Wednesday, June 13, 2012

A piano student's lament: how music lessons cheat us out of our second most fascinating and imaginative art form

One of the mathematicians most often cited when Reform math advocates critique traditional math is Paul Lockhart’s A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form. His book 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:

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.
In Lockhart’s nightmare, the mission of the primary and secondary schools 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."
As for 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."
But luckily:
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!"
Lockhart stacks the deck just a tad by imagining that no one except the music professionals actually get to hear what music sounds like. Transposed to mathematics, this would be the equivalent of not telling students that the symbol 10 stands for the number of fingers on their two hands, or that the symbol + stands for the process of combining two different quantities into a single quantity. In this respect, Lockhart’s nightmare is completely irrelevant.

But in nearly all other respects Lockhart's nightmare was my reality. During my 12-odd years of piano lessons, I had to:

*practice meaningless drills until I learned how to read those curious black dots and lines to the point of mindless automaticity

*practice meaningless scales to the oppressive tick of the metronome

*practice even more meaningless and repetitive finger exercises to the point of mindless automaticity and a punishing buildup of finger muscles.

Surely true musical artists like Vladimir Horowitz and Misha Dichter weren't forced through such mindless, trivial, time-consuming, soul-crushing tedium. Surely, from the first day they lay finger tips to keyboard, they grasped immediately the beautiful patterns in the lines and dots before them, and, as their souls communed with Scarlatti and Chopin, the music coursed seemlessly out of the tips of their fingers.

Just imagine how many other people might have discovered the joys of piano playing if they, too, had enjoyed the same freedoms as the professionals must!


Auntie Ann said...

My mom always played the piano on her own, never took a lesson, and managed to self-teach herself a lot. Finally, in her late 50's she found a music teacher. She was assigned some scales, but she wanted to know the point of them. The teacher said that it helps you memorize pieces. Since my mom could memorize almost anything after playing it a couple times through, she pointed out that she didn't need the scales. Her teacher agreed, and mom got to play real songs instead.

Barry Garelick said...

The purpose of scales is to know how to play pieces in various keys. This means flattening or sharpening certain notes automatically. It increases fluency.

Piano lessons florida said...

Too much of pressure can sometimes make hard to learn the lessons properly.It is very much required to go through to the scales and points but if a person can play piano freely without memorizing points and scales, then we should leave that person there and help him to learn some free notes instead of forcing him to learn the specific scales.

Brian Rude said...

Katharine, would you say that you had a good piano teacher, or a poor one? Or were there several teachers? In twelve years I can easily imagine as many as five or more piano teachers. Did they all teach the same? Do one or two stand out as better teachers than the others, or worse?

At the moment my main question is, did they all teach the same? And, more generally, do all piano teachers teach the same? I ask this because it gets at an idea that I think is very important in the field of education, but mostly overlooked. Educational writers are quick to assume that there is a uniformity of teaching in a given subject. We see or hear phrases like "The way math is taught in America . . . . " as if there was no variation among teachers, no variation among localities or cultures, and as if every one gets the same picture when someone says "the way it is taught . . . ". It has always seemed to me that that is not at all the case. I would expect to find substantial variation in how any subject is taught. I would expect that some of these variations are blatant, easily recognized by observing one minute of instruction. I would expect other variations to be very subtle, apparent only after careful observation and analysis.

We know something about the variation in how math is taught, enough to keep the math wars going. We have some idea of the typical algebra classroom of the 1950's, the ideas of the "new math" of the 1960's, and the ideas of the "fuzzy" math of the present. But those are pretty gross pictures. Are those gross variations the only variations worth investigating?

Brian Rude said...

Suppose an educational investigator spends ten hours watch Mrs. Jones teach algebra in a high school, and discusses with Mrs. Jones why she does what she does, and then spends another ten hours watching Mr. Smith teach another section of the same course using the same book, also discussing with Mr. Smith why he does what he does. Would the pictures of these two examples of teaching be identical? Surely not. Would the pictures of the teaching of these two teachers be substantially the same, differing only in minor details? Well, who is to say what constitutes "substantial"?

Let us turn the question around a bit. Imagine a student who takes three months of the course from Mrs. Jones and then for some reason finishes the rest of the year with Mr. Smith. What would this student tell his friends about a comparison of these two teachers. Let us assume this particular student has no ax to grind, and is a reasonably conscientious and intelligent student. Would details emerge over time that would be of interest to us, people who are interested in teaching and learning?

