<p>Smartly said curiousmother!</p>
<p>So, how do you get to Carnegie Hall?</p>
<p>OMG, I could barely get past the first sentence... Tiger Woods? I don't think any of us can even begin to imagine the hours and hours of practice that went into developing his game. Another example: Kobe Bryant. You see him leap and twist and dunk a b-ball and all you see is "natural talent" but then you read about how he takes something like 1000 shots (or some equally insane number, I forget) every day in practice.</p>
<p>But is mental practice the same as physical practice? Does an individual need the same level of automaticity in performing a mental activity such as arithmetics or higher mathermatics as an athlete or an artist, to the extent that thinking no longer enters into it?
In learning a language, constant practice leads to fluency, and lack of use leads to atrophy. But English or history or anthropology? Or math or physics?</p>
<p>According to the research on what is called deliberate practice all manner of performance requires significant practice in order to achieve mastery. No evidence has emerged which would suggest there is such a thing as talent.</p>
<p>Significant practice, sure. But equally important is comprehension and also knowledge of when to dribble and when to throw the ball into the basket. Same with practicing solving equations. You've got to know what problem you are trying to solve. </p>
<p>As for talent? I've made my peace with being the math-challenged parent of a math whiz. Without any practice, he solved a math problem faster than I could... in 3rd grade. He did not even know it was an algebra problem.</p>
<p>Anecdotes are often compelling, but research into expert performance finds that even with child prodigies, it is practice that differentiates them from their peers.</p>
<p>Yes, the research is very compelling. I have the book under review at home now, checked out from my alma mater's library, and I am finding interesting research findings on almost every page. The bibliographic notes in that 900-plus-page quarto book are wonderful.</p>
<p>
[quote]
but research into expert performance finds that even with child prodigies, it is practice that differentiates them from their peers.
[/quote]
</p>
<p>Indeed. But if there are such individuals as child prodigies, then talent must exist, contra post 24.</p>
<p>Prodigy is simply a label, not an explanation nor and indication of something called talent.</p>
<p>Okay, so every Suzuki violin player who has ever massacred his or her parents ears is just a David Oistrakh manqu</p>
<p>Marite, I am not sure we can equate math with music learning. Clearly there is a strong correlation between interest in math and interest in music. Einstein is one of the best known examples. In spite of this correlation, there seems to be some basic differences in learning in these areas. It is common to see very large differences in the ability of kids (and adults) to grasp math concepts. Some kids learn math very quickly and progress at a rapid rate. They can begin to understand calculus and advanced math concepts when other kids of the same age are struggling with fractions and solving simple equations with one unknown. Math can be frustrating to both pupils and teachers. Instruction, tutoring and practice all help, but sometimes it seems they don't help much. Typically math learning comes in spurts. All of a sudden a kid has developed to the point where they get it. This is great when they get it at or beyond the appropriate grade level. It is not so good when they don't or can't grasp the concepts and are behind the grade level requirements.</p>
<p>I don't see much similarity with music. Some kids have perfect pitch, good manual dexterity and more musical ability. Maybe I have never seen a musical prodigy, but it seems that even the kids with a lot of musical ability need to spend thousands of hours practicing in order to develop strong skills in playing a musical instrument. Maybe "perfect" practice helps. Certainly it is important to have a good teacher, but equally important that the practice is motivated by a love of music.</p>
<p>edad:</p>
<p>That was precisely the question that I posed in post #23, which I reproduce below:</p>
<p>
[quote]
But is mental practice the same as physical practice? Does an individual need the same level of automaticity in performing a mental activity such as arithmetics or higher mathermatics as an athlete or an artist, to the extent that thinking no longer enters into it?
In learning a language, constant practice leads to fluency, and lack of use leads to atrophy. But English or history or anthropology? Or math or physics?
[/quote]
</p>
<p>And the implication is, of course, that math and music or sports ARE different kinds of activities and that the amount of pratice needed in one arena is not necessary in another.</p>
<p>
Marite, I am not sure we can equate math with music learning.
Isn't that what Marite said?
But is mental practice the same as physical practice? Does an individual need the same level of automaticity in performing a mental activity such as arithmetics or higher mathermatics as an athlete or an artist, to the extent that thinking no longer enters into it?
</p>
<p>I've got three kids: a math whiz who could beat me at math in 6rd grade (but I'm a Physics major) and did not need any practice until he got to a 300-level university courses; an almost-whiz (who, I believe, would benefit greatly if she was allowed to skip 2/3 of the math practice required at school... or 3/4) and a non-math kid who could not reach his siblings' level in math no matter how much he practiced. Now tell me that "there no such thing as talent" :D</p>
<p>Marite, we cross-posted... but I found even better quote of yours on the first page and want to post it:
There is a difference between knowledge and skills. You don't need a lot of practice to cultivate knowledge. Just enough to acquire it.
