Do the math to teach the math
But hit record first
This is the most useful advice I’ve ever heard1 about teaching math:
Do the math to teach the math.
The idea is that you’ll teach the material better if you work through it yourself beforehand. But with tests to grade and emails to respond to, it can feel easy to skip. This is especially true since the product of your effort, at least at the planning stage, is intangible.
I can now thank COVID-19 for making this something that I never skip. Since my students could not always attend my live classes, I recorded videos of the most important parts of my lessons before teaching them live.2 These videos only take me 5 to 10 minutes to make, depending on the material.3
Without even meaning to, I am doing the math to teach the math. And I find that every single time I go through a lesson I make changes to my plan afterwards, either to the words I use to explain the problem, the steps I take to solve it, or even the problem itself.4 This is precisely why you should do the math to teach the math: it’s about seeing if it will actually work how you’ve imagined it will work. And often, when teaching is concerned, it’s impossible to know if something will work until you try it.
In terms of cost-benefit analysis, this is an incredible return on an investment of just a few minutes. It gives me the opportunity to practice my lesson before teaching it and it gives my students a recording they can watch again if they didn’t get it the first time.
Do the math to teach the math, but hit record first. That way you — and your students — have something to show for it.
First from one of my graduate school professors, Lisa Lavelle, and then in another form from Greg Ashman, as quoted here. The section of interest begins at 1:52:25.
For example, if I’m teaching a lesson on the distributive property, the video will show me explaining and using the distributive property, but not doing an unrelated warmup activity, announcing an upcoming test, and so on. Not only do I want the videos to be as short as possible, I also want them to be as reusable as possible.
I don’t necessarily rerecord the video after I make changes to my plan. If a change will only result in a slight improvement to the video then I’ll just leave myself a note in the slides to record it differently when I teach the same material next year. F*ck it, ship it.