Long Term Goals

Over at Number 2 Pencil there's been a bunch of discussion about Jeb Bush being asked about an FCAT question. They've mulled over the content of the question and the skills needed to answer it, and they've lamented about what kids these days can't do. The general consensus (with which I agree) is that it's reasonable that Jeb Bush didn't know the answer off the top of his head.

For me this raises another question: how much of what we teach do we expect our students to remember over the long term?

I would hope that my students come away with a deep enough understanding of the main ideas, themes, and concepts that they can reconstruct the details in the future. I would much rather have one of my calculus students remember (years later) that the derivative is a generalization of slope or a rate of change rather than just recalling the formula to find derivatives of polynomials. I would hope that my underprepared freshmen would be able to estimate the cost of installing carpeting — even if they couldn't set up an algebraic expression for it.

For our students to leave our classrooms remembering the major ideas, we need to teach those ideas. If a class focuses on computations and algebraic techniques, what will students remember long term?

And why do I still remember (almost 18 years later) that the measure of the inscribed angle is one half the intercepted arc?