The educational investigator who watches Mrs. Jones and Mr. Smith teach will write something. Will we get a good picture of how these two teachers teach from what he writes? The student who somehow ended up in both of their classes can also, if we ask him, give us a picture of the teaching of Mrs. Jones and Mr. Smith. How will the pictures from these two perspectives differ?

Now let us change the scenario a bit. Suppose an educational investigator watchs ten of your piano lessons, let’s say when you were twelve years old, and let’s say your most pedantic piano teacher, and then goes across town, or perhaps across the state, and watches ten piano lessons given to another twelve year old by a teacher with quite a different musical and personal history. I wonder how much in common these two pictures would have. Would the differences be minor? Could they be substantial? Could differences that first appear minor turn out to be very substantial when explained by one of the teachers.

I'll try to explain my point now, my big point, at least a point bigger than assuming, or not assuming, that a given subject is taught uniformly by all

Brian Rude said...

teachers. I have long felt, and argued at times, that simple accurate comprehensive description is a beginning point of any science, an absolutely essential beginning point, but a beginning point that is mostly missing in education. Yes, the educational investigator I mentioned will write something, about both math teachers or about both piano teachers. Will it constitute a simple, accurate, and comprehensive description? The student who experienced both teachers won't write anything, but he might be able to tell us things worth knowing if we know what and how to ask.

Where do we go to find simple, accurate, and comprehensive description of and algebra class of 1950, and of 1965, and of 2012? Does it exist? My point is that is should exist, and that we shouldn't expect any real progress in the study of education until it does.

Now let my explain why a discussion of piano lessons elicts interest in me. I never took piano lessons as a kid, but I played piano. My mother taught me enough that I got the idea of note reading. I studied music in college rather extensively and took some piano lessons as a result of that. Today at age sixty eight I play piano every Sunday for our church. This is not saying much, as it's a pretty small congregation. But it makes me think, what happened to all those piano lessons of every other member of our church. We're pretty educated, most of us have degrees, some advanced. The vast majority of our small group had years of piano lessons as children. Yet none of them want to play simple tunes on the piano to accompany the hymns in our service.

So I ask, and have often

Brian Rude said...

asked in recent years, is there something wrong with the way piano is taught in our culture?

I can quickly jump to an answer, yes, there is something wrong with how piano is taught in our culture. But more importantly, I think, is the question, how is piano taught in our culture? Well, don't we all know how piano is taught in our culture? My answer, of course, is no, no we don't know how piano is taught in our culture. Any person has a memory of how piano was taught to him or her, but is that the way it was for everyone? How would we know?

My wife had something like five or six years of piano lessons as a kid? What happened? No trace remains that I can tell. Many of my friends at church would say the same. What happened to all those years of piano lessons?

When our youngest daughter was in high school a little over a decade ago she was very musical. She did well on violin and saxophone and was in various singing groups. Music was important to her. In her senior year she gave at least passing attention to the idea of being a music major in college. My wife and I suggested that maybe she should therefore take piano lessons, something that somehow had never come up before. She did, and I looked forward to hearing some piano music in the house. She knew so much music already that she ought to progress rapidly. When I would ask her how the piano lessons were going she would say, fine, she's supposed to work on scales and exercises. She liked her teacher. Everyone liked her teacher, but I reluctantly concluded after a few months that the teacher was not doing a very good job. I don't recall every hearing her play a simple tune on piano. She was supposed to do scales and exercises, and I guess they were not very motivating to her.

So my daughter's piano experience and your description of your twelve years makes it easy to believe piano teaching is often done wrong. But surely it is often done right, though the evidence for that doesn't seem to be at my fingertips.

So if piano teaching in our culture is done wrong, then I would like to first ask, how is it done? Where can I go to read simple, accurate, and comprehensive descriptions of how piano teaching is done.

I’m sure you have some basis of comparing your piano experience with other’s piano students. Do you think your experience is the norm? I would think not, but I have no way of knowing.

Katharine Beals said...

Hi Brian,

Many apologies both for my delay in replying, and for the fact that that I didn't intend anyone to take my commentary about my piano experience seriously! Rather, it was intended as satirical extension of Lockhart's Lament.

Scales and exercises (including those that help you learn how to read music), while a drag, made me a much better player than I otherwise would have been. The same is true, at a much, much higher level of course, of the piano greats like Horowitz, etc. I doubt many people get very far at all with classical music performance without doing drills.

Brian Rude said...

Okay, that makes more sense now. I did have the feeling that maybe I was missing something important. I just didn't know what it was. I feel a little foolish, but it was a nice opportunity to once again make a few points that I think are important.

