"The answer is D because..."

Test corrections are the most valuable and productive use of my students' time I can think of.  Nowadays, I don't even return graded tests; rather, I give each student a blank copy of the test, along with notation about which questions they didn't earn full credit on.  They can see the original graded test (and their grade) only after getting all corrections checked off.

But test corrections are only useful if students explain their understanding thoroughly and correctly.

The first time we do test corrections, a few clueless (or intellectually lazy) students just write "I put C, but now I know the answer is D."  Um, really?  You call that a correction?  How does that help you understand the original problem?  More to the point, how does that convince *me* that you understand the original problem?  Begone, foul dwimmerlaik, and bear thy feeble "correction" with thee to the houses of lamentation.

Of course, there are teachers in other subjects who accept such baloney as a "correction."  Which is why many of us get pushback when we give credit for test corrections - parents and administrators and colleagues default to "oh, whoops, the answer was B, I've learned that now" in their own understanding of what "test corrections" mean.  No.  Duh.  They're much more than that.

However.  Even though most students and most physics teachers recognize that justification of the correct answer is required... it's still all too easy to accept a correction that doesn't truly show understanding.

A block of mass m is not touching a surface.  You pull up on the block with a tension T which is bigger than the weight of the block.  Which way is the block moving?

(A) down

(B) up

(C) the block can not move

(D) the block could be moving up or down.

"The answer is D because the net force is upward here."  How does this show understanding?  I mean, the net force is indeed upward.  And the answer is indeed D.  But has this student shown their personal understanding?  Or have they just quoted the answer their friend gave them with a vague handwave at a physics term?  Thing is, I don't know.  And so a better correction is necessary.

"The answer is D because the object could be slowing down or speeding up."  Well, this is also a true statement that doesn't show understanding.  How do you know the object could be speeding up or slowing down?  And what does that have to do with the direction of motion?

At this point, a student is likely to be getting frustrated with me.  They keep saying correct things, and I keep sending them back to the dungeons!  What do they have to do to get a correction checked off around here?!?

Answer: They have to start with a fact of physics.  

Legitimate starting points for all justifications include facts from our fact sheet (like "acceleration is defined as the change in speed every second"), problem solving procedures we've learned (like 1. free body diagram, 2. components, 3. write newton's second law in each direction), or equations (like "x = vot + 1/2at^2).  

I think we should all train our students that any other starting point at all, especially "The answer is D because..." is incorrect on its face.

"When an object speeds up, acceleration is in the direction of motion; when an object slows down, acceleration is opposite the direction of motion.  [These are facts from our fact sheet.]  Here the acceleration is upward, because the problem says the unbalanced force is upward, and acceleration is in the direction of the unbalanced force.  So the object could be moving up and speeding up, or moving down and slowing down.  D."

There's no way this student doesn't understand the problem.  There's no way that this student is merely parroting what a friend told them.  (At least, if they've obeyed the five-foot rule.  A friend might have told them what to do, but the student must have phrased the answer in their own words because they can't just copy.  And the five-foot rule is easy-peasy to enforce in class.)

Most importantly, this student has corrected a misconception. They likely originally said the object was moving upward because the unbalanced force was upward.  By quoting the facts, they are forced to confront how their intuition about how the world works is at odds with how physics actually works.