Monday, October 24, 2005

For the Calculus Midterm

Nothing yet to report from the quiz -- still grading. The irony here is that they did better on the implicit differentiation questions than the polar coordinates questions. I covered polar coordinates the first half of last week. Implicit differentiation was started on Thursday by a sub (I had, shocker, a dentist appointment) that the students described as "very confusing" and who "went too fast"; I recapped implicit differentiation on Friday to a less-than-full-house (the Big Game was Saturday). The take-away lesson for me is that the students will do more work outside of class when you make no sense.

The next exam is coming up on Friday, and it covers chapter 3 (ninety million ways of finding dy/dx). Despite my love for sneaky, conceptual questions, I am planning on making most of the exam fairly computational. My thought being that unless you can take derivatives quickly and accurately, you don't deserve an A in calculus. I can put the sneaky questions on the final.

Right now the plan on how to distinguish the A students from the B students will be the length of the exam: the A students will finish it, and the B students will run out of time. I haven't yet figured out where on the test to put the following problem: I'm going to ask them to find the 105th derivative of either y = sin x or of some 97th degree polynomial. If I make this the first question on the exam, the scores will be much lower than if I make this the last question on the exam.

What I've had the most trouble communicating to my students is that there is one more step to learning the material once they can do the calculutions easily -- that they need to reflect upon what they've learned and how it all fits together. Right now a lot of my students still see math as a catalog of types of problems, and they expect me to demonstrate one prototype problem of each possible kind that might appear on the exam. For them a chemistry application with the quotient rule is different from an economics application with the product rule is different from a biology application with the chain rule. I can't get them to think about the relationship between the various problems that we've done and to see that in all of these settings we're given a function involving variables and parameters and that their task is to identify which is which and to select and apply the correct method of differentiation.