Monday, May 20, 2013

A piano students' lament

In his A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart opens with an allegory about a musician, who awakens from a nightmare in which the “curious black dots and lines” that “must constitute the ‘language of music’” become the center piece of what has become a universally mandated music curriculum. He proceeds to describe just how tedious this curriculum is for all concerned:

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.
And then, of course, he famously proceeds to connect this musical nightmare to the way K12 mathematics is supposedly actually taught: all meaningless, mindless drill.

As Alfred North Whitehead writes back in 1911, however, mindlessness is often a virtue:
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
Furthermore, while no sane piano teacher would ever make "curious black dots and lines" the centerpiece of music instruction, some of the best ones give top priority to mind-and-soul-numbingly tedious muscle exercises. I was reminded of this reading an accomplished pianist's recent New Yorker memoir about his "Life in Piano Lessons." Here's an excerpt (the student/narrator is Jeremy Denk, and the teacher is William Leland):
Learning to play the piano is learning to reason with your muscles. One of the recurring story lines of my first years with Leland was learning how to cross my thumb smoothly under the rest of my hand in scales and arpeggios. He devised a symmetrical, synchronous, soul-destroying exercise for this, in which the right and left thumbs reached under the other fingers, crab-like, for ever more distant notes. Exercises like this are crucial and yet seem intended to quell any natural enthusiasm for music, or possibly even for life. As you deal with thumb-crossings, or fingerings for the F-shart-minor scale, or chromatic scales in double thirds, it is hard to accept that these will eventually allow you to probe eternity in the final movement of Beethoven's last sonata. Imagine that you are scrubbing the group in your bathroom and are told that removing every last particular of mildew will somehow enable you to deliver the Gettysburg Address.
Of course, a certain amount of grit and gruel also underlies good writing. The Gettysburg Address doesn't just happen, either.


Anonymous said...

"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. "

Lockhart expects us to find this claim to be ridiculous. He undercuts himself because actually, it is true for most people. There are the outliers (him, no doubt) who can fly in the worlds of math and music without practicing the basics. Most of us, however, need the practice and the routines in order to stand, much less fly. As a medium-level practitioner in both music and math, I know that without the ability to read music fluently I would not be able to participate in the world of music at all. And without the standard algorithms, practiced continuously in grades K-10, I would not today be able to function in the math-dependent world I inhabit.

Barry Garelick said...

Lockhart also mischaracterizes math teaching as being devoid of teachers or books that provide challenging problems that elicit wonder. He also fails to realize that not all students are going to be captivated as he was, by such challenges. Unfortunately, Lockhart's Lament has become the anthem of the fuzzies, pointed to as evidence that the world of education is hopeless because no one is listening to them. In fact, the world of education IS for the most part following the fantasies of the fuzzies and may be a big reason for the poor showing of students in K-6 math.

TerriW said...

Lockhart must have really hated The Karate Kid.

cranberry said...

Of course, a certain amount of grit and gruel also underlies good writing. The Gettysburg Address doesn't just happen, either.

Lincoln was a famous near-autodidact.
Abraham went to school when he was 6, 7, 11, 13, and 15 years old. All the time he went to school did not add up to a year. Abe did, though, remember much in between his schooling. At age 21 he could read, write, do arithmetic, and cipher to the rule of three, which was as much as most teachers in Indiana could do.

He reputedly read constantly, anything he could get his hands on; he practiced oratory.

In Lincoln's special case, I think one must credit genius.

Anonymous said...

What interests me most about this blog is that it seems to express the way that education is routinely viewed in Asia. I live in Singapore, and I feel as though your views on education are wholly espoused by the Singapore system and by Asians across the world. In Singapore, every school and parent believes in the need for clear instruction, daily practice, rigor as opposed to fun and games, and high expectations particularly in Math. Furthermore, Singaporeans tend to believe that anyone can be successful in Math if they work hard, as opposed to the dominant Western belief that Math achievement is mostly a result of innate talent. While Westerners have historically criticized Asian education systems for being too "mimetic" and "rote oriented," your blog recognizes that there is, in fact, value to daily practice (of anything - math, music etc.).

The educational terrain in Singapore is changing rapidly as a result of technology and globalization, and my hope for Singapore's schools is that they will combine the best of the West (more exploratory learning and more room for personal expression and creativity) with the best of the East (rigor, commitment to foundational skills, daily practice, and a belief that all children can learn if they work very hard.)

Anonymous said...

One more observation: Perhaps constructivist education systems that require students to make huge intuitive leaps are designed for gifted students. This sort of makes sense since the goal of American schools seems to be creativity and innovation as opposed to basic skills, and most people believe that creativity is a sort of hardwired gift.

In contrast, systematic curricula that require students to build their knowledge block by block (like Singapore Math) are designed for your average student. This makes sense in a Singaporean context because the goal here tends to be to have an efficient, orderly and competent workforce. (It is true, however, that the Sing government is now trying to encourage creativity and innovation far more than ever before.)

Maybe that's the difference: Singapore designs a curriculum with the expectation that every child on the island will learn basic Math well, but the US designs curricula with the expectation that the gifted will be able to make sense of it, and they will become more creative and innovative as a result.

So all Singaporeans will be able to do basic Math, but we may not produce many creative geniuses. In contrast, the US will produce more creative geniuses, but its average Joe won't know a thing.

Barry Garelick said...

