Rigor and Pedagogical Clarity

As an educator, are you concerned more with rigor or clarity?

Grant Sanderson, the amazing math communicator who runs the 3Blue1Brown YouTube channel, addresses how we are often tempted to pursue rigor at the expense of clarity. Even as educators, for whom clarity should be paramount, it’s a pitfall.

The point of rigor is often to add more clarity. But the thing that I suspect might happen now and then is that, because the rigor gives you this very clean, nice thing to think about, and because thinking about pedagogical clarity is a lot messier – you know, it’s harder to define, you can’t put a bow around it, there’s not one point when you’ve gone from not done to completely done – that after scratching the itch of knowing that something’s been written completely rigorously it’s easy to call a work done when maybe we shouldn’t call it done yet. And there’s context where this is maybe okay (research papers come to mind) but in things that are more explicitly pedagogical (textbooks come to mind) I would propose that maybe it makes sense to invite into the culture a similar focus that we already have on the rigor of it but instead onto something for the pedagogical clarity.

Grant Sanderson, from his talk about Math pedagogy and communication

He goes on to list this checklist for rigor:

  • Are the definitions unambiguous
  • Has each object in each theorem been given a clear definition?
  • Is each claim given a rigorous justification?

His checklist for pedagogy includes:

  • Do definitions have motivating examples?
  • Do proofs feel rediscover-able?
  • Is there personality?
  • Are there enough diagrams?
  • Is relative importance highlighted?

While Sanderson is talking specifically about math education, I think the point is valid even in something like music education. In our attempts to make absolutely clear theoretical explanations, we can lose the thread of making the ideas clear and relevant to our students.