I saw this, and I have a reaction:
Topic that I ruminate on a lot came up in my class:
There are ways to engage students in what I think can be fairly called math modelling in contained (1-3 hour) segments, i.e. @ddmeyer's 3 act math
The same seems less true of science ed.; modeling phenomena takes lots of time
— Joshua Rosenberg (@jrosenberg6432) March 26, 2019
I think of this as a matter of the complexity that we are exposing students to. Part of what makes these math modeling experiences engaging is that they are relatively simple. Not to say of course that these problems are easy for students. They aren’t. But when they are engaging it’s because the context is new, but the structure is discernible to students. That’s what engagement is: that feeling of novelty, along with the feeling of I-can-do-this.
And the reason why students can do this is typically because we’ve chosen a dataset that matches either a proportional, linear, exponential or quadratic function, or a pair of these functions. (True: it’s hard to choose the appropriate variables, and if you choose the wrong variables you won’t have very much fun. For that reason teachers usually make the smart choice to help students choose useful variables before they have time to tackle some task.)
Anyway I don’t want the point of this to be that the modeling experiences we create in math class are easy or pointless. That’s not what I’m trying to say. What I am trying to say is that part of what makes them engaging is that they are relatively simple modeling problems. And what makes them relatively simple is what makes them mathematical modeling problems as opposed to scientific ones. What I mean is, students don’t know the context in depth, we are telling them that they know enough to make predictions — they are relatively protected from the complexity.
What makes scientific modeling a different kind of engaging is that it’s in a way more serious contextual work. You learn to see new variables and new factors, and then you’re trying to coordinate them into newer, more powerful models. But there is a sense in which this is more serious work than mathematical modeling, which (by dint of being part of math class) engages less with the context.
I’m not trying to hate on mathematical modeling here, but I am trying to articulate something that I’m moving towards. I really do think kids deserve a chance to connect with applied math problems, “real world” math. At the same time, I’ve been frustrated with what passes for “real world” in math because it doesn’t take the context seriously. I have a great respect for complexity and people who study it. I’d hate for students to get the message that math can just march in and math all over the place and solve everything. You have to have some humility and learn about the world before diving in with an equation!
One question I’m asking myself these days is whether there is a way to take the contexts more seriously in math class. Is there a way I could bring more applied math into my classes without getting lost in the complexity, or ignoring it entirely?