Is it possible to start with a digression? Sure, whatever. Lets do this.
I always scratch my head when I hear people complain about scientists doing research and then concluding “the obvious.” It's like these people don't know what science is. You don't know something is obvious until it has been confirmed, yo. How many times have scientists made startling discoveries that upended what we thought was obvious? I don't know the actual number, but I'm pretty sure it is “lots.”
Digression over! Speaking of the obvious, I have been wondering over some received wisdom. It goes like this: “Practice everyday. Are you practicing? No. Is it a day? Yes. Then why aren't you practicing?”
Why aren't I practicing? Maybe because, possibly, practicing every day isn't the best way to do learn something. Do I know it isn't the best way to learn an instrument? No. Is mayonnaise an instrument? That depends on how much you practice with it. Horseradish, however, is most certainly not an instrument. Get that wanna be poser outta here.
Bear with me. I may not know that practicing everyday is not the best way to use your time, but I have a suspicion. And I would like it tested. Here is how my suspicion goes.
First! Let us say you are training for a marathon. What do? You start by running not a lot, you start by running a little. And then? And then you rest. And then you run a little again, and then you rest, and then you run a little more, and then you rest, and then... No 'and then!'
I mean, there's more 'and then.' You 'and then' until you've run a marathon. But the key here is, you regularly rest your muscles as part of the training. If you don't rest your muscles, you can do some serious harm. You rest or you run until you're forced to rest. Given a choice, I would rather just rest, thank you very much.
*two hours later*
SECOND! Have you ever been working on a problem and got stuck? The answer is yes. We all have come across problems we've got stuck on. You know what usually happens? You work on the problem until you get a nose bleed. Then you give up and go do something productive like play Farmville. Then you go to sleep. Then you wake up the next day and BAM! All of a sudden you wonder why you were having trouble with your problem. It's so obvious! How did I not see that before?!
Turns out, this happens a lot in music practice, too. A particular passage, for whatever reason, just seems intractable. Then you go to sleep, wake up the next morning refreshed, and you find the passage has become tracted. Good job brain! But I've noticed that giving yourself distance from even pieces you “know” helps.
Weird.
Third! This doesn't have to do with learning so much as balance. There's more to life than music. In fact, I wonder if our musicianing is in fact hampered if you don't have a life outside of it. I once read that Stravinsky, Poulenc, and some other musical cats got into a giant drunken pillow fight at a soiree. Arnold Schoenberg played tennis. Mendelssohn traveled. A lot. Mozart partied all the damn time. And yet, somehow, they all managed to produce masterpieces, this despite wasting their time doing so many non-musical things. How 'bout that.
In any case, I'm not making any definite conclusions. I'm just sayin'. There's a physical aspect to music, and we know that physical rest is important, especially for injury prevention (Leon Fleisher is out there somewhere, finding himself nodding in agreement, to what he does not know, but he knows it is important). There's also a mental aspect to music, and we know that rest is often a crucial part of problem solving (what, you think Newton was sciencing under the apple tree? No way. He was napping). And we know that having a social life is important for basically everything (this is more for those people who are in music school practicing 20 hours a day: seriously, go home and have a drink).
So it strikes me as not only possible, but very likely that we, as musicians, do not need to practice music everyday, and that we shouldn't feel guilty if we miss a day or two. In fact, if you do miss a day, you probably did yourself a favor. But I don't know that. I'm just pondering on something obvious that may not be as obvious as it's cracked up to be.
Showing posts with label teaching cello. Show all posts
Showing posts with label teaching cello. Show all posts
Sunday, June 15, 2014
Wednesday, June 11, 2014
Beyond Good and Bad Musicians
At a pub with a friend. Irish folk band playing Irish folk music. Music is out of tune, the singer's tone is a warbler, the bass is out of sync with the drums, and everything about the music is objectively terrible.
Friend says, “Oh god, they are terrible.”
I says, “What are you talking about? They're awesome!”
At an open mic. Some beginners are playing beginner music. The music is out of tune, the singer's singing is swinging, the bass is trying to follow the drums but this is problematic because there aren't any drums, and everything about the music is objectively terrible.
Afterward, beginner says to me, “Oh god, I was terrible.”
I says, “What are you talking about? You were awesome!”
