I think we agree that we need a structured curriculum that gets students from point A to point B. Of course, our curriculum needs to allow for exploration, discovery, and fun, as Paul Lockhart says. But still, in order to prepare people for the real world, we need to take them from point A to point B. But if we’re honest, only 2% of students (I’m being generous) will be in fields where anything beyond Algebra is required of them. And usually, by point B we mean Calculus or something like that (in RM’s case…it may mean Multivariable Calculus/Diff.Eq. or HL Math). We just accept that point B is always Calculus. But most students will never use Calculus directly. This is a tough thing to come to grips with: It’s absolutely true that 98%++ of students will never apply directly the math we teach. What do you think of that?
Here’s a 3 minute talk by Arthur Benjamin, who suggests we change “point B” to be Statistics, not Calculus, as a response to this very dilemma.
Arthur Benjamin is a professor at Harvey Mudd College and an all-around cool guy. You might enjoy his other, more light-hearted TED talk (performance, really) in which he does “Mathemagic,” found here.