I didn't write any comments one way or another, because no one would have read them.  I just made anyone who didn't write this statement redo the problem.