A Mathematician’s Lament, Part 2: What is Math?

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What is math? Is math a science? Simply a class? No. Math is an art. You probably didn’t expect that one. I sure didn’t. Why would math be an art? There is nothing creative or individual about math. Or so I thought. Mathematicians use imagination, creativity, and wonder (just like painters, musicians, and writers do) to brainstorm ideas and possible solutions to problems.

Lockhart is saying in this section that in today’s world of mathematics, the imagination, creativity, and wonder side (the art) of math has been lost. Math is not presented as an art, but as a set of rules. Today, when approached with a problem or difficult question, students (including myself) yearn for a formula or step-by-step process that will lead us to the answer without much effort–or brainpower. We don’t approach the situation with imagination, wonder, or creativity. In my high school math career, I have been presented with formula after formula and been told, “This is how you solve the problem.” I’m good at plugging in numbers to the slope formula and endless other equations, but am I really good at math? My mathematical “thinking outside the box skills” have been lost, if really, they were even present. Now in Calculus, I am being forced to actually think. Like, legit thinking. And quite honestly (I think the majority of my classmates would agree with me) it’s hard.

As I was reading this section, and now while I am responding, I am experiencing some interesting feelings. I feel a bit cheated. Why have I been presented with millions of formulas from the get-go, and not encouraged to at least attempt to find my own, creative solution (and maybe I have been, but it just doesn’t seem to be so)? To actually practice math as an art? I find that I now have an aversion to problems that require other skills beyond formula-crunching. Would this not be the case if my math education had been presented differently? How am I to change my approach to math since I am already far along in my mathematical career?

I think approaching math as an art, and not as a set of rules (at least from the start…Lockhart doesn’t not believe in providing formulas and step-by-step processes, just not right at the beginning.) would be more beneficial to the students of today. And even though it may be more difficult…more imagination, creativity, and mathematics needs to take place in the math room!

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5 responses »

  1. I know I’ve stepped back from a well crafted mathematical proof and looked on it as if it was a painting. I’ve also looked at math problems as if they were abstract pieces of art that I’m not meant to really understand haha

  2. I’m glad that calculus is making you think. The content that you learn may or may not show up later in your life, but the quantitative reasoning that you are developing will be helpful no matter what station you end up in.

    I think you have a really excellent point about step-by-step addiction. There’s the silly picture painted for students that any work is good work, and that those who are lethargic are the only ones with issues.

    This isn’t true, as you point out, because following recipes can only get you so far; without a creative flare, food, math, and art all become paint-by-numbers, which is much easier than thinking but yields slightly similar products in some cases. This is often rewarded by teachers, which really is nothing more than rewarding students who happen to have slightly faster developing brains who can internalize abstraction a bit better at an earlier age.

    I’m very proud of you for grappling with these ideas at such a young age!

  3. It’s so encouraging and refreshing to hear something like this coming from someone your age. You feel like you’re already far along in your mathematical career–don’t let that make you feel like it’s too far, though. Even though I was “good” at math (and by “math,” I mean math-by-memorization as you describe) growing up, it wasn’t until after I graduated from college that I grew to fully appreciate it and decided that I want to teach it. Now, after getting my first degree in psychology, I’ve changed course and am getting a master’s in math ed–so trust me, it’s never too late!

    I didn’t appreciate calculus the first time through; it was the first math that really challenged me, and I loathed it for that. After going back and re-learning it the proper way, many years later–as it seems like you’re learning it the first time around–I came to fully appreciate it for all that it is.

    I haven’t read the article you’re referring to, but I certainly will now. Best of luck for the rest of your school year!

  4. I’ll throw my “congrats” on the pile too – congrats on your powerful reflections about your own realizations. I think you are getting at the heart of the matter, a deep but usually ignored truth that lies underneath “learning” – John Dewey talked about Knowledge being a verb instead of a know, that “knowing” doesn’t mean some things stuffed in our head, but instead is inextricably tied up with powerful social experiences in the world. I think your realization that math is an art might be related to Dewey’s ideas. Great work! (brief background on me: I’m a former high school psych and philosophy teacher and current avid follower of Think Thank Thunk)

  5. Mr. Cornally- I was excited (although I’ll admit– a bit intimidated) about the “Projects” we started yesterday in class. I thought this was an excellent opportunity for us students to step outside our comfort zones and challenge our minds.

    Amanda- It is always reassuring to know that someone has been, at one point, in the same boat as yourself. Thank you for the encouragement!

    Rob- With the help of this publication, I am beginning to grasp that knowledge isn’t just having thousands of facts or formulas memorized, but understanding concepts and being able to think creatively. I appreciate your feedback!

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