I’ve just read a kind of homage to Dan Meyer. It is typical of the genre and similar to Meyer’s own writing. The key features are the hubristic claims – that Meyer will ‘save’ maths – coupled with absolutely no evidence at all to support them. As ever, we are supposed to simply feel that the argument is right. We are meant to evaluate it on its truthiness.
Critics – and Meyer has acknowledged that I am one of them – are dismissed by Meyer as ‘ideologues’. So that’s OK then. Game over. Except that it’s not. Much as it serves a rhetorical purpose to paint me as a crotchety old has-been who just doesn’t like change, this won’t wash. Call me ‘Gradgrind’ or the child-catcher from chitty-chitty-bang-bang; call me any names you want but this won’t alter the fact that I have absolutely loads of evidence to support my position.
Meyer likes to paint my argument as an arcane point about when to explain: He just wants to change the order around a bit and do some problem solving before explicit instruction. What’s wrong with that? There is some evidence to support an approach such as this known as ‘productive failure’. However, it is not strong, with most studies being poorly controlled. This is probably the best study and yet if you read the method you’re likely to spot the problem: The kids who get direct instruction first then have to spend a whole hour solving a single problem that they already know how to solve. I wouldn’t call that optimal.
However, the broader point is that this is a bit disingenuous: Meyer simply does not value explanation in the way that I do. In his TED talk he discusses taking away the scaffolding of a textbook problem so that students have to work out more for themselves. This is clearly going to increase cognitive load and particularly disadvantage students with the least knowledge to draw upon. It will frustrate them.
And Meyer’s explanations must come after this struggle. Mathematical principles are only there to help solve mundane problems about basketballs or whatever. Ironically, this leads to an impoverished kind of maths where kids are given formulas they might need just-in-time, rather than those relationships being built in a systematic and concept-driven way. It is small wonder then that, despite feeling right and being truthy for about a hundred years, proponents of this kind of maths cannot point to any hard evidence to support its use.
In Meyer’s latest desmos venture, it seems that even this limited use of explanations is set-aside in what sounds very much like full-fat, 100%, unashamed discovery:
“In the parking lot lesson, students draw and redraw their dividers, getting immediate feedback as cars try to pull into their spaces; only gradually do they begin to work with numbers and variables. Other modules ask students to share their models with the class, which allows them to revise their thinking based on the ideas of their peers.”
Almost everyone agrees that this kind of thing doesn’t work. So why would we buy it? What’s the evidence?
When pressed, Meyer and his advocates will suggest it is all about motivation. What’s the point in having the most effective way of teaching maths if it turns kids off the subject? Surely, the biggest issue we face is apathetic students who don’t want to engage?
I think this theory of motivation is wrong. Evidence is starting to build that it doesn’t work this way around. Rather than motivation causing students to engage in maths and achieve, it seems that achievement in maths causes students to feel motivated. This simply confirms that our main priority must be to teach maths well. This can best be done by breaking it down into digestible pieces that are fully explained to students. This will give them a sense of success.
So I have thought about this stuff a bit. It’s not just ideology. And, crucially, I can point to evidence to support my claims.
Meyer would do well to read this seminal blog post by Paul Graham on how to disagree. If he does, he will see that calling people names is the lowest level of argument.