Even creative geniuses need to learn basic math. Forcing students to work in groups and explain answers that require a facility with language not yet acquired, will leave even some creative geniuses out in the cold. Forcing students to use inefficient algorithms in order to foster an "understanding" that reform math advocates seem to think does not occur with standard algorithms will also leave some creative geniuses out in the cold. Katharine's point is that even the most talented musicians must learn music in the manner that Lockhart says is soul-killing.

Anonymous said...

Some students must be learning math through these reform methods; otherwise, how would school systems in the US justify using them?

Maybe very bright and creative kids can learn intuitively and independently. When I read American books on education, they seem to suggest that America has very self-motivated and talented kids who learn math by playing in the woods and observing natural patterns, by cooking and playing games, or by imagining and dreaming. In fact, they seem to suggest that your brightest minds are more or less self-taught through play and discovery.

We Asians are a much less interesting and talented bunch: our parents and teachers teach us using text books, and while we enjoy playing in the woods, we rarely learn Math there. We are good at Math because we work hard at it every day, in school and at home.

Americans seem so consumed by the romantic ideal of creativity, discovery, and play as the basis to all learning. We Asians are so boring in comparison. We believe that hard work and daily practice are the basis to all learning. I'm inclined to believe that a balance between these two perspectives is ideal, but it seems hard for people/societies to find this balance.

Coming back to Katharine's post: musicians need to practice and drill every day, but they also need to be immersed in a rich, musical world to nourish their love of music and to counter the "soul-killing" aspects of drill. One without the other (drill without inspiration or inspiration without drill) leads to a lopsided individual/society.

Katharine Beals said...

"Some students must be learning math through these reform methods; otherwise, how would school systems in the US justify using them?"
That's a very good question. I wish school systems would try to answer it with accurate, empirical data. They don't.
To the extent that they attempt to justify Reform Math *without* empirical data, those in charge assert that discovery math levels the playing field for everyone.
In fact, it does the opposite, but only because those with means are getting their math education outside of school, and because the few very talented math autodidacts out there are finding the time to learn on their own.
Speaking of autodidacts, it's important not to assume that people who demonstrate exceptional ability without any formal education do so without working extremely hard on their own--as Abraham Lincoln clearly did.

Anonymous said...

I keep coming back to the piano student's lament and can't get past the fact that it's stunningly wrong.

I play music every day. My son plays music every day. And as often as not we center our playing around "curious black dots and lines." How could it be otherwise? We learn to play music, and in order to learn to play it we both listen to it and read it.

It's true that some musicians manage to get by without ever reading music - mostly folk or pop musicians - but the idea that you should intentionally refuse to learn to read music because it somehow takes the fun out of it is both absurd and childish. It's the kind of idea an ill-tempered seven year old would come up with, and that an evenly-tempered eight year old should have outgrown.

The analogy is quite good, but not to Lockhart's benefit. Yes, learning math without being allowed to learn algorithms or methods developed by others is kind of like learning a new piece without being allowed to see the sheet music, or memorizing poetry without being allowed to read it. But this is not a good thing, it's a bad thing. One of the things these methods have in common is that they're terribly inefficient and show deep disrespect for the time of the student.

It seems like teachers are going on a philosophical strike against teaching. They want to flip the classroom so that they get to hang out and play with kids all day, but the teaching is something pushed onto the parents instead. No phonics, no math, no music theory, if your kids are going to learn that, they'll do it at home or with tutors their parents hire.

There are many things wrong with the way schools work. Being stuck in large groups all day long, squadrons of desks, bells ringing, work on the topic the schedule shows. I hated it, and I don't send my son to school. But they are throwing out the baby with the bathwater. The only good thing schools had going for them was that they were actually teaching something. Now it's the same large groups of age peers, following the schedule strictly, bells for this and that, peer pressure, bullying, horrible food, lord of the flies playground, but without the content. How in the world is that better?

It must be so darn nice to sit on the top of a mountain as a famous mathematician and professor and look down on the simplistic and stultifying way multiplication is taught to third graders at schools that don't cost 35K a year. The public school third-graders have no bread? Well, let them eat cake!

cranberry said...

Speaking of autodidacts, it's important not to assume that people who demonstrate exceptional ability without any formal education do so without working extremely hard on their own--as Abraham Lincoln clearly did.

He did work extremely hard, as the page I linked earlier in the thread stated. Abe received most of his education from the books he read. As he grew up, he became fascinated with books. He loved to read every minute of his spare time. When he went out to plow a field, he put a book under his shirt and read at the end of rows when the horses were resting. His best friend, Dennis Hanks, said, "I never saw Abe after he was 12, that he didn't have a book in his hand or in his pocket. It just didn't seem natural to see a guy read like that." Books were scarce in the backwoods, and each book he got was precious. (...)He read the Bible several times and other books such as Pilgrim's Progress and Aesop's Fables. His favorite book had a very long title: The Life of George Washington, With Curious Anecdotes, Equally Honorable To Himself and Exemplary To His Young Countrymen. (...)George Washington later became one of Lincoln's heroes. One time, Abe walked twenty miles to borrow a book about the United States. In fact, he loved reading so much, he even read a spelling book. He used school books such as Murray's English Reader and Pike's Arithmetic.

At the time, however, his self-education would not have been seen as superior to the education most other members of Congress had received at schools such as Exeter and Andover. I found this online:

Abraham Lincoln did not study Latin and Greek, as far as I can tell. His formal schooling would have had to been focused on the essentials a farmer's child might have been able to use. At the time, his overall education could have been seen as progressive--in a modern sense--in that he followed his interests wherever they led, without being restrained by the contemporary expectation that an educated man would read Latin and Greek, and recite memorized classic authors.