Let me be clear. I teach music. And when I teach music, I have to point out all of the missed notes, the wonky intonation, the miscounted beats, and all the rest of that nonsense. That's what my job is, kind of. It's just that somewhere along the way, we forget that all of that is nonsense, and we miss the point entirely.
In fact, we not only miss the point, we set ourselves on a one way track towards musical masochism.
“I'm not playing good, therefore I'm not good, and therefore I can't do other stuff good, too.”
I mean, when I put it like that, learning to play music suddenly sounds like an awful idea. “But wait!” you say, putting on your best Billy Mays impression. “I don't mean the person is bad! I mean the music is bad!”
Sure, but here's language being tricky again. If that's really what you mean, then why don't you say what you mean rather than hope people guess you mean what you mean. The music is awful. But we don't say, “Wow, this music is terrible.” We say, “Wow, they're bad,” or, “This composer is terrible,” or “What a shitty band!” We rarely talk about the music. We talk about the people making it.
The most common musical critique is not a musical criticism, but a moral one.
Step back a bit. If I'm paying some of my hard earned money to hear someone play music, I would rather the music be something well done than poorly performed. I get that. But that's not what I'm talking about, straw man. You and your head full of straw... no wonder you get so confused.
No, what I'm talking about is something more fundamental. Which is music, which was around for a really long time before money stepped into the picture. “How is it,” I think to myself, “that such a natural human expression as music, sung to babies, played at dances, in farm fields, in churches, on pirate boats... How is it that such musical expression has become an indictment of a person's character rather than a person's ability? Oh right, Plato.”
Actually, I don't think it's Plato's fault. I'm pretty sure he was just clearly expressing a sentiment that was widely intuited. That is to say, music alters behavior so music can be used to instill virtue or vice. To be doubly fair to Plato, I'm fairly certain he was also talking about what the music expresses rather than how well the music is expressed. It was all that “Darned kids, get off my lawn!” kind of stuff.
In short, there's no getting to the wherefores in a short blog post like this. But I can say it's taken a wrong turn somewhere along the line. I have had to assure not a few students that just because they are not playing good does not mean that they, too, as a person, are therefore not good. Few of them believe me. I know they don't believe me because after I reassure them, they nod their heads and then return to the music in wide-eyed terror or dismay.
So here's the problem, writ large for people who wear bifocals. Nobody starts good at anything. You have to learn. But the way we talk about “not playing well” is to instead say “you're bad at playing,” which if the human brain actually processed statements in their entirety wouldn't be so bad, but it usually just stops at “You're bad,” and then slinks off in shame.
If we follow that logic to its not at all distant conclusion, we must therefore acknowledge that not only are our children terrible, terrible, truly awful people for not knowing how to do much of anything well, but also that everybody is terrible because there's always something you're not going to be good at. In my case, I am not good at not ending sentences prepositions with.
Oops, I did it again.
Friend says, “Oh god, they are terrible.”
I says, “What are you talking about? They're awesome!”
At an open mic. Some beginners are playing beginner music. The music is out of tune, the singer's singing is swinging, the bass is trying to follow the drums but this is problematic because there aren't any drums, and everything about the music is objectively terrible.
Afterward, beginner says to me, “Oh god, I was terrible.”
I says, “What are you talking about? You were awesome!”
Let me be clear. I teach music. And when I teach music, I have to point out all of the missed notes, the wonky intonation, the miscounted beats, and all the rest of that nonsense. That's what my job is, kind of. It's just that somewhere along the way, we forget that all of that is nonsense, and we miss the point entirely.
In fact, we not only miss the point, we set ourselves on a one way track towards musical masochism.
“I'm not playing good, therefore I'm not good, and therefore I can't do other stuff good, too.”
I mean, when I put it like that, learning to play music suddenly sounds like an awful idea. “But wait!” you say, putting on your best Billy Mays impression. “I don't mean the person is bad! I mean the music is bad!”
Sure, but here's language being tricky again. If that's really what you mean, then why don't you say what you mean rather than hope people guess you mean what you mean. The music is awful. But we don't say, “Wow, this music is terrible.” We say, “Wow, they're bad,” or, “This composer is terrible,” or “What a shitty band!” We rarely talk about the music. We talk about the people making it.