I agree completely.</p>
<p>One of my kids has phenomenonal ability in both. He has perfect pitch and true musicality, as well as exceptional math skills. We know lots of very strong musicians, who are also very strong in math. I don't think it is a coincidence.</p>
<p>On edit: Now I have read the whole thread:</p>
<p>One cannot practice to a level of true musicality, no matter how much practice one does. I can hear the difference in the first few bars between the kid who "has it" and the good practicer (sometimes, that kid is both...mine isn't).</p>
<p>Having natural proclivity makes less practice necessary, whatever the task. I know I have to work much harder in certain areas than others. The same is true for most of us, who are not graced with equal skill or ability, and practice will make things easier, but never put us at the level of the person with true proclivity.</p>
<p>Marmat: Hi and thanks!</p>
<p>Allmusic: I, too, know lots of people who are great at both math and music. Alas, not true of my kids. The one with perfect pitch is uninterested in math and science and the mathy kid is uninterested in music. But I also believe that there is a connection between math and music. The Algebra Project uses music to teach fractions.</p>
<p>I guess - in fact, I know - I have a tin ear. I am not sure I know the meaning of "true musicality" and I am sure I could not identify a kid who had it, especially if they had not practiced enough to become proficient. It seems that it would be important to identify kids who have true musicality. Many kids go to music schools and few will ever succeed as performers. I have a niece who spent 4 years in music school, spent an additional year training with a private tutor and was eventually told she would never make her goal of a career in a professional orchestra. My D is trying to do a double degree with engineering and music so that she keeps her options open. She has been told be numerous teachers that she can make it as a professional musician. Who knows? I would never be able to make that determination. She certainly does not have perfect pitch and continues to work at ear training. She is a long way from being proficient with her instrument and needs additional years of training and experience. So what is musicality -- some sense of pitch, rhythm, and timing, some form of expression in the music, proficiency with an instrument, some sort of joy found in music, or is it mainly just hard work?</p>
<p>
[quote]
a math whiz who could beat me at math in 6rd grade (but I'm a Physics major) and did not need any practice until he got to a 300-level university courses
[/quote]
</p>
<p>Ah, but I often wonder if kids like these are not "practicing" in a way that you did not observe, that may be almost as automatic and natural as absorbing a native language.</p>
<p>We acquire fluency in our native language by practicing our comprehension and speaking skills in a very natural everyday way.</p>
<p>"Talent" may be the ability for some people to "practice" in a way that is just as natural to them as acquiring a native language is to the rest of us. </p>
<p>Some people view the world in mathematical terms and thinking mathematically comes as naturally as breathing to them. </p>
<p>Just because you don't see somebody sitting down and slaving away at math problems with pencil and paper doesn't mean that they aren't "practicing." </p>
<p>A four-year old once remarked--out of the blue, a propos of nothing--"Did you know, Mom, another way to square a number is to raise it to the fourth power and then take its square root?" The child had just been standing around, passing time while waiting at a city bus stop, mulling around number patterns in her head before reaching this conclusion. A casual observer would have had no idea that she had been "practicing" mathematical thinking. There was no pencil and paper involved, no assignment, just "messing around with numbers in her head."</p>
<p>There is some intriguing but admittedly controversial evidence that much of the assigned "practice" typical of formal conventional education is counterproductive.</p>
<p>Here is a link to a widely cited classic paper reporting results of a fascinating multi-year experiment:</p>
<p>As always, one can poke holes in the methodology of the study (conducted in the 1930s) but this paper has been influential to people trying to design new and hopefully better pedagogies.</p>
<p>Wisteria:</p>
<p>That is something I've been wondering about, too. What does it mean to "practice?" When speaking a foreign language, speaking it is tantamount to practicing it; constant use is necessary to acquiring and maintaining fluency. If one has to stop and wonder what is the right word and translate it from another language, one is not truly fluent. But if I am a voracious reader and read constantly, does it mean that I am practicing language arts? Or merely reading? </p>
<p>If my S, as was his wont, tried to solve algebra problems his older brother brought home from school, was he "practicing" math, problem-solving, or merely contributing to the family conversation? It certainly was not doing 20 exercises with only the numbers changed.</p>
<p>Edad, when I think of musicality, the innate kind, I think of lyrical expressiveness, probably more so than polish. I have heard some very studied and proficient high school students, on various instruments (although can best judge on those my own son plays); while they may have their notes down perfectly, some play quite woodenly, without joy or interpretation. </p>
<p>While one can practice to polish, one cannot practice to deep joy and understanding of phrasing and such. The joy component is huge, but one can play joyously, and still quite badly. It is an odd combination of expressiveness, love for the instrument, practice and innate ability that most likely contributes to successful professional musicians (don't ask me though...mine is not even in conservatory yet!).</p>