Last weekend my wife and I had the privilege of sharing a meal with Scott Miller, David Sladkey, and each of their wives. Awesome food, excellent conversation. It was the highlight of a great weekend at the DuPage Valley Math Conference.
At one point, David asked an intriguing question that sparked a lengthy discussion. I’ll share the question here in the selfish hope that I’ll be able to hear a few more opinions, and continue my own pondering (and learning) in the process.
Here’s the question:
Suppose a teacher gets to divide 100% between two categories: teaching ability and content knowledge. What’s the ideal breakdown?
Update: Several commenters reframed the question as pedagogy vs content knowledge. I find that shift in language helpful. If you prefer that formulation—or if you’d like to push back and offer your own related question—go for it.
Update: I want to learn more about this, shared by elsdunbar: “Deborah Ball describes a horizontal content knowledge as ‘[A]n awareness of how mathematical topics are related over the span of mathematics included in the curriculum.'”
Related post: These thought-provoking comments have sparked a new set of questions for me.