The most common musical critique is not a musical criticism, but a moral one.
Step back a bit. If I'm paying some of my hard earned money to hear someone play music, I would rather the music be something well done than poorly performed. I get that. But that's not what I'm talking about, straw man. You and your head full of straw... no wonder you get so confused.
No, what I'm talking about is something more fundamental. Which is music, which was around for a really long time before money stepped into the picture. “How is it,” I think to myself, “that such a natural human expression as music, sung to babies, played at dances, in farm fields, in churches, on pirate boats... How is it that such musical expression has become an indictment of a person's character rather than a person's ability? Oh right, Plato.”
Actually, I don't think it's Plato's fault. I'm pretty sure he was just clearly expressing a sentiment that was widely intuited. That is to say, music alters behavior so music can be used to instill virtue or vice. To be doubly fair to Plato, I'm fairly certain he was also talking about what the music expresses rather than how well the music is expressed. It was all that “Darned kids, get off my lawn!” kind of stuff.
In short, there's no getting to the wherefores in a short blog post like this. But I can say it's taken a wrong turn somewhere along the line. I have had to assure not a few students that just because they are not playing good does not mean that they, too, as a person, are therefore not good. Few of them believe me. I know they don't believe me because after I reassure them, they nod their heads and then return to the music in wide-eyed terror or dismay.
So here's the problem, writ large for people who wear bifocals. Nobody starts good at anything. You have to learn. But the way we talk about “not playing well” is to instead say “you're bad at playing,” which if the human brain actually processed statements in their entirety wouldn't be so bad, but it usually just stops at “You're bad,” and then slinks off in shame.
If we follow that logic to its not at all distant conclusion, we must therefore acknowledge that not only are our children terrible, terrible, truly awful people for not knowing how to do much of anything well, but also that everybody is terrible because there's always something you're not going to be good at. In my case, I am not good at not ending sentences prepositions with.
Oops, I did it again.
Monday, June 9, 2014
Playing Music is Hard
Fair warning: I am about to split a hair to make a point. It is true, splitting hairs is a past time not a few find tiresome, but considering a point is a definite space of no dimensions, I would say that a split hair is entirely too generous for the task.
Alas, it must suffice.
Speaking of tiresome things, allow me to point to the point that will point to my point. I have a general sense, as a teacher, that many people have an intuitive understanding that playing an instrument is not easy. This may seem a small thing to be irked by. And it is. But it is not the mindset that I find irksome, it is the conclusion towards which such a mindset inevitably leads.
The problem is this. Saying “Playing an instrument is not easy,” really amounts to saying almost nothing at all. Because, for sure, you have said what it is not, but neither have you said what it is. I could say, for instance, “Playing an instrument is not easy, but... it's not that difficult, either.” Such a statement is a perfectly valid statement. Hence the hair. Assuming something is “not easy” is not the same as assuming something is “difficult.”
If I return to my previous statement, now with my updated assumption, I can say “Playing an instrument is difficult, but,” but I cannot follow that but with “...it's not difficult.” I mean, I can. “It's difficult but not difficult.” There, I did it! Hooray me! If you wish to stop here, I wish you the best, but I don't have high hopes for your future prospects.
For the people who continue on because they are not satisfied by statements of utter nonsense, compare “It's difficult” to “It's not easy, but it's not difficult,” and you can see how framing the problem in the positive (it is this) as opposed to the negative (it is not that) makes for a statement rather more clear.
“So what?” cries the, I must imagine, increasingly exasperated reader, who has not yet grasped my true point because I have not yet pointed it out. “So it's difficult and not not easy. No need to be pedantic. I know what you mean!” But that, there, is precisely the point. You do not know what I mean, because if you did, you'd understand why I, as a teacher, find a student who assumes learning an instrument is merely “not easy” far more difficult to teach than a student who assumes that learning an instrument is, in fact, immensely difficult.
For you see, or are about to see after I tell you, that a student who begins with “It's not easy” can slip, with great ease, into the territory of “but it can't be that difficult.” And as soon as they make that step, and they almost all do, they have started down the path which ends with the instrument being almost impossible rather than simply difficult. Because if “it can't be that difficult,” then that means it won't take that much effort, which means I don't need to practice how my teacher says I need to practice, so I won't because what my teacher is suggesting is to put lots of effort into something which, while not easy, is surely not so difficult as to require the kind of effort my teacher is requesting of me.
