- The validity of an idea about mathematics education and the plausibility of that idea are uncorrelated.
- Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected.
There are no easy answers. That much is obvious to anyone who has taught math.
This isn’t very helpful, though that’s not the point — the point is humility. That said, I’d like to hypothesize a potential corollary to Begle’s laws.
- Every challenge a teacher faces has a solution.
- That solution is enormously conditional; that is, a different teacher in a different classroom with different students will need a different solution to what seems like the same challenge.
This underscores the same points as Begle: there are no easy answers, and humility is key. At the same time, it reflects the type of discourse I am interested in when talking about teaching. I don’t want to hear about the “next big thing”, or some magic pill that will help all of my students brilliantly solve trig equations. Instead, I want to hear about a humble new idea: when it works, when it doesn’t work, and why we think that’s the case. When we build knowledge around teaching that is truly conditional, and reflects the enormous variance between classrooms across the country and around the world, we are both building useful pedagogy and respecting the judgment and professionalism of teachers everywhere.