I’ve been truly enjoying Dan’s blog post series (from last year!) on the “Fake World.” I’d highly recommend you go read those posts if you haven’t already. It deftly exposes the fallacy of authenticity-as-engagement. I would like to offer a defense (three, really) of applied mathematical tasks.He offers three arguments. Here's the third:
Also, by dismissing the “real-world” as a lever to engagement, you’re giving teachers a kind of out. I’ve had conversations with sanctimonious math teachers and district instructional coaches that cite Paul Lockhart as a reason to keep doing what they’re doing. I’ve read Lockart. I love Lockhart. But his books aren’t about instructional practice. While much of “Measurement”, say, can and should be handed over to students to explore, it’s frustrating to kids who have only experience math in the abstract.Of the three, this is the only of his argument that draws blood for me. If you love math, you end up loving the fake world, and it's tempting to think that others will share that love. But the fake world is tough for kids. It's very, very different from the world in which they inhabit.
But so is the real world, no? Dan's done a great job making that case. So if the fake world isn't real for kids, and the real world isn't real for kids, then that means that...
...the world is fake for kids.
And that sounds closer to the truth for me. The world, as experienced by a mathematician, is very different than it is for your average civilian. You learn a bunch of math, and you start seeing things differently. You talk differently. You find yourself asking all these questions that nobody else asks.
And that's because no content is a "natural" context for mathematics. Or rather, no content is inherently engaging, and the world needs a different language for talking about student interest than engagement with content.
We have to change the conversation. Content isn't engaging, not all on its own. Pedagogy partnered with dumb content can only take you so far. What we need is a way to talk about partnering great content with effective pedagogy, what I'm calling "teaching" until someone comes up with a better term for it.
(Heavily influenced by this post from Larry Cuban.)