That logic may sound so convoluted as to be unlikely, but it happens every time. Every. Time. To illustrate, this is a summation of every teacher-student conversation ever after the student comes to the above conclusion:
“Student, did you practice your scales?”
“Yes.”
“Good, then this shouldn't take too long. Play a D major scale for me.”
“I'd really rather not. Lets play Beethoven, instead.”
“-.-”
“Ugh. Fine.” *student fails to play a D Major scale*
“Oh. Ok. Sure. Uhm. Look at this piece by Beethoven. What is its theme?”
*student shuffles uncomfortably*
“It's a SCALE. How can you play this piece by Beethoven, which is infinitely more difficult than playing a scale, if you can't play a scaaaaaaaaale?”
And then you waste an entire lesson going over D Major again because they didn't think it was that important, and they didn't think it was important because their mindset led them to believe it was not important. Because it's not easy, but it's not hard. It's just something in between. So lets cut out all the boring stuff and short cut ahead to Magical Christmas Land where everybody only eats cake and never gets diabetes and vegetables are regularly assembled to do all your math homework.
Unfortunately for them, and every teacher who teaches them, learning to play a musical instrument is not “of middling difficulty.” It is “of excruciating difficulty.” The human brain being what it is (that is to say, both lazy and full of its own self importance), anything “of excruciating difficulty” is rather inconvenient to its notion of preconceived greatness. Also, anything “of excruciating difficulty” represents a rather uncomfortable amount of work. So I sympathize. Anything “of excruciating difficulty” represents exactly the anti-thesis of what the human brain is all about.
So the brain shoots itself in its metaphorical foot. Again. Starting from “It's not easy, but it's not hard” may seem to be a better place to start, psychologically speaking, than “It's difficult,” because if it's difficult we may not ever start at all. There is some truth to that, but it comes at the price of great harm to one's future efforts. You wind up making it more difficult on yourself than it is, which is already quite difficult. So how to begin?
Like this.
“It's excruciatingly difficult... but it's also possible.”
Once you reconcile yourself to the difficulty of the task, everything becomes possible. It becomes possible because you realize there are no short cuts, that, in fact, the short cuts take you the long ways around back to where you started. That if you sit down and do the work that is required of this difficult task, it is merely difficult. And once it is merely difficult, it is simply a matter of doing what needs to be done, and nothing more.
Start by doing what is necessary. Then do what is possible. And suddenly, you are doing the impossible.
--- St. Francis of Assisi
Alas, it must suffice.
Speaking of tiresome things, allow me to point to the point that will point to my point. I have a general sense, as a teacher, that many people have an intuitive understanding that playing an instrument is not easy. This may seem a small thing to be irked by. And it is. But it is not the mindset that I find irksome, it is the conclusion towards which such a mindset inevitably leads.
The problem is this. Saying “Playing an instrument is not easy,” really amounts to saying almost nothing at all. Because, for sure, you have said what it is not, but neither have you said what it is. I could say, for instance, “Playing an instrument is not easy, but... it's not that difficult, either.” Such a statement is a perfectly valid statement. Hence the hair. Assuming something is “not easy” is not the same as assuming something is “difficult.”
If I return to my previous statement, now with my updated assumption, I can say “Playing an instrument is difficult, but,” but I cannot follow that but with “...it's not difficult.” I mean, I can. “It's difficult but not difficult.” There, I did it! Hooray me! If you wish to stop here, I wish you the best, but I don't have high hopes for your future prospects.
For the people who continue on because they are not satisfied by statements of utter nonsense, compare “It's difficult” to “It's not easy, but it's not difficult,” and you can see how framing the problem in the positive (it is this) as opposed to the negative (it is not that) makes for a statement rather more clear.
“So what?” cries the, I must imagine, increasingly exasperated reader, who has not yet grasped my true point because I have not yet pointed it out. “So it's difficult and not not easy. No need to be pedantic. I know what you mean!” But that, there, is precisely the point. You do not know what I mean, because if you did, you'd understand why I, as a teacher, find a student who assumes learning an instrument is merely “not easy” far more difficult to teach than a student who assumes that learning an instrument is, in fact, immensely difficult.
