Creative Thinking

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NPR’s Robert Krulwich on Intuitive Mathematics

Last month, when Vi Hart’s math doodling video (below) was zooming around the internet, Robert Krulwich (NPR science correspondent and host of the fabulous Radiolab) made a wonderful connection. 

You may have noticed she’s a touch angry about how math is taught in America. She thinks it can be done better — more intuitively, joyously.

So does Paul Lockhart, a math teacher at Saint Ann’s School in Brooklyn, NY. A few years ago, he wrote an essay, “A Mathematician’s Lament,” that’s been all over the internet. I just discovered it. 

Lockhart, too, laments the imagination-starved way in which mathematics is taught in this country. His essay begins like this: 

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made — all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language — to jiggle symbols around according to a fixed set of rules: “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”

In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. “I’ll have to get my son a music tutor. He simply won’t apply himself to his music homework. He says it’s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs.”

…Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream. “Of course!” he reassures himself, “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!”

Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done — I simply wouldn’t have the imagination to come up with the kind of senseless, soul crushing ideas that constitute contemporary mathematics education.

(Lockhart’s full essay is available here as a PDF.)

This is precisely one of the ideas we’re attempting to tackle in this course - creativity and intuition are essential tools not only in arts education, but across all disciplines. How can we build a curriculum that opens up the creative mind for all kinds of students, tackling all kinds of problems? 

Filed under creativity intuition math npr robert krulwich vi hart visual art paul lockhart

  1. sncharper reblogged this from creativethinkingmsu and added:
    This is exactly why I thought about going into teaching.
  2. glassorigami reblogged this from avenuesinthesunset
  3. claireiskoal reblogged this from fuckoff1234567
  4. fuckoff1234567 reblogged this from antbf
  5. seinquest2000 reblogged this from elesheva
  6. dreambigger-darling reblogged this from theaceae and added:
    You know, lately, I’ve realized that I never hated math. I just had some truly horrific math teachers who convinced me...
  7. ohnyet reblogged this from elesheva
  8. theaceae reblogged this from creativethinkingmsu and added:
    I Hate Math! (Not After This, You Won’t) “A Mathematician’s Lament” - Paul Lockhart, a math teacher at Saint Ann’s...
  9. simsian reblogged this from creativethinkingmsu
  10. whichtrex reblogged this from creativethinkingmsu
  11. morningstar08 reblogged this from creativethinkingmsu
  12. avenuesinthesunset reblogged this from creativethinkingmsu and added:
    I don’t have any idea how to reform the way mathematics is taught to students, but this is a thought-provoking read.
  13. dr-johndorian reblogged this from creativethinkingmsu
  14. unironicenthusiast reblogged this from creativethinkingmsu and added:
    I want to read this whole essay. I WANT YOU TO READ THIS. It is serious, it is true, it is how I feel every day. You...
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