I am not a Mathematician. I am a Math Teacher. And Lockhart makes what I do look and feel like I'm injecting mind-numbing drugs directly into my students' bloodstreams while the school administration and their parents hold them down. The kids struggle and kick and scream .... but we all calmly and passionately tell them over and over and over again that it is for their own good and they will thank us some day. And we smile and prime the syringe.
And across the country my readers sigh .... "Yeesssss ... that is how it was .... that is how it is ...
"
And I feel pulled many ways .... Lockhart has put many of my own emotions into his Lament. In fact, his Lament goes a long way towards explaining why at age 45, after 22 years of classroom teaching, I couldn't take it anymore. Yet there are also several parts of the Lament I feel compelled to question. Probably the "teacher" in me vs the "mathematician" in me.
So .... without further ado .... the opening lines of A Mathematician's Lament by Paul Lockhart ...
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.”
In the higher grades the pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college
when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.” Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one. “To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. Most of
them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it. I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.”
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!”
Ha!! How absurd for sure!!! Lockhart also goes on to use a "paint-by-numbers vs. Art" nightmare in a similar fashion. Very well written. Very apt. Then he follows with this ....
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, soulcrushing ideas that constitute contemporary mathematics education.
Everyone knows that something is wrong. The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right.
Amen to that, Paul Lockhart!!! He sure knows what the students say!!! The other thing they say a lot is "when are we ever going to use this?" Sadly ... my answer to that was always .... "Well ... you'll need it to pass the standardized tests and you'll need it for your next Math class." Totally true statements on my part, but not really an answer to the real question my students were asking .... which was ... "When are we ever going to use this in our real day-to-day life in the Real World?"
Descarte's Rule of Signs? Well, you will use that whenever you are sitting around wondering what the graph of a really long high-powered polynomial looks like and you don't have a graphing calculator handy.
Cramer's Rule? Well, you will use that whenever you are working on solving a matrix equation which you created from a system of equations which you created from a real-life problem involving milk and bread and eggs and how much you spent on these 3 items on 3 different visits to the grocery store.
You get the drift ....
My thoughts on all of this tomorrow ..... feel free to comment today ...
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