"Hey, Mr. Lipshutz, I need help! I spent two hours last night on this problem, and I still can't match the book's answer. It says the ball goes 12 m/s, but I keep getting 1.2 m/s."
What do you say, Mr. Lipshutz?
"Let me see your work, Andy. Looks like you've used a correct approach -- it's a projectile, so you made two kinematics charts. Your horizontal and vertical accelerations are correct, and you added the velocity components properly using pythagoras. Can't see a problem, so it must be a just a math error; don't worry about it. Good job. See you in class."
But... but... but... but Andy spent hours on that problem trying to find his mistake, and you shrugged it off as "just" a math error. What kind of monster are you? Don't you value your student's time and effort?
Um, yes, yes I do. In fact, that's precisely why I won't go through his algebra line-by-line to waste even MORE time trying to find a trivial error.
Come on, man. Would it have killed you to look through his algebra for a moment, or even to have gone through your own solution with him? It would have made him feel better.
The class reacts viscerally to the teacher's actions, his words, even his moods. Had I validated Andy's hyper-concern about the correct answer, then every other student would have been similarly focused on the final answer to the exclusion of the correct physics. As students observe and hear about my reaction to Andy, they will gradually realize that the process of physics problem solving is about so much more than the correct answer.
His friends might TELL Andy, "Geez, Mr. Lipshutz sure was a jerk, he should've helped you." However, they might be THINKING, "Wow, I hate how Andy's so obsessive about getting every last little thing right. But I don't have to be that way -- Mr. Lipshutz just said so!"
You say that, but I bet Andy still lost points for failing to get the right answer.
Because I want to make my grading reflective of my expectations, a minor math error on a problem set loses only a minor fraction of the available points. On an AP exam, a correct solution with a trivial math error is going to earn something like 13-15 of 15 points; my homework is graded similarly.
It might be eye-opening for Nick to see that he got the same score as Andy, even though he only spent 20 minutes on the problem. Perhaps he and others might see that obsessive drama isn't worth the investment of time and emotion.
So, you're just going to make Andy lose points on the problem without helping him? That is awfully punitive for what you're calling a "trivial" error. You know, he's trying to get into the Naval Academy, and his grades are really important to him right now. I'd expect that a teacher would support that goal.
First of all, students should be learning physics, not gaming their grade. The above statement marginalizes me as a tool, one whose use is merely to wedge Andy into a particular college. Furthermore, I resent the implication that my refusal to finish Andy's homework for him equates to lack of support for his academic goals. If a few points on a single physics homework assignment truly will make the difference between admission or rejection to a particular institution, Andy should be considering alternate college plans.
And finally, it is in fact my job to help my students differentiate between trivial and substantial errors in problem solving. Imagine that Andy had gotten closer to the right answer, but that he added vertical and horizontal velocities algebraically rather than with the pythagorean theorem. That would have been bad physics, regardless of the final answer, and I would have helped him understand the correct way of adding vector components. I am teaching Andy the difference between correct and fallacious physics, not correct and incorrect answers. That's what I'm paid to do.
The whole point is, I care about Andy's progress as a physics student, I want Andy to be successful in my course as well as in all of his classes. I also want all my other students to be successful. By communicating in every way that physics problem solving is not meant to be an onerous multi-hour task suited only to anal-compulsive perfectionists, I make the class as a whole feel better about their work.
Minimize drama. From the beginning, teach your students to "let it go."