AP Physics C in April - don't worry about math!

I'm working on the final set of test corrections with my Physics C - mechanics independent study student.  This person did well on the test - earned a 4 on a typical AP scale.  But that's only 50-65% of the available points, so there are plenty of items to correct.  

This student had AP Physics 1 with me two years ago.  He is in AP Calculus BC.  

In the first part of the year, I had him focus on the mathematics that overlay the concepts he learned in Physics 1.  He watched all the "AP Daily" videos for Physics C, he practiced new mathematical techniques like integration to find displacement/work/center-of-mass-location/rotational inertia.  He's got those techniques down, now - at least, he'll do the math right most of the time if he sets up the problem right.

And there's what we're concentrating on now - setting up the problem right.

AP Physics C students usually want to do math.  They plug into equations, manipulate, see if the answer is right... and if not, they try a new approach, until (a) they get what they think is the right answer, or (b) steam comes out of multiple orifices.  Neither result is useful.

I don't want to see much math right now, for these corrections.  I want to see facts and concepts.  How should this problem be approached?  How do you know the problem should be approached that way?

For example: I don't want to see plugging and chugging into energy or momentum equations until I see a clear statement of what is conserved and why.  How do we know?:

Mechanical energy is conserved when there is no net work done by external forces.  (And when there’s no internal energy conversion.)

Angular momentum is conserved when no net external torque acts. 

Momentum in a direction is conserved when no net external force acts in that direction.

I need to see these facts, along with a statement as to why they apply.  Then I need to see that they used the right formulas for each term - including direction of momentum - and/or that they made a correct energy bar chart.  That's it.  The actual mathematics to finish the problem isn't relevant right now.

As this student has brought me corrections, I've deliberately checked off a few which were set up correctly, but led to the wrong answer due to a math error.  And, I've send him back to try again for a few corrections in which he got the right answer, but didn't communicate the starting point clearly.

All this works, except when he notices that his answer is wrong, but I tell him the setup is correct.  "I've got to get it right!  It's going to bug me forever if I don't!"  I totally get it!  But, trying to find a math mistake is not a productive use of time.  Usually the issue here is something like a squared term not being copied correctly from step to step in the mathematics; or, accidentally canceling a 1/2 in most but not all terms. 

These little math mistakes are difficult to find in a half-page worth of work; but, given a new problem from scratch, this student - or any competent AP Physics C student - would NOT generally make such a mistake!  Rather than spend 20 minutes doing and redoing a problem until the math works out, why not move on to the next one?  

Most of the errors that students make come from starting with the wrong approach.  Most of the time, the right approach leads to the right answer.  So in our limited review time, we're going to focus on the right approach.  We'll let the chips fall where they may on whether the math gets done right.