My students have been giving me a run for my money recently with “when am I ever going to use this???” It’s a good question, and it come from the message math teachers send, implicitly and explicitly, that math is important to learn because you will need it in (insert your favorite) the real world/your job/everyday life/etc.

I’ve been refining my elevator speech for math — my succinct response to the question, “why math?” that underscores its importance, whether we are working with proportions, exponential functions, the real number system, or conics. Here is my current best draft.

*I don’t teach math because I believe you will need it in your job, or in your everyday life. You may — and learning math will certainly keep options open for your future — but that is not why I teach math. I hope your history teacher is teaching about the Revolutionary War not because it is relevant to your everyday life, but for you to gain more context for understanding our world. I hope your literature teacher is teaching Animal Farm not so you can get a job, but so you gain a new perspective on your interactions with others.*

*Mathematics is the practice of solving problems — identifying relevant information, creating models, thinking strategically, contextualizing and decontextualizing, constructing arguments, and examining the logic of others. This takes hard work and a great deal of knowledge — knowledge of numbers, computation, mathematical structure, problem-solving strategies, and a wide variety of mathematical content. To be an educated person means having this knowledge and knowing how to apply it — as one small part of what we hope you leave school with. The questions we answer that lead to this learning may come from the workplace, or they may come from something lying in the street — but the purpose of the problem is the learning of mathematics, and these are problems worth solving.*

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howardat58“Mathematics is the practice of solving problems”

I think that this is too narrow a view. More on the whole notion of regularity and pattern together with a quantitative approach would be helpful. Along the way some problems get solved and some reveal themselves as impossible. Math is a way of thinking, and of representing aspects of reality in an amazingly concise manner.

A question – How many of the “problems” addressed in a school math course can be solved without any math at all? Most school math problems are artificially window dressed to hide or disguise the math the kids have just studied. it is not surprising that they see through the subterfuge.

dkane47Post authorI think you make a good point about the ultimate goals of mathematics education — however, with the tools I have now, I still think this is a good description of what my class looks like on a day-to-day basis

johnthallAs I progressed further and further into my college career and began seriously questioning why I wanted to teach math specifically, my mind always came back to the idea that learning mathematics is essentially learning how to think in different ways. In looking back at my mathematical career, time and again I was confronted with problems and concepts that challenged my thinking. I wasn’t just learning concepts; I was learning how to think about ideas differently. I carry this philosophy into my classroom each day and I openly tell students we are learning how to think. I always get looks of confusion from students, but I ask them to think about how differently they approach problems (inside and outside of math class) compared to the same time last year. It’s nice to hear that I’m not alone in these thoughts!

dkane47Post authorThanks, John! I love that perspective to frame math for students. Remind me of number talks in particular.

Dan MeyerIt’s great to have a well-articulated explanation for “why math?” Next question is how does that explanation inform your instruction – your lesson planning?

Dan MeyerNot hypothetical! I’m very interested in your thoughts here, Dylan. How does this elevator speech trickle down into your lesson planning?

dkane47Post authorI think this has three influences on my lesson planning —

First, “application” tasks act as a means, not an end in and of themselves. One end is students learning math, and I choose tasks — application, inquiry, worksheet, whatever — to meet that end. This week I taught the “Domino Skyscraper” three-act. It’s an engaging task, but I didn’t choose it because it would prove a point about how useful exponential functions are. I chose it because the questions I had been asking with exponential functions leaned too heavily on percentage of growth or decay, and students had gotten into a groove of (1+r) or (1-r) without making the association with repeated multiplication. That three-act reinforces some of the important pieces of exponential growth, and is a fun way to engage students in some mathematical thinking.

Second, and this is stealing Karim’s ideas at Mathalicious, application tasks act as a means to learn about the world. We modeled the spread of Ebola with both exponential functions and logistic functions and compared and contrasted. Again, I didn’t choose that lesson to prove a point about how useful exponential functions are. You can understand what’s happening without the nitty gritty of the math, but it’s a chance to ask questions about the world. I put together some Desmos graphs for students to drag around that take away some of the mathematical load necessary (students weren’t actually writing functions). My goal wasn’t for students to recreate the exact work that someone in the “real world” does to do that modeling, it was to use the model to learn something about the world. The two feed off of each other — the world tells us something about the math, and the math helps us to see the world.

Those two inform my decisions for application tasks in class. The last consequence of the elevator speech is that I don’t feel like I have to have an application problem or a justification for the use of math in every lesson. The math justifies itself, because math itself is worthwhile. That helps to free me up to use puzzles or challenges or whatever other problems will engage students in thinking mathematically, without feeling like I have a responsibility to show my students the usefulness of math.

danmeyer55351818Sounds coherent! Thanks for elaborating.

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