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A piano teacher my junior year of high school had me do exercises I didn't understand. A teacher in my college audition heard the result of those lessons and st

A piano teacher my junior year of high school had me do exercises I didn't understand. A teacher in my college audition heard the result of those lessons and started me down another path of exercises. Essentially, the one teacher had communicated certain skills through me to the next teacher without my knowledge. During one particular lesson my junior year of college, everything clicked and I began to play a melody with more control and direction. It was only at that moment that I could hear and feel the result of those exercises. Furthermore, that teacher later speculated about the lessons my previous teacher had taught me. That speculation lined up pretty well with what I remembered of the exercises she gave me. And it was only then that I understood the efficacy of those lessons toward connecting a melodic line on the piano. That's about 4 1/2 years and two mentors setting me toward developing a skill (in addition to others, granted), the process of which I didn't really understand for another half year after that. And that's the best case of someone willing to do what seems like arbitrary work, and lacking the skills at the time to rationalize persuasive reasons to avoid doing that work. In my experience adult students are experts at talking themselves into the skills they think they already have, and talking themselves out of the will to learn new ones. So without a decent mentor I'd speculate most people are hopelessly incompetent at assessing their circle of competence. Or at least they are if we widen the circle from "getting ahead in business" to "life."

dhosek 6y ago
There's a lot of this in mathematics education. Unfortunately, a lot of math teachers don't realize themselves the importance of the things that they're setting up in students' education. Having been through the educational process for getting a secondary math education certification, it felt like too much of this was left implicit. Worse still, there were cases like in abstract algebra where students would do exercises on the group a+b\sqrt(-2) without any indication of the significance that this would play later in the algebra course. Heck, high school algebra, I think students learning that being able to solve for x in ax+b=c equations turns into a goal or transforming more complex problems into that simpler problem.
- lmkg 6y ago
  My advisor for my math degree told me straight-up "You don't really understand a math course until you take the next class in the series." I'm really glad he told me that, because it sharpened my perception of how well I understood different subjects. It also shaped which classes I took for the rest of college, tending towards depth over breadth. Too many students think that math is just an arbitrary collection of arbitrary steps. It all makes sense, but you have to have at least one teacher contextualize it for you in order for all of it to click.
  - riverlong 6y ago
    Hell, I don't think anyone really understands fractions until they've taken Elementary Set Theory and constructed the reals, and I don't think anyone really understands high-school trig until they've taken real analysis, etc. It's a great feeling to come back to the "simple" topics from early in school, and to realize how much rich knowledge they communicate, and the level of detail that really sits underneath them.
- jerf 6y ago
  There's also cases where we have students spend a long time on truly useless stuff because none of the teachers involved understand that it's essentially useless. The example I'm seeing with my kids right now is "mixed fractions". They bang on and on about them... but they're just a special case that is basically used by cookbooks, and not much else. You don't need to know what 37 8/17s + 98 3/24s is, because the only mixed fractions you're likely to see are ones you'd see in recipes. 3½ is pretty large as mixed fractions come in the real world. I don't think I've ever seen in my entire life a mixed fraction as large as 12 4/5. They're always written some other way; 64/5, 12 + 4/5, 12.8, but never a mixed fraction. In high school, I remember spending endless hours on trig identities. They are useful only in a similarly small situation. (And I actually think they're a fun target to fire Taylor polynomial expansions at, as a good exercise for using them and understanding infinite series, but even then, rather than "memorize this pile of identities" it becomes "prove or disprove this statement:", which is different.) There's a dozen things that time could be better spent on, by purely pragmatic or purely academic standards. But nobody responsible for the curriculum realizes this. I also recall some really abortive graph theory introductions and set theory... I'm not even sure I see the value in the terrible "15 minutes in high school" types of introductions of those topics. Nobody comes away with anything of either (again) academic or practical value, despite the huge value of the topics themselves.
rhapsodic 6y ago
This is similar to an anecdote in Effortless Mastery by Kenny Werner. Would you mind sharing what those exercises were?
Terretta 6y ago
Imitation before Understanding before Innovation
- DoingIsLearning 6y ago
  As someone with a toddler that really resonated. Thanks.
  - Viliam1234 6y ago
    With a toddler, you don't have much of a choice. Explaining won't work, and immitation is an instinct. Question is whether this remains true in older age. Curious people are going to think about things anyway, so the choice is not between explanation and mindless repetition, but between correct explanation and random misunderstandings. Seems better to provide the correct one (and of course then do as much repetition as necessary).
- jancsika 6y ago
  There is a problem I can think of in music that fits that cliche-- pianists who imitate the interpretation of others. There are some who are amazingly adept at imitation, and often the downside is a difficulty in coming up with their own interpretation. The problem I'm describing is different. By college I already had a set of skills that I made my own. I also already had an idea about how I wanted the music to sound. The problem was mainly that I had no idea that the skills I had already learned got me part of the way toward playing a melody with greater lyricism. Worse, I had no idea to what extent I could execute that better, or what it would feel like to execute it. It took a few years of trusting that someone wiser might know things I don't to put those things together.
zszugyi 6y ago
What's fascinating to me is the amount of knowledge and teaching experience that has to go into designing those exercises. How long and how many teachers and students did it take to come up with a good set of exercises to develop towards a certain skillset?
- jancsika 6y ago
  It's difficult to say. On the one hand I thing such lessons can be so effective because they are generally one-on-one. That already goes a long way to disseminating knowledge, especially when compared to the "knowledge dissemination theater" that is the large lecture hall. On the other, musicians construct these insane pedagogical family trees. So-and-so's teacher was a student of so-and-so, who was a student of so-and-so, and now we're already back in the 19th century. My personal opinion is that a lot of that is more inspirational than practical. But it certainly has an effect. There's also the easter egg that teaching can accelerate one's own mastery. It's basically forcing one to do rubber-duck debugging as a full-time job. Add to that an ever-expanding knowledge about the physical aspect of playing instruments (how to avoid injury, how to maximize practice time), and I think that's where a lot of the knowledge comes from.
rkangel 6y ago
I read a post recently talking about people learning to be artists. The point they were making was that the 'taste' to judge good from bad is inherent in a good artist, but the ability to produce good art develops over a long time. That means that artists spend a lot of time producing work that their taste declares as below standard. It's not until you've been working for a while that your ability catches up with your judgement. This lag, causes a lot of people to give up concluding that they're not that good.
- disqard 6y ago
  Perhaps you were referring to this Ira Glass quote [0], maybe not. Either way, this is a good thought to share, so I'll link it here. [0] https://gointothestory.blcklst.com/the-gap-by-ira-glass-9651a750408f https://gointothestory.blcklst.com/the-gap-by-ira-glass-9651...
  - rkangel 6y ago
    That is exactly the quote I was looking for, thank you. I promise to bookmark it this time!
- jancsika 6y ago
  > The point they were making was that the 'taste' to judge good from bad is inherent in a good artist, but the ability to produce good art develops over a long time. Taste develops as a function of accumulating knowledge, preferably from making art. > It's not until you've been working for a while that your ability catches up with your judgement. So if you grant for the moment what I wrote above, you'll see there's an alternate way of thinking. That is, if an artist is comfortable making art at an introductory level, their taste will be refined the more art they make. That refined taste feeds back into a virtuous cycle of making more and better art which further refines the test. Alternatively, the artists you describe are reinforcing frustration at nearly every level (my own experience being such artists eventually are unable to break out of that frustrated, self-critical mindset).
infogulch 6y ago
One might realize that you only need to grow your circle of competence so far before you're able to function reasonably well in the world, but you miss that in order to live meaningful life you have to live on the circle even as it grows.

