Practice makes you good at learning, but being smart makes you good at practice.*
-- me (this morning)
*A less pithy, but more accurate quote might go: Practice makes you good at learning, but being smart increases the likelihood of initial success which increases your motivation to practice, and, thus, your willingness to practice.
You're pretty pithy this morning, Ken, even when you're less pithy. No telling how it will go after breakfast.
A much more long-winded, but still fairly pithy (if it's possible to be pithy and long-winded at the same time. Someone will likely want me to provide math proof that it theoretically can occur.) article appeared today in TCRecord:
"Family (Dis)Advantage and the Educational Prospects of Better Off African American Youth: How Race Still Matters"
Family (Dis)Advantage is another predisposing factor. When God and man team up to deal you a band hand of both cards, it takes strong instruction like DI and a handful of other program architectures to improve your prospects.
I don't know about your less pithy quote: it seems to me that being smart also helps you to derive more out of practice, thus making you in a quite literal sense, "good at practice".
I'll take a look at that article, Dick.
CrypticLife, I'm thinking that (likelihood of initial) success is pretty close to deriving more out of practice. Or, at least, that's what I was getting at.
Okay, so I'm easy to please. I like both quotes!
An old baseball coach of mine used to say, "Practice doesn't make perfect. The perfect practice makes perfect." In keeping with the "pithy" theme, I suppose one could say, "Garbage in, garbage out." Wide applicability, no?
"Wide applicability, no?"
Not really. The coach switched referents in mid-sentence. An instructor should strive for setting up a "perfect practice" but the practice can be far from perfect and still have a positive effect. If the student were "Perfect" the student wouldn't need the practice.
To increase expertise requires "determined practice" on the part of the individual.
The coach wanted the players to share his aspiration of perfection. It worked for you, but it doesn't really have "wide applicability" as stated.
Back to the practice field.
KDeRosa - how about if being smart leads you to read far more into the practice than the designer of it intended, and thus you fail to achieve initial success?
Dick - there is an asymmetry in proofs. If you want to claim that something can exist, then one example is sufficient to show that. So one long-winded and pithy quote is enough to show that long-winded and pithy quotes can occur. If you want to show that something can't exist, though, you've got a tough problem as it's possible that the thing exists somewhere you haven't looked. Some things can however be shown not to exist by mathematical proofs.
For example, I can show that the prime numbers are infinite with a proof by contradiction.
Theory: Prime numbers are infinite.
Proof: Assume the opposite, there is a largest prime number, N.
Now multiply all the prime numbers from 1 to N together and add 1, so 1*2*3*5*7*11*...*N + 1.
You now have a number that is divisible by none of the existing prime numbers. So therefore either this number is either prime itself or is divisable by some other prime that is larger than N. Therefore there must be another prime number larger than N. Therefore our starting assumption is wrong. Therefore there cannot be a largest prime number. QED.
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