When meeting with a class at the beginning of any given year I’m almost always asked in some form, “How much work do we need to show?” Generally students seem to want this question answered so they aren’t doing more work than necessary, which mathematically is a pretty good idea. My answer is almost invariably, “Show enough work that the person one grade or one math class lower than you would understand your work.” I know it’s a little vague, but I want to stay away from rigidity as much as possible. If I make a list of my expectations then I have kids focusing on a list of specifications rather than on mathematics. Regardless, the question focuses on the Content of the student’s work, not on how it’s presented. This year I’ve decided to get a bit clearer on my content expectations while not getting too rigid. I am now telling my students that their content should be…
Correct is pretty obvious. I’m looking for truth. Clarity is as much if not more presentation oriented, but I believe deserves a place in the content section. If it isn’t clear (aka, I can’t read it), then I can’t get at the truth/correctness of it. Concise needs a little more explanation to get at my meaning.
Concise doesn’t always mean good. If I present a lecture to a class on Albert Einstein and simply say, “Albert Einstein was a man. Albert Einstein frequently wore sweaters. Albert Einstein was a physicist.” In this lecture, my information was correct, clear and concise, but I completely missed the point. Mathematically, being concise ought to mean…
- No extraneous work (don’t distract the reader)
- Give “elegant” solutions (see ‘no extraneous work’)
I plan to expand on simplify in another post. So this is what I have for general content requirements. I should expect to see Truth, Beauty and Goodness (Correct, Clear and Concise) on every homework paper, every quiz, every test and every response you give orally in class. By the way, my students should expect the same from me. It’s a goal, but also a work in progress. I’d love your comments.