Infomercial Pedagogies
Infomercials are great at establishing the need for their products. In an infomercial, there is generally a “don’t you hate it when …” moment where it tries to establish just how inconvenient life is without its product. And then there is a “well you should try …” moment where the infomercial introduces the product that will make life convenient again.
Math class might take note here! Here’s Howie Hua doing this week something we might call “Infomercial Pedagogy.”
Don’t you hate it when your standard algorithm requires you to make exchanges all the way across the minuend? Well you should try thinking about subtraction as the distance between two numbers instead!
Joe Herbert suggests this process of identifying the need for new math ideas might be a useful project for students. Me, I feel pretty convinced that, because we’re forcing students to spend 10-12 years of their only childhood learning mathematics, the obligation to identify the need for new math ideas rests with the teacher, and the curriculum, instead.
For example, here is one of my favorite examples from our curriculum. Don’t you hate it when you try to sketch a scale drawing and it doesn’t quite work out as you intended?
Well you should try a grid and numerical precision instead!
By starting with the knowledge students already have and helping them encounter the limits of that knowledge, we’re making learning math feel more purposeful. But by connecting old and new knowledge, we’re strengthening both and making learning math more effective as well.
BTW
If you find these ideas interesting and want something more theoretically grounded than infomercials, definitely check out Guershon Harel’s paper on the necessity principle.
You might also enjoy the Directory of Mathematical Headaches which leaps from a different metaphor than infomercials.