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. 

How do I "grade labs"? In class.

I had students write lab reports for the first six or so years that I taught.  I worked hard on getting students out of their write-as-much-random-bullcrap-as-they-can-shovel report voice, and into writing clear, concise, and precise prose.  But it took enormous amounts of time and political capital to turn students from writing procedures like this

We came into lab today in order to accomplish the goal of discovering the effects of a pendulum.  First we found our partners, mine was Willie.  He and I cut a sting precisely to multiple lengths, measured precisely.  We tied a lab mass which is called Bob to our precisely cut string and let the mass go from rest at a carefully and precisely measured angle that was not too big for Mr. Jacobs to holler at us.  We recorded all our data carefully in our lab notebook.  I forgot to say we measured the period of the pendulum, too.

into writing this

A pendulum of various lengths l, measured with a meterstick, was released from rest at a small angle from the vertical.  The period T was measured with a stopwatch by timing ten back-and-forth cycles and dividing by ten. 

I mean, it seems so simple... but it's not.  Convincing just one student to adopt the simple but appropriate style in the latter paragraph took multiple re-writes, several writing conferences, and too often several arguments with students, advisors, and parents.  ("What do you mean, I failed, I wrote lots of words about a pendulum, didn't I?  That's not worth even a C?  My English teacher gives me a C for that!  This is entirely unfair.")

Multiply the time and mental effort investment by the 50 students in my classes, and, well... it just wasn't worth it.

So what do I do if not lab reports?

Nowadays, we do most lab analysis in class. The students collect data collectively, but they graph or re-graph that data individually - especially if they are linearizing a graph.  Next, they draw best-fit lines and take slopes using far-separated points on the best-fit lines that aren't data points.  This is all on a worksheet that looks like an AP Physics 1 free response problem - a grid for graphing is provided, and several questions are asked with space included for responses.

Students are asked to describe their procedure in "no more than three sentences", including what they measured and how they measured it.  They're asked to explain the physical meaning of the slope of the best-fit using direct reference to the y = mx + b equation of a line.  And then they are asked to determine that physical meaning, with an uncertainty.

Because we're doing this in class, students come to my desk after each part for me to check.  If it's right, they get a stamp and move on.  If it's wrong, they get immediate feedback and do it again right there - with 15 peers working on the same thing, so that they can ask questions and get help without trouble.

This is so, so much better than having students write lab reports or even answer lab questions at home.  See, they tend to do the work at home for the sake of getting done, right or wrong be danged.  (If you think the grade is what motivates the student, you're sorta wrong.  B or C students do the work as quickly as possible, right or wrong.  A students spend way too much time stressing about perfection, still getting the answers generally wrong, they just get angry and uptight about it.  And D or F students don't do the work at all.)

By working in class, everyone focuses not just on finishing, but on doing it right - in fact, they can't finish unless it's right.  And then if someone is slow, they can finish at home... but they've listened to me give feedback to all of their classmates, and they've had feedback themselves on the first part of the lab sheet, so they're more likely to get it right than if I had just sent everyone home to write a lab report.