A goal I have for this coming year—or rather a commitment I’ve made, as John Spencer reminds me—is to more consciously cultivate values in my classroom. Specifically, I want to help my students to think about learning and about mathematics. Thoughts have been kicking around in my head for a while, and so I’d like to make a first stab at sharing some of them. Hopefully you’ll be able to give me some feedback and/or find something here useful to your own thinking.
I don’t often get asked “why are we learning this?” or “when are we going to use this?” or other “what’s the point?” questions. Maybe it’s the kids, or me, or the stuff we do, or who knows. I do know that this is a live question, whether it comes out or not, and that it’s a question where math teachers usually find themselves on the defensive.
So regardless of whether the questions comes up, I want to address them and teach about them. Especially:
- In what ways can math be a part of your life?
- In what ways will math be a part of your life?
Getting kids asking these question in personal ways is most important—of themselves, their peers, their parents, their parents’ friends, other teachers, and so on. I’m planning to put together some assignments, journal reflections, and/or free-choice projects to help them to seek out answers.
But I also have my own answers that I want to share with them, and with you. It’s in four parts. It’s not meant to be canonical—just the way I’m thinking right now.
- Math can be a useful tool in everyday activities. When shopping, managing money, estimating, or reading about and discussing issues, some mathematical ideas and skills come up time and again. These might be lumped under the generic heading “numeracy”.
- Math can be a social token. The classes you take, what you score on the SAT, whether you consider yourself a “math person” or not. Your relationship and experiences with mathematics can be and often are a status symbol, a tattoo, for your whole life. It can be a burden, a weapon, a bridge, a currency, or a welcome mat.
- Math can be a tool to investigate the world. There are parts of mathematics that are essential tools in any specific human pursuit—especially the physical and social sciences. If you want to do physics or economics, play poker or create mathematically-inspired art, there’s some specific parts of math that you’re going to need to know for each one.
- Math can be a constant companion and source of enjoyment. You can do math for fun. You can explore parts of math that excite you, work on problems and puzzles that are tough but gratifying, let math concepts become your playthings and color your life.
A chart came to mind as I pondered these different roles that math can play.
I especially want to point to the distinction between required and opt-in categories. There are mathematical situations we’ll all encounter, regardless of the lifepaths we take. At some point we’ll all do, for instance, some money-related calculations, and at some point we’ll find ourselves in a social-token situation.
Other math experiences are opt-in. There is math that will be very important to understand if you want to be a physicist or a juggler, but that you can easily enough ignore if you don’t. There are of course questions about what kinds of foundations students need in various mathematical disciplines so that they aren’t later shut out of opportunities. Drawing the line between a math education for a generalist and a specialist is a live question for me (and maybe you), but I feel like the governing math ed consensus wrongly forces kids to specialize in ways they’d rather not. I think this has to do with how unclear the meaning of “math is useful in life” usually is.
It also has to do with the fact that math as a social token is such an enormous but often understated or unseen force in our world.
I’m particularly excited about sharing this idea of math as social token with my students, especially in the context of the other three roles. I feel like it’ll help them take greater command of their own mathematical identities.
Students have a fair amount of control over these four aspects of their mathematical lives, and they certainly have control over their attitudes towards these aspects. I think that pointing them out could be wonderfully empowering for students.
Classroom experiences and institutional structures that support these different values of course look different from each other. I feel like just articulating them to myself helps me to think about how I’d like to talk about math with my students.
What do you think of my answers? What would you add, subtract, merge, or reframe? Or do you have a different way of thinking about this altogether?
And if you can point to resources for having kids think about these issues, I’m all…clicks?
This is well said:
“Drawing the line between a math education for a generalist and a specialist is a live question for me (and maybe you), but I feel like the governing math ed consensus wrongly forces kids to specialize in ways they’d rather not.”
Good stuff. I’ll think on this. We’ll talk.
The more I grapple with this issue, the more I shy away from the notion of utility. Here is one attempt: why teach simultaneous equations – what you call system of equations. There’s a lot of blah blah in there but it goes to show that we all inevitably face the challenge of relevance.
I agree with Paul that you articulated well the line between generalist and specialist. This goes a long way in the debate against subject ‘silos’ in high school.
Unlike Paul, it is less easy for me to say “we’ll talk”.
Yeah, the trouble with invoking a utility argument in favor of any particular piece of mathematics is that–except for some rather basic skills–the usefulness of any bit entirely depends on what a person’s goals and ambitions are. A hammer is very useful, but not for swimming. While it seems daunting to shape a student’s mathematical education based upon his/her own goals and ambitions, asking that question has to come before making most utility claims.
I’m interested in finding good ways of helping kids to find and love the math that gets them closer to their dreams–not vague “go to college” dreams but “the I’m really into X and want to do it; could I?” dreams. Now that’s utility. And I’m also interested in doing everything I can to share the pleasure and gratification of doing math just because. A kid who’s building a personal, intimate relationship with mathematics is a pretty rockin’ thing.
What I missed to add was instead of utility, I work more towards giving context (real or imagined) so the maths is in a ‘story’, if you like, and that’s usually purpose enough. Also, I highlight ‘mathematical thinking’ more than the maths itself sometimes because such skill is “useful” in everyday life and specialist pursuits. Here’s my latest example: Walking the walk.
I agree with you re: dreams. I recently used that ‘context’ in an Inquiry-based learning, albeit for Information Processes and Technology course (Computing Studies – year 11). This post has a graphic of it. I reckon you can tweak the idea to suit your outcomes. I can honestly say that the students engaged with the topic well and enjoyed it as well.
so much easier to say all these outside the constraint of 140 chars! #justsayin :)
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hello. may i use your article for a math project in school?
Sure thing, Bianca. What is the project? I’d be curious to see your final product when you’re done with it.