Friday, August 3, 2012

My favorite math moments - vanilla geekery

Joey asked me if I have a favorite math moment. Truthfully, after spending nearly a decade tutoring math to college students ranging from the most basic remedial stuff to calculus and trigonometry, I have several.

Euler's identity:

e+1=0

Oh. my. God.

When I first discovered this I was astounded. I'll let you read wikipedia's explanation of the mathematical beauty if you want. I was convinced that somehow, locked within this equation, was the secret of the universe.

How. HOW did the irrational base of the natural logarithms, raised to the power of the square root of negative one times the (also irrational) ratio of a circle's circumference to its diameter... equal negative one? HOW? It astounds me even now. I've worked it out, and it comes out right and proper as it should. It's astounding.

I loved introducing this concept to a student who was just being introduced to imaginary numbers, and watching his or her eyes grow wide. Well, when the student was intelligent enough to grasp the awesomeness. They weren't always. Sometimes they'd just go "Huh?"

Why do I need to learn this?

I don't know if this is really a favorite or if it's just one of those things I loved to hate - but if I had a dime for every time a student said this to me, I'd have a sizable sum of money. My favorite answer, after years of it, was from a book I once read titled Everything Bad is Good for You. You don't learn algebra to use algebra any more than you go to the gym to learn how to use a treadmill. You do both because they build a certain kind of muscle - in the case of algebra it's a problem solving muscle. Algebra gives you the tools to solve problems you may not otherwise know how.

Another thing I'd always tell them is that you never know where you're going to wind up. I certainly never thought I'd wind up being a (mostly math) tutor for a third of my life.

Holy crap I've got it!

The lightbulb moment. When any student gets it. You've been working with the person for hours, possibly days, and the light in his or her eyes has dulled. He's resigned himself that he's never going to get it. She will plod through the exercises as you guide her, but she's never going to understand and she will fail her test.

And then, suddenly, the light returns. He's got it. She's got it. He flies through the next page worth of exercises with no difficulty at all. They can't even be called problems anymore, because they don't present any.

Guiding a person to that moment is fantastic. It happened far less than I would have liked - many students had just resigned themselves to achieve low scores and be happy just to pass, but the ones who struggled at first and then suddenly had it? Oh, yeah, that's a high.

23 comments:

  1. I loved this post especially the way you used the teaching of imaginary numbers to help spark the enthusiasm of your students. I can see that you are a kind and generous person.

    In college, I helped children with math as well. I agree, watching the light in their eyes as they "get it" is a magic moment.

    Thank you for sharing your favorite math moment.

    Hug,
    joey

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    1. You're pretty awesome yourself.

      Thank you for the idea. :)

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  2. Love the title: vanilla geekery!!!

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    1. It could be its own blog! Thanks. :)

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  3. How can your equation contain the secret of the Universe when my equation contains the secret of the Universe? Hee. Maybe I'll post mine someday.

    My answer to why learn algebra is, it's fun!:)

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    1. It IS fun. But a lot of the folks there never thought it was. They seemed to think it was torture.

      Hm, now I'm drawing parallels between math geeks and kinky people in my head. ;)

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    2. I think you may be onto something with the math geek and kinkery... I enjoy both as well!

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    3. I'm not sure it's only math geekery. Could it be ANY sort of geekery? I'm a music geek. And I have my own secret to the universe. Having said that, I always emphasise the importance of mathematical concepts in the study of form and harmony.

      And yes, when they finally get it, the a-ha! moment, that's the best part of teaching!

      BTW - have you noticed many of us are either in the education or health-care industries?

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    4. The parallels I was drawing were toward seeing something that many people seem to think of as pain and/or torture as fun, so I'm not sure.. but there are a fair few folks out there who'd think musical forms or watching sci-fi would be painful too, so MAYBE!

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  4. I loved your post, because the awesomeness of Euler's identity is beyond words. The five most important numbers in the whole of mathematics united in a single, simple, beautiful formulation. Two transcendental numbers, the basis of imaginary numbers, unity and nothingness. Pure beauty.

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    1. I know. Glad that you get it, and thanks for speaking up. :)

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  5. I love math too! Euler was the bomb.

    What do you get when you cross an elephant with a grape?

    Elephant-Grape-sine theta

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    1. It's interesting to see all the math geeks come out of the woodwork. :) I love it!

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  6. I'm afraid I'm one of those in the the "HUH?" group, lol. Though I always knew you were one smart chica :)

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    1. I spent a fair amount of time going "HUH?" myself, until I had my lightbulb moment at around 20, that I could do ANYTHING and math was part of ...all the things. :)

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  7. One of my favorite classes in college was Complex Variables ... So excited about a whole class on imaginary numbers!! I love that there are so many math geeks in this kinky world.

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    1. I took algebra and trigonometry as an elective. :) People were all like, "Wtf?" I love it too!

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    2. I know, I took probability as one...too funny.

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  8. Oh goodness, way to take me back with that one. I was first introduced to i in 9th Grade while taking Algebra 2, and my teacher had the exact same reasoning as you mention; learning to solve problems is the reason. Critical, analytical, reasonable, and logical thinking skills are more valuable than memorized formulas. I've long since forgotten the Algebra and Calculus I learned in High School, but the reasoning skills remain. As an IT guy, I have no more valuable a tool kit.

    Stay SINful
    Mr. AP

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    1. It's been a while since I helped anyone with some stuff, and I realized a few days ago I've actually forgotten the quadratic formula. I'm sure it's somewhere in my physical memory as many times as I have written it, but yeah, solutions are the answer. :)

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  9. Faerie was always the one who said "huh?" ...... I'm the one who's still saying "huh?" I never ever 'got' algebra. Complete mental blockage. Maybe if I'd had a teacher like you lol!

    Dee x

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Thank you for reading. I hope you'll let me know you were here - I like friends!