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Lockheart’s Lament and Other Problems You Didn’t Know About

April 23, 2009

So with my recent change in status to benefiting from the government’s largess, I have decided to cease railing my new overlords for their cheritable actions towards very rich people and take up a less politically charged mantle: Math education. Wait, does that rile you? Are you pro-Axiom of Choice? My bad. Just bear with me.

I’ll go ahead and post a link to the good gentleman I’m utterly ripping off, as he says everything I do but more eloquently. No worries good people, it’s safe for work. If, like many people, you cannot toil yourself through this 25-pager, no worries and what fortune! Because I’m summarizing all of it as well as adding in my own limited experience and non-empirical anecdotal evidence, because I care.

There are so many problems with math education that any math student with itchings towards teachings finds him or herself in paroxysm of madness and frothing anger whenever they end up tutoring some poor sap in high school, middle school, or lower school. For one, math, like all pre-secondary educational programs, is treated unbelievably like it can be taught the same to all students. The perception that it’s this dogmatic set of routines that’s the same for everyone doesn’t help, either. Let me state it for the record, and you can believe me or not but understand I grueled for years more than any sane person would over this: Mathematics is an art form, with all the levels of appreciation, creativity, deeper and abstract understanding that comes along with that.

If one looks at a fine gentleman like Liebniz, circa early 1700’s, there in his study, developing the calculus, you will not see him jotting down notes or cranking out multiplication tables and slope equations like some form of machine. Looking into a dimly-lit German window, you would see a man, one hand over his substantial aristocratic stomach, the other held in midair, tracing lines in the atmosphere and drawing fingers close together, imagining fluid motion, catching the essence of what we mean when we say ‘close’, and only then taking some nearly inconsequential at this point equation down, simply as a book marker for his creativity.

Our friend Lockheart is dead on when he makes this point using triangles and the curiosity of a child. Sure, you can teach someone to paint by having them reproduce other paintings day in and day out, of increasing complexity and with increasing requirements on time and shortcuts, for 12 damned and horrible years. And sure, you put any painting in front of them and they will rapidly be able to reproduce it like some Van Gogh xeroxer. Are they an artist? Have they been learning art? Why is math education any different?

Artists are born through guided exploration, playing games with the paper and with their instruments, and the same is true of a mathematician.

“NO!” some of you scream, hands held outward as if holding me back. “You’re crazy. You and Lockheart are suggesting NOT making children memorize their tables, NOT knowing how to add out of second grade, NOT knowing how to recite the quadratic formula to the tune of Frère Jacques out of high school?!” Oh yeah, all of that. Are you wondering how we can expect our students to have all this information before they get to college? I’m wondering how they do now. Many don’t. And many ‘artists’ with the aforementioned method would fail out of disinterest and boredom and be jaded to art for the rest of their life, looking at artists as if they’re supermen or crazy. Sound familiar?

We don’t expect our children to know how to balance their budgets or do their taxes or fill out lease forms for cars and loans, all of which are immensely valuable skills they will need later on in life. Why is math treated differently? I’ll tell you why: Because we’re trying to stave off overpopulation by boring our children to death before they can reach reproductive age. Which has backfired utterly, since many high schoolers would rather screw off than attend Algebra even another single day.

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