For you see, or are about to see after I tell you, that a student who begins with “It's not easy” can slip, with great ease, into the territory of “but it can't be that difficult.” And as soon as they make that step, and they almost all do, they have started down the path which ends with the instrument being almost impossible rather than simply difficult. Because if “it can't be that difficult,” then that means it won't take that much effort, which means I don't need to practice how my teacher says I need to practice, so I won't because what my teacher is suggesting is to put lots of effort into something which, while not easy, is surely not so difficult as to require the kind of effort my teacher is requesting of me.
That logic may sound so convoluted as to be unlikely, but it happens every time. Every. Time. To illustrate, this is a summation of every teacher-student conversation ever after the student comes to the above conclusion:
“Student, did you practice your scales?”
“Yes.”
“Good, then this shouldn't take too long. Play a D major scale for me.”
“I'd really rather not. Lets play Beethoven, instead.”
“-.-”
“Ugh. Fine.” *student fails to play a D Major scale*
“Oh. Ok. Sure. Uhm. Look at this piece by Beethoven. What is its theme?”
*student shuffles uncomfortably*
“It's a SCALE. How can you play this piece by Beethoven, which is infinitely more difficult than playing a scale, if you can't play a scaaaaaaaaale?”
And then you waste an entire lesson going over D Major again because they didn't think it was that important, and they didn't think it was important because their mindset led them to believe it was not important. Because it's not easy, but it's not hard. It's just something in between. So lets cut out all the boring stuff and short cut ahead to Magical Christmas Land where everybody only eats cake and never gets diabetes and vegetables are regularly assembled to do all your math homework.
Unfortunately for them, and every teacher who teaches them, learning to play a musical instrument is not “of middling difficulty.” It is “of excruciating difficulty.” The human brain being what it is (that is to say, both lazy and full of its own self importance), anything “of excruciating difficulty” is rather inconvenient to its notion of preconceived greatness. Also, anything “of excruciating difficulty” represents a rather uncomfortable amount of work. So I sympathize. Anything “of excruciating difficulty” represents exactly the anti-thesis of what the human brain is all about.
So the brain shoots itself in its metaphorical foot. Again. Starting from “It's not easy, but it's not hard” may seem to be a better place to start, psychologically speaking, than “It's difficult,” because if it's difficult we may not ever start at all. There is some truth to that, but it comes at the price of great harm to one's future efforts. You wind up making it more difficult on yourself than it is, which is already quite difficult. So how to begin?
Like this.
“It's excruciatingly difficult... but it's also possible.”
Once you reconcile yourself to the difficulty of the task, everything becomes possible. It becomes possible because you realize there are no short cuts, that, in fact, the short cuts take you the long ways around back to where you started. That if you sit down and do the work that is required of this difficult task, it is merely difficult. And once it is merely difficult, it is simply a matter of doing what needs to be done, and nothing more.
Start by doing what is necessary. Then do what is possible. And suddenly, you are doing the impossible.
--- St. Francis of Assisi
Friday, June 14, 2013
Building Epiphanies
I finished my little summer break recently, and have started teaching again. For those who don't know, I teach private cello lessons. It's often kind challenging, and you have to be a little bit careful about well meaning but over bearing mothers who are making their kids do a thousand and one different extra-curricular activities, but... it's a lot of fun. At least, it is to me. I know other people who hate it, which makes me wonder why they're doing it. I mean, ok, money, but come on. The money isn't that good in private teaching. If you chose private teaching to make lots of money, well. You chose poorly.
Early on in my blogging, I wrote a couple of times about a book called "How People Learn." I thought it was a good book while reading it, but I'm convinced it's actually a great one. That's because I took some of the principles laid out in the book and used them in my lessons. The impact was immediate and profound. When you see a student's bow grip and bow stroke change dramatically for the better, and when even the student realizes they've hit on something good because they can feel and hear the difference, then you know you've got a winner.
All in all, they were some phenomenal lessons. When I did my post-teaching debriefing with myself (where I ask myself what I did well, what I did poorly, what was ok but could have done better, what I missed, etc.), I spent a lot of time thinking about what went right. Clearly, a lot of it came from the book, but there was something that happened that the book didn't cover very much. The students all had, within the lesson, epiphanous moments. Ah-ha moments. And I realized during my debriefing that those moments, while not consciously engineered, were not accidents either.
