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!
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.