So maybe the state of piano teaching in our culture is not in bad shape after all. Maybe it's in pretty good shape. Again, I don't have much of any way to know. But I still wonder about all those years and years and years of piano lessons in the past of many of my friends, the lessons that appear to have vanished into a black hole.

And now I’m wondering about Lockhart’s Lament. Maybe it is totally a put on. People who like it (and I am not one of them) seem to accept it as genuine. Could it be that he meant it as satire?

Katharine Beals said...


I think that lots of skills drilled and developed in childhood activities end up vanishing into holes unless they are pursued in adulthood. Most adults don't have the time to keep up all the activities they devote time to in childhood.

For those who don't pursue STEM fields, this might include most of algebra. Foreign language skills may similarly vanish.

That doesn't mean that these skills were poorly taught, or that they shouldn't have been learned. There may be some residual benefits to having once played an instrument or learned algebra or Spanish; more importantly, no one can predict what will turn out to be important in adulthood.

If Lockhart's Lament is satire, he really ought to speak up instead of quietly chuckling to himself!

Brian Rude said...

Good point, Katharine, that much of anything we learn is lost over time if we don't keep it going some way. My three semesters of college German are mostly gone. Botany was very interesting, both the freshman introductory course I took as a college freshman and the plant taxonomy course I took, for some long forgotten reason, some years later. But the knowledge that remains from those two courses is pretty meager. I majored in math as an undergraduate, but when I decided to get back into math in late middle age I knew I had forgotten most of the college math I had ever known. I spent a full year working hard to recover that math before entering graduate school in 1998. Examples of disappearing knowledge are easy to come by.

There is another concept that I think is very important here. That is the idea of opening doors. Even a year of piano lessons opens the door to music, as does learning a musical instrument in fifth grade. Taking high school chemistry opens the door to more chemistry. Once a door is open a student may decide not to walk through that door. That happens very often, but that doesn't mean it was not worth while to open that door. Many courses I took in college opened doors for me, doors that I peeked through, but totally walked away from when the final exam was over. The value of opening doors does not have much to do with the size of residual knowledge. I consider opening doors one of the very important reasons for education.

But I want to get back to the idea of "residual knowledge". What do we know about it? What should we know? Has residual knowledge been the focus of educational research? Should it be? Surely the concept of residual knowledge is important. We invest heavily to learn. Surely that investment ought to be thoughtful and informed. Having at least some idea of what knowledge will remain surely could help us decide what to study. Once again I am prompted to argue that the science of teaching and learning is so primitive as to hardly exist.

Getting back to piano lessons,

Brian Rude said...

and the question of where they go - my subjective opinion is that my residual knowledge from two botany courses, or my residual knowledge from three semesters of German, is not nearly as meager as my wife's residual knowledge or skill from her years of piano lessons as a kid. There seems to be a special black hole for piano lessons. Is my subjective judgment all wrong about this? How would we know? Is age of learning important in these examples? Is the nature of the learning important in these examples. Piano playing has a strong component of motor skill, but also a strong component of knowledge. Is that important? How come we never forget how to ride a bike? Is it even true that we never forget how to ride a bike?

What are we to think when we are told, as we seem to be now and then, that some high percentage of a certain age group cannot correctly place the Civil War and the Revolutionary war in the correct time order. Can we argue there is something seriously wrong with the way history is taught in our culture? Or can we just say, "Well, people forget a lot."? Well, sure, people forget. But forgetting the order of the Revolutionary and Civil war? That boggles my mind. If history can be well taught throughout twelve years of school and then degrade to that low level in a few years, then where does that leave us?

Maybe the study of residual knowledge would indicate that it is entirely a matter of ongoing cultural props, or the lack thereof. If your culture does not provide some props for a subject, it will disappear entirely. Or maybe the study of residual knowledge would indicate the right amount of overlearning is crucial. I have long argued for a “four year rule” in this regard. You will only retain knowledge of a subject that is about four years back from what you studied. By this rule you better take four years of high school math if you want to really remember the arithmetic you learned by the end of the eighth grade. Or maybe the study of residual knowledge will show that there is something about the way that a subject is taught that determines whether it will be retained to a substantial degree.

Or the study of residual knowledge might show something entirely unexpected.

It is often observed that the residual knowledge of a subject may seem small, but that it is important. We hear sentiments to the effect that after you forget all the facts of a subject, what's left is education. Well, maybe. Maybe not. I don't know. That's believable, but is that all we can say about it?

FedUpMom said...

George Orwell said that he forgot all his Greek (which he had studied extensively) within a few years of leaving Eton, but the snobbery he learned there stayed with him forever. I'll look for the quote (it's a classic!) ...