Wednesday, February 27, 2008

Problems I Can't Fix in the Lecture Hall

Yesterday one of my students from the Calculus Circus came by my office hours. We were working on a problem of finding the critical points of f(x) = x3 + 3x2 - 45x + 10. He correctly found the derivative, f'(x) = 3x2 + 6x - 45. At my direction, he set it equal to zero: 3x2 + 6x - 45 = 0.

And then in an attempt to solve it, he tried the usual incorrect strategy selected by students who can't do algebra.

3x2 + 6x = 45

I stopped him before he factored out the x and asked, "What technique are you using to solve this equation?"

He said, "I don't know."

I explained that "I don't know" is usually unsuccessful in algebra and pointed out that this is a quadratic equation there are only two ways he should consider solving a quadratic equation: factoring or the quadratic formula.

He's probably going to go back to doing things the wrong way. But this is the type of misconception that I can't fix in a lecture hall.