Thursday, September 29, 2005

Calculus: More Fun than a Barrel of Monkeys

The next calculus exam is on Monday, and I've got a pretty good draft of it that I still need to proofread and check for length.* I don't need to think too much more about the difficulty, as it is (to my students) "too hard." Most of my students have taken calculus in high school; at present the class average is a D.

Not only is the class average a D, but over the past week or two, the derivative of the class average has been negative. Not enough data to know for sure, but I'm pretty sure that the second derivative is also negative.

How was I able to shave almost five percentage points off the class average in the time period of two quizzes? I keep asking questions like this:
The amount of fun F (measured in delight) in a barrel is a function of m the number of monkeys in the barrel, so F=f(m). What are the units on f'(m)? What does f'(m) measure? Write a sentence that describes the practical meaning of f'(12) = 7. Write a sentence that describes the practical meaning of f'(104) = -3.

My students are masters at taking derivatives of functions of the form \sum a_i x^{n_i}** and other algorithmic tasks. Not so good with the thinking stuff.

So I told the class yesterday (and posted a note to such effect on the internet -- not just here, but on a page that my students have all been told about***) that almost a fifth of the points on the exam will be interpretation problems like these.

And so, dear reader, you have probably already guessed what that means: Student responses should appear in this space by Tuesday.

*Could I write a screed about how the graphing calculator makes it so that it takes less material to make the exam "too long"? Yes, I could.

**Well, they would be if they could keep straight the difference between "is zero," "is unchanged," and "isn't defined." Oooh, that pesky contant term.

***Why do I worry about my students reading my blog? They don't even check the class webpage (whose URL appears on the first page of the syllabus) that contains a very specific list of what will be on the exam as well as solutions to the problem sets. Sometimes I even post the solutions before the problem set is due.