Yes, I think the relativism idea is a big part of this. Just this week I was teaching about blackbody radiation. There are a couple of tricky integrals involved, but, to me, the big idea is simply that Planck found that letting the oscillators in the wall of the cavity only have discrete energy levels makes the theory fit the data. At the last minute I changed my plans for the day from helping with the integral to discussing whether my students would be brave enough to embrace a model that has such weird ramifications (a pendulum can only have certain amplitudes). I’m glad I did it, but if my colleagues found out, I’d catch some heat. Ugh.

Thanks Andy – I really want to dig in to figuring out that reluctance because doing so would help sell others on a computational approach. It has to be more than just an institutional ‘this is how we do things’ argument, no? I don’t mean to suggest that students get NO benefit from doing hand calculations themselves. I think we overstate its importance because our first inclination when we see students that don’t have automatic skills is that they haven’t practiced enough.

I also agree that there is a level of relativism in play here – as an algebra teacher, I’d love all of my students to have their integer operations down. In Calculus, I’d love it if my students can factor quadratics and solve equations effortlessly. The goal in those courses, however, is not to make sure they have those pre-requisite skills, it’s to get them to understand new ideas. Those new ideas don’t necessarily require those skills be solid to develop intuition or understanding, especially with computers around.

The last thing that feeds into this is that few people actually do backward design for learning. The default plan is usually a sequence of ideas that starts with a definition, poses examples around that definition that get gradually more complicated, and then application problems appear. This is not usually how true discovery happens in the real world. In the real world, we start with a problem to be solved, try to attack it using the models we already understand.