I've been thinking recently about written solutions to problems. Between the revision of the 5 Steps to a 5 book that's coming out in 12 months, an editing assignment, the recent AP exam, and my own exams, I've been looking at a whole lot of text that tries to explain the answers to problems.
I've done a good bit of problem writing*, and I've discussed problem writing on this blog before. But I haven't discussed much about writing solutions. Now, I don't necessarily recommend you have a written solution available to every problem you assign. But you will, at some point, need to write out the solution to a problem you posed. Here are three important pieces of advice:
* When you write problems for your class, can you PLEASE get rid of the subjunctive wherever possible? Say, "Determine the weight of a 3 kg wooden mass," not "If a block of wood has mass 3 kg, what is its weight?" I thank you in advance.
(1) Use everyday language, words and sentences that you might reasonably expect an intelligent novice to understand. When explaining the meaning of variables in applying Torricelli's theorem, why say "...where v is the horizontal velocity of efflux from the fluid containment system, d is the depth of interest, and g is the local gravitational field in SI units"? Use a diagram, and say "v is the speed of the water, d is the water's depth." If you need to define g at this point in the course, you've got trouble.
Similarly, try to avoid jargon. I know that the θ term in magnetic flux = BA cos θ is difficult to define. But it's worse than useless to start the explanation with "Let n-hat represent the outward unit normal vector to a given face of the box..." Rather, say something like "the flux is biggest when the magnetic field lines penetrate directly into the box face, and zero when the field lines point along the face."
Certainly don't sacrifice the accuracy of a solution. I ain't sayin' that. Remember your audience -- you're not writing for your Ph.D. advisor, you're writing for a novice. Make it short, sweet, and readable.
(2) Don't add extraneous information, however interesting that information is to you or to your favorite professor. Consider writing the solution to, "Explain what it means to take the component of a vector." After giving a basic definition, why tell the student that "it is customary to resolve vectors into components on mutually orthogonal axes"? You just totally lost your audience, 'cause (a) any student who needs to be answering this kind of basic question would not consider an option other than mutually orthogonal axes, much like cows generally don't consider the benefits of stick over automatic shift; and (b) Your readers don't know what "mutually orthogonal" means. Trust me. And if they do, they probably belong in a different class.
Other examples: If your class only studies inviscid fluids, don't add asides about what would happen if viscosity weren't negligible; if you're only considering spherical, not elliptical, orbits, then don't make a throwaway comment in a solution about how an elliptical orbit would behave.
I know some readers will make the (completely reasonable) point that your top students might be very interested in these asides, and that you don't ever want to quelch their curiosity. Yes, I agree. Answer those students' questions, turn them on to exciting resources in their textbook and online... but don't confuse the whole class in a written solution in anticipation of a possible question from your smartest student.
(3) Use consistent, clear, common-sense notation. I don't personally care whether you use d, x, or s for distance. Just be consistent -- don't mix these variables from one problem to the next. It won't confuse you, because you're a strong, experienced physicist who recognizes that the notational label is subordinate to the meaning of the physical quantity represented. No, it will confuse most of your students, who sit there saying, "what is s? I thought we were looking for the distance the particle traveled."
You'll have to make some judgement calls -- do you use T for the period of an orbit or a pendulum, like your textbook does? Or is that too easy to confuse with T for tension? Maybe use P for period? Either way, just be clear and consistent.
However, please please PLEASE don't use ν for frequency.* Yes, I know that many textbooks write E = hν and v = λν. Apparently, according to my colleague, the AP chemistry exam still uses this notation. The AP physics exam used "nu" until about 10 years ago.
* Every one of you just read that as "vee" until you got further in the sentence. Right? Right. It's a Greek nu, I swear. And "nu" is a wonderful word to know in scrabble.
Just replace the "nu" with an f for frequency. You'll not have any notational contradictions, and your students will not be confused. If your textbook uses the nu, tell them to ignore it and use f. Everyone will be happier.