One of the most difficult aspects of teaching is classroom mangement. If it's lacking or flawed, then that house of cards that is your lesson will all come a-tumbling down
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I love the juggling analogy (of course). Here's another one for you:
I am fond of comparing the way I learn things in juggling with the way I learn things on the piano. On the piano, there seems to be a theorem that as tempo -> 0, practice -> theory. If you're frustrated by not being able to play something at full speed, you can always find a tempo where it's doable. Then you can start working your way up to full speed gradually.
In juggling, slowing down helps a little, but eventually you get to the point where trying to keep the pace slow becomes just as difficult as doing the trick. I think this makes progress in juggling proceed in a much more punctuated series of plateaus. Invariably, when you first start practicing a trick, it just falls apart and gravity takes over. Depending