Reporting from the AP reading here in Kansas City, where I've discovered that Jack Stack barbecue is excellent, but still no match for Gates. And, where I've been immersed for days now training people on the rubric for the 2017 AP Physics 1 exam problem 3.
Based on my experience here, I think it's worth a reminder to teachers about the expectations for "deriving" an equation on an exam.
Introductory physics is all about communication of ideas, and not as much about getting the One True Answer to a problem. Physics is not a math class.
Students in my class may whine (early on, at least) about not getting full credit for a poorly presented problem that nonetheless includes the correct answer. Okay, so your English teacher requests an essay with textual evidence analyzing Shakespeare's characterization of the Romeo/Juliet relationship. Your entire essay: "He loves her." You earn a failing grade, of course. How effective or intellectually honest do you think it would be to whine that your essay deserves an A because the answer is right? I mean, the answer is in fact right...
A derivation, like any physics problem, is an exercise in communication -- but a derivation requires communication primarily in mathematics. Just because the answer is right, just because a student knows in her head what mathematical steps she intends to take, that doesn't mean the derivation has served its purpose.
So what SHOULD we expect from students on derivations?
1. Start from first principles, and explain what first principles you're using. That means something from a "facts of physics" list: Newton's laws, Kirchoff's laws, conservation principles, the definition of acceleration or impulse or power... most anything on the AP equation sheet or on my fact sheet will work.
2. Communicate the reasoning for each step. I think words are best here -- an annotated derivation can hardly fail to earn credit where correct. Try circling terms and explaining what they mean. Try telling the reader why you've substituted various terms into the equation you began with.
3. Show enough detail that a strong physics student at another school can understand without asking for clarification. The audience should NOT be the expert physicist. I personally don't need to derive an expression for the acceleration of a three-body system connected over a pulley, because I've done so many of those problems that I can write the answer based on memory and instinct. My students, though... they need to start with Newton's second law for the system, explaining what expression is used for each term and why that expression is relevant.
4. Use algebra to communicate, not to solve. I often see students take three steps merely to rearrange terms in an expression, using annotations like "commutative property" and "divide both sides by m." Assume the audience knows how to do math. Use the way the math is laid out to highlight reasoning. For example, if you have energy terms before and after a collision, write all terms clearly in a single line, with before the collision left of the = sign. Label each term with a circle and a couple of words.
I'm sure readers - both blog readers and AP Readers - may have some further thoughts. Please post in the comments.