Let me wrap up this summer’s series by offering some time at the microphone to two groups of critics.
You can’t be in the business of creating headaches and offering the aspirin.
That’s a conflict of interest and a moral hazard, claims Maya Quinn, one of the most interesting commenters to stop by my blog this summer. You can choose one or the other but choosing both seems a bit like a fireman starting fires just to give the fire department something to do.
But “creating headaches” was perhaps always a misnomer because the headaches exist whether or not we create them. New mathematical techniques were developed to resolve the limitations of old ones. Putting students in the way of those limitations, even briefly, results in those headaches. The teacher’s job isn’t to create the headaches, exactly, but to make sure students don’t miss them.
To briefly review, those headaches serve two purposes.
One, they satisfy cognitive psychologist Daniel Willingham’s observation that interesting lessons are often organized around conflict, specifically conflicts that are central to the discipline itself. (Harel identified those conflicts as needs for certainty, causality, computation, communication, and connection.)
Two, by tying our lessons to those five headaches we create several strong schemas for new learning. For example, many skills of secondary math were developed for the sake of efficiency in computation and communication. That is a theme that can be emphasized and strengthened by repeatedly putting students in a position to experience inefficiency, however briefly. If we instead begin every day by simply stating the new skill we intend to teach students, we will create lots and lots of weak schemas.
So creating these headaches is both useful for motivation and useful for learning.
Which brings me to my other critics.
This One Weird Trick To Motivate All Of Your Students That THEY Don’t Want You To Know About
There is a particular crowd on the internet who think the problem of motivation is overblown and my solutions are incorrect.
Some of them would like to dismiss concerns of motivation altogether. They are visibly and oddly celebratory when PISA revealed that students in many high-performing countries don’t look forward to their math lessons. They hypothesize that learning and motivation trade against each other, that we can choose one or the other but not both. Others even suggest that motivation accelerates inequity. They argue that we shouldn’t motivate students because their professors in college won’t be motivating.
I don’t doubt their sincerity. I believe they sincerely see motivation as a slippery slope to confusing group projects in which students spend too much time learning too much about birdhouses and not enough about the math behind the birdhouses. I share those concerns. Motivation, interest, and curiosity may assist learning but they don’t cause it. In the name of motivation, we have seen some of the worst innovations in education. (Though also some of the best.)
But there are also those who do care about motivation. They just think my solutions are overcomplicated and wrong. They have a competing theory that I don’t understand at all: just get students good at math. It’s that easy, they say, and anybody who tells you it’s any harder is selling something.
And, yeah, I’m sorry, friends, but I do have a hard time accepting such a simple premise. And I’m not alone. 62% of our nation’s Algebra teachers told the National Mathematics Advisory Panel that their biggest problem was “working with unmotivated students.”
I see two possibilities here. Either the majority of the nation’s Algebra teachers have never considered the option of simply speaking clearly about mathematics and assigning spiraled practice sets, or they’ve tried that pedagogy (perhaps even twice!) and they and their students have found it wanting.
Tell me that first possibility isn’t as crazy as it sounds to me. Tell me there’s another possibility I’m missing. If you can’t, I think we’re dealing with a failure of empathy.
I mean imagine it.
Imagine that an alien culture scrambles your brain and abducts you. You wake from your stupor and you’re sitting in a room where the aliens introduce you to their cryptic alphabet and symbology. They tell you the names they have for those symbols and show you lots of different ways to manipulate those symbols and how several symbols can be written more compactly as a single symbol. They ask you questions about all of this and you’re lousy at their manipulations at first but they give you feedback and you eventually understand those symbols and their basic manipulations. You’re competent!
I agree that in this situation competence is preferable to incompetence but how is competence preferable to not being abducted in the first place?
If that exercise in empathy strikes you as nonsensical or irrelevant then I don’t think you’ve spent enough time with students who have failed math repeatedly and are still required to take it. If you have put in that time and still disagree, then at least we’ve identified the bedrock of our disagreement.
But just imagine how well these competing theories of motivation would hold up if math were an elective. Imagine what would happen if every student everywhere could suddenly opt out of their math education. If your theory of motivation suddenly starts to shrink and pale in your imagination, then you were never really thinking about motivation at all. You were thinking about coercion.