Public health initiatives are perhaps the greatest ever victory for the marriage between civic policy and science. We don't cure polio -- we get vaccinated against polio. So, so many diseases have been wiped out. Many chronic conditions have been mitigated by not just vaccinations, but also by initiatives we take for granted such as employee hand washing and "no shirt, no shoes, no service."
Into this atmosphere dives the physics teacher, someone who stands directly on the boundary between civic policy (in the form of the education establishment) and science. It's not a surprise that we instinctively take our philosophy from that of public health, that an ounce of prevention is worth a pound of cure. We forewarn our students about common mistakes. We take pains in our presentations and instructions to minimize incorrect answers on the problems we assign. We'd rather students listen to us and avoid mistakes rather than submit silly wrong answers on homework or tests.
Problem is, when it comes to understanding physics, that philosophy is dead wrong.
Look, I know you don't want your students to mess up. So you give them hints and warnings ahead of time. "Be sure not to use kinematics when the acceleration isn't constant.", you say.
How effective have those warnings been? Evaluate objectively. On one hand, I expect that you've thrown up your hands and screamed at the students* who used kinematics to solve for the maximum speed of an object on a spring, despite your advice. "They didn't listen," you'd say. Possibly, possibly... it's equally likely that they did listen but didn't make the connection between your advice and the actual problem solving process when the moment was right.
* Or at least at their homework papers, which can no more hear your wails than can the Cincinnati Bengals coaching staff when I wail at the television.
Either way, the class time you took attempting to prevent these canonical mistakes has been wasted. So has the political capital you used in insisting that your students sit and pay attention to your warnings. (Don't underestimate the concept of "political capital." You can only demand so much attention from your students; use it wisely.)
What if, instead of trying to prevent the mistake, you allow your students to make a mistake? What if you practically set them up to make a canonical mistake? Then, when they screw up, they have the context for preventing future occurrences of the same mistake. They used kinematics for non-constant acceleration; they got a wrong answer and lost points. NOW, you can explain why kinematics doesn't work, that the work-energy theorem is the way to go. NOW your students will listen, because they have a personal and immediate interest in figuring out how to rectify the mistake they just made. Next time they're likely to remember both the incorrect and correct approach. That's a natural learning process.
"Oh, that's cruel, Greg," say some readers. "We shouldn't punish our students by setting them up to lose points. Possibly a couple of students would have avoided the mistake if you had gone over this sort of question before assigning it.
Huh? I'll leave the emotionally loaded and incorrect language of "punish" for another rant.
My approach makes perfect sense if you're taking a long term view of physics class. Saving a student a couple of points on this problem set is insignificant compared to building a lasting understanding of physics concepts such that he can perform well on the AP exam, the course final, on his college physics tests, in his job. Setting a student up to make mistakes, which in turn create contextual learning opportunities, will save the class numerous lost points in far higher-stakes situations.
And finally, consider those couple of students who got the answer right initially due to your warning. Ask them, "how did you know that you should use energy methods rather than kinematics?" The answer is very likely to be, "because you warned us about this issue in class yesterday." How does that build understanding? You want them to build good problem solving habits and skills. In introductory mechanics, those habits include, "check whether acceleration is constant when deciding on an approach." Those habits do NOT include, "get my teacher to tell me how to solve this problem."
In physics teaching, an ounce of cure is worth a pound of prevention.