Last week, I caught myself saying something to a pre-service teacher as we planned a Grade 1 lesson for the making of 10s. I asked her,
"Why would the students need to know how to make up 10s?"
When she was auspiciously silent, I filled the space with a statement said entirely tongue-in-cheek. It was only upon reflection, that I kicked myself for not being able to shut up and allow her to think. I said,
"...because my job is to convince teenagers they need logarithms, and that is much more difficult."
So what is my problem with relevance and math's application to the "real world"? (pause to allow the shudders down my spine to digress). Well, in a nutshell, I think that justifying the study of mathematics through a claim that we are somehow doing kids a solid by preparing them for the real world a) ignores the fact that for students, school is their real world, and b) is an extension of a myriad of things us teachers do just to appear "teacher-y".
I lump finding strained applications to the "outside world" in the same category as creating rubrics with vague language gradations so we can somehow move closer to understanding the difference between "often" and "frequently". These are hairs that never need to be split, because in doing so, we cheapen the activity which we are trying to understand. In the case of mathematics, grasping at some semblance of relevance is insulting.
Here, I would like you to image a well-reasoned exposition of all the possible justifications for teaching math. Math as beautiful, math as employable, math as a pursuit of pure reason, etc.
You can imagine my surprise while I was listening to a podcast during a morning walk and heard mathematician Edmund Harris say:
"In a massive intellectual land grab, I claim mathematics is everything that you can think about without reference to the real world."
You are trying to tell me that the very thing that defines mathematics is the only thing we, as teachers, try to use to get kids to learn it? This could stand as the largest piece of educational irony in history.
Here is my alternative; I believe it provides a much steadier footing for mathematics education as well as a productive pedagogy therein. What if we stopped thinking of math as tool only useful for other things, and began to think of it as a discipline that a) has self-contained beauty and utiliy and b) has the sneaky tendency of becoming relevant to the world around us? Why do we need to tether worth to application? Can't application be some sort of serendipitous occurrence? A cherry on top--so to speak?
Skeptic: Fine then, but if we lose the "real-world", how will we motivate students?
Me: Glad you asked.
First, real-world is a crappy motivator. Again, that is teachers being teacher-y. We are creating a reason why we think this would be worthwhile, and projecting it.
Second, if we forget about relevance and "real-world", the project of schooling stops being one of spoon-feeding isolated topics, each with some white-washed and over-simplified connection to the natural world. The project of teaching mathematics is creating the conditions to harness the inescapable human tendency to make meaning. Our job isn't to tell why something is relevant, it is to open a space for which the problems become relevant.
Skeptic: Wow... how romantic.
Me: Isn't it, though?
Think about your "best" or "favourite" lesson. Seriously interrogate the relevance it held. Here are two examples of low-hanging fruit from the internet. First, Barbie Bungee is an ageless task where students are asked to determine how many elastics will allow a Barbie to safely bungee jump off of a certain height. This task occurs in the real-world, but I am doubtful that a student's full-time profession will fall at the juncture of extreme sports and children's toys.
Second, Marble Slides (from Desmos) are amazing. I have witnessed student forays into uncharted territory of engagement. Sure, they evoke the principles of physics, but, again, I don't recall seeing too many job postings or graduate degree programs being offered in marble rolling.
The point is not to attack these lessons, but rather point to what makes them great. They are so irrelevant that students find themselves lost in their contexts. They afford them a chance to return to their roots as natural mathematicians and entertain their irresistible urge to make meaning.
Please stop looking to embed math class in reality. I'm begging you. The task of teaching mathematics is actually much more difficult than that. We need to focus on creating experiences where students can suspend reality and simply be lost in a state of mathematical vertigo for a while.