dhosek 6y ago

There's a lot of this in mathematics education. Unfortunately, a lot of math teachers don't realize themselves the importance of the things that they're setting up in students' education. Having been through the educational process for getting a secondary math education certification, it felt like too much of this was left implicit. Worse still, there were cases like in abstract algebra where students would do exercises on the group a+b\sqrt(-2) without any indication of the significance that this would play later in the algebra course. Heck, high school algebra, I think students learning that being able to solve for x in ax+b=c equations turns into a goal or transforming more complex problems into that simpler problem.

lmkg 6y ago
My advisor for my math degree told me straight-up "You don't really understand a math course until you take the next class in the series." I'm really glad he told me that, because it sharpened my perception of how well I understood different subjects. It also shaped which classes I took for the rest of college, tending towards depth over breadth. Too many students think that math is just an arbitrary collection of arbitrary steps. It all makes sense, but you have to have at least one teacher contextualize it for you in order for all of it to click.
- riverlong 6y ago
  Hell, I don't think anyone really understands fractions until they've taken Elementary Set Theory and constructed the reals, and I don't think anyone really understands high-school trig until they've taken real analysis, etc. It's a great feeling to come back to the "simple" topics from early in school, and to realize how much rich knowledge they communicate, and the level of detail that really sits underneath them.
jerf 6y ago
There's also cases where we have students spend a long time on truly useless stuff because none of the teachers involved understand that it's essentially useless. The example I'm seeing with my kids right now is "mixed fractions". They bang on and on about them... but they're just a special case that is basically used by cookbooks, and not much else. You don't need to know what 37 8/17s + 98 3/24s is, because the only mixed fractions you're likely to see are ones you'd see in recipes. 3½ is pretty large as mixed fractions come in the real world. I don't think I've ever seen in my entire life a mixed fraction as large as 12 4/5. They're always written some other way; 64/5, 12 + 4/5, 12.8, but never a mixed fraction. In high school, I remember spending endless hours on trig identities. They are useful only in a similarly small situation. (And I actually think they're a fun target to fire Taylor polynomial expansions at, as a good exercise for using them and understanding infinite series, but even then, rather than "memorize this pile of identities" it becomes "prove or disprove this statement:", which is different.) There's a dozen things that time could be better spent on, by purely pragmatic or purely academic standards. But nobody responsible for the curriculum realizes this. I also recall some really abortive graph theory introductions and set theory... I'm not even sure I see the value in the terrible "15 minutes in high school" types of introductions of those topics. Nobody comes away with anything of either (again) academic or practical value, despite the huge value of the topics themselves.