Either that, or we were terrifically, miraculously lucky.
Here's what I think happened.
The Will to Power
One of the biggest points "How People Learn" makes is, you don't teach the facts, you teach the principle. If you teach the principle, the facts will make sense and come naturally on their own. That's basically what the whole book is about, actually, and how to approach that fact of learning/teaching. I have puzzled over what the principles of movement are since I wrote about that particular pedagogical problem. Talking with numerous friends and a few teachers, here is what I have come up with.
1. Strength is highest in your core (torso), decreases as you move away from the core, and is lowest at the periphery (feet and hands). This is pretty easy to observe, actually. The muscles in your hand are far smaller than even the muscles in your forearm.
2. Strength is not the same as tension, and tension must be balanced: too loose, and you'll drop your bow; too tense, and you will hurt yourself.
3. Finally, movement starts from the muscles you activate and moves outward. If the movement starts from the wrist, the hand will move; from the forearm, the wrist and hand and fingers. etc.
The principle at work is thus quite simple: effective and relaxed movement starts from strength (the core) and radiates outward; but in order for that strength to be leveraged, it must be channeled. Too little tension, and the strength dissipates, too much and the strength is blocked. While not strictly part of the above principle, it should be noted that twisting (torque) is more effective than pushing (force), and that we should strive to gain mechanical advantage (give me a large enough lever and a fulcrum, and I can move the world) wherever we can.
Learning Bug in the Teaching Web
Once I had settled on the principle, I set about trying to teach it. But I didn't start with the principle, as the book tended to suggest. I instead hid the principle at the center of discussion, and led my students around the periphery, covering a wide variety of apparently unrelated problems. I did a number of the tricks in the book: Socratic method; teasing out assumptions; testing assumptions rather than simply correcting them; creating hypotheses and testing those. Those were all quite effective.
But then, slowly, gradually, I led my student towards the actual issue, the thing that tied everything together. When we got there, a most fascinating thing happened: an epiphany. And not just a random one, either! In teaching, we don't want to rely on chance... Natural epiphanies can be enlightening, but they are rather flighty birds, to be sure. No, this epiphany was instinctively (or accidentally) constructed. As soon as the principle became clear, the student went: "Oh. Oooooh!"
Thinking about what an epiphany is should make it quite obvious that this was the most natural reaction in the world. An epiphany is simply the sudden realization that a number of unrelated facts or problems are all related by an underlying idea. And that's exactly what we made. Epiphanies. The best part? Epiphanies are some of the most powerful aids to memory we can come across. It is very difficult to forget something that comes in the form of an epiphany. In its most extreme form, think of religious conversion. Now scale it back to earthly levels, and that's exactly what we've got.
Now go out and make some epiphanies happen!
Daily Recommendation
As usual, I have a couple of pieces in keeping with the theme. The first is a little piece by Claude Debussy called "Dr. Gradus ad Parnassum." The title alludes to what is perhaps the first musical text book in Europe, "Gradus ad Parnassum" by Johann Joseph Fux. The book is a series of exercises in counterpoint (the art of writing one melody against another), and was studied by a Haydn, Beethoven, and Mozart, among many others.
The second is the 4th movement of Mozart's Symphony 41. It, too, allegedly uses a motive found in Fux's text, but uses it brilliantly in a 5 voice fugetta (little fugue) featuring four themes all more or less at the same time.
Claude Debussy: "Dr. Gradus ad Parnassum," from the Children's Corner Suite.
Amadeus Mozart: Symphony 41, K. 551* 4th movement.
*Mozart's works were written before number works with an opus number was common. His pieces were all catalogued by 19th century scholar Ludwig von Köchel. Hence the "K." Like K-mart. Except klassier.
Early on in my blogging, I wrote a couple of times about a book called "How People Learn." I thought it was a good book while reading it, but I'm convinced it's actually a great one. That's because I took some of the principles laid out in the book and used them in my lessons. The impact was immediate and profound. When you see a student's bow grip and bow stroke change dramatically for the better, and when even the student realizes they've hit on something good because they can feel and hear the difference, then you know you've got a winner.
All in all, they were some phenomenal lessons. When I did my post-teaching debriefing with myself (where I ask myself what I did well, what I did poorly, what was ok but could have done better, what I missed, etc.), I spent a lot of time thinking about what went right. Clearly, a lot of it came from the book, but there was something that happened that the book didn't cover very much. The students all had, within the lesson, epiphanous moments. Ah-ha moments. And I realized during my debriefing that those moments, while not consciously engineered, were not accidents either.
Either that, or we were terrifically, miraculously lucky.
Here's what I think happened.
The Will to Power
One of the biggest points "How People Learn" makes is, you don't teach the facts, you teach the principle. If you teach the principle, the facts will make sense and come naturally on their own. That's basically what the whole book is about, actually, and how to approach that fact of learning/teaching. I have puzzled over what the principles of movement are since I wrote about that particular pedagogical problem. Talking with numerous friends and a few teachers, here is what I have come up with.
1. Strength is highest in your core (torso), decreases as you move away from the core, and is lowest at the periphery (feet and hands). This is pretty easy to observe, actually. The muscles in your hand are far smaller than even the muscles in your forearm.
2. Strength is not the same as tension, and tension must be balanced: too loose, and you'll drop your bow; too tense, and you will hurt yourself.
3. Finally, movement starts from the muscles you activate and moves outward. If the movement starts from the wrist, the hand will move; from the forearm, the wrist and hand and fingers. etc.
The principle at work is thus quite simple: effective and relaxed movement starts from strength (the core) and radiates outward; but in order for that strength to be leveraged, it must be channeled. Too little tension, and the strength dissipates, too much and the strength is blocked. While not strictly part of the above principle, it should be noted that twisting (torque) is more effective than pushing (force), and that we should strive to gain mechanical advantage (give me a large enough lever and a fulcrum, and I can move the world) wherever we can.
Learning Bug in the Teaching Web
Once I had settled on the principle, I set about trying to teach it. But I didn't start with the principle, as the book tended to suggest. I instead hid the principle at the center of discussion, and led my students around the periphery, covering a wide variety of apparently unrelated problems. I did a number of the tricks in the book: Socratic method; teasing out assumptions; testing assumptions rather than simply correcting them; creating hypotheses and testing those. Those were all quite effective.
But then, slowly, gradually, I led my student towards the actual issue, the thing that tied everything together. When we got there, a most fascinating thing happened: an epiphany. And not just a random one, either! In teaching, we don't want to rely on chance... Natural epiphanies can be enlightening, but they are rather flighty birds, to be sure. No, this epiphany was instinctively (or accidentally) constructed. As soon as the principle became clear, the student went: "Oh. Oooooh!"
Thinking about what an epiphany is should make it quite obvious that this was the most natural reaction in the world. An epiphany is simply the sudden realization that a number of unrelated facts or problems are all related by an underlying idea. And that's exactly what we made. Epiphanies. The best part? Epiphanies are some of the most powerful aids to memory we can come across. It is very difficult to forget something that comes in the form of an epiphany. In its most extreme form, think of religious conversion. Now scale it back to earthly levels, and that's exactly what we've got.
Now go out and make some epiphanies happen!
Daily Recommendation
As usual, I have a couple of pieces in keeping with the theme. The first is a little piece by Claude Debussy called "Dr. Gradus ad Parnassum." The title alludes to what is perhaps the first musical text book in Europe, "Gradus ad Parnassum" by Johann Joseph Fux. The book is a series of exercises in counterpoint (the art of writing one melody against another), and was studied by a Haydn, Beethoven, and Mozart, among many others.
The second is the 4th movement of Mozart's Symphony 41. It, too, allegedly uses a motive found in Fux's text, but uses it brilliantly in a 5 voice fugetta (little fugue) featuring four themes all more or less at the same time.
Claude Debussy: "Dr. Gradus ad Parnassum," from the Children's Corner Suite.
Amadeus Mozart: Symphony 41, K. 551* 4th movement.
*Mozart's works were written before number works with an opus number was common. His pieces were all catalogued by 19th century scholar Ludwig von Köchel. Hence the "K." Like K-mart. Except klassier.
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