rhapsodic 6y ago

This is similar to an anecdote in Effortless Mastery by Kenny Werner. Would you mind sharing what those exercises were?

Terretta 6y ago

Imitation before Understanding before Innovation

DoingIsLearning 6y ago
As someone with a toddler that really resonated. Thanks.
- Viliam1234 6y ago
  With a toddler, you don't have much of a choice. Explaining won't work, and immitation is an instinct. Question is whether this remains true in older age. Curious people are going to think about things anyway, so the choice is not between explanation and mindless repetition, but between correct explanation and random misunderstandings. Seems better to provide the correct one (and of course then do as much repetition as necessary).
jancsika 6y ago
There is a problem I can think of in music that fits that cliche-- pianists who imitate the interpretation of others. There are some who are amazingly adept at imitation, and often the downside is a difficulty in coming up with their own interpretation. The problem I'm describing is different. By college I already had a set of skills that I made my own. I also already had an idea about how I wanted the music to sound. The problem was mainly that I had no idea that the skills I had already learned got me part of the way toward playing a melody with greater lyricism. Worse, I had no idea to what extent I could execute that better, or what it would feel like to execute it. It took a few years of trusting that someone wiser might know things I don't to put those things together.

zszugyi 6y ago

What's fascinating to me is the amount of knowledge and teaching experience that has to go into designing those exercises. How long and how many teachers and students did it take to come up with a good set of exercises to develop towards a certain skillset?

jancsika 6y ago
It's difficult to say. On the one hand I thing such lessons can be so effective because they are generally one-on-one. That already goes a long way to disseminating knowledge, especially when compared to the "knowledge dissemination theater" that is the large lecture hall. On the other, musicians construct these insane pedagogical family trees. So-and-so's teacher was a student of so-and-so, who was a student of so-and-so, and now we're already back in the 19th century. My personal opinion is that a lot of that is more inspirational than practical. But it certainly has an effect. There's also the easter egg that teaching can accelerate one's own mastery. It's basically forcing one to do rubber-duck debugging as a full-time job. Add to that an ever-expanding knowledge about the physical aspect of playing instruments (how to avoid injury, how to maximize practice time), and I think that's where a lot of the knowledge comes from.

rkangel 6y ago

I read a post recently talking about people learning to be artists. The point they were making was that the 'taste' to judge good from bad is inherent in a good artist, but the ability to produce good art develops over a long time. That means that artists spend a lot of time producing work that their taste declares as below standard. It's not until you've been working for a while that your ability catches up with your judgement. This lag, causes a lot of people to give up concluding that they're not that good.

disqard 6y ago
Perhaps you were referring to this Ira Glass quote [0], maybe not. Either way, this is a good thought to share, so I'll link it here. [0] https://gointothestory.blcklst.com/the-gap-by-ira-glass-9651a750408f https://gointothestory.blcklst.com/the-gap-by-ira-glass-9651...
- rkangel 6y ago
  That is exactly the quote I was looking for, thank you. I promise to bookmark it this time!
jancsika 6y ago
> The point they were making was that the 'taste' to judge good from bad is inherent in a good artist, but the ability to produce good art develops over a long time. Taste develops as a function of accumulating knowledge, preferably from making art. > It's not until you've been working for a while that your ability catches up with your judgement. So if you grant for the moment what I wrote above, you'll see there's an alternate way of thinking. That is, if an artist is comfortable making art at an introductory level, their taste will be refined the more art they make. That refined taste feeds back into a virtuous cycle of making more and better art which further refines the test. Alternatively, the artists you describe are reinforcing frustration at nearly every level (my own experience being such artists eventually are unable to break out of that frustrated, self-critical mindset).

infogulch 6y ago

One might realize that you only need to grow your circle of competence so far before you're able to function reasonably well in the world, but you miss that in order to live meaningful life you have to live on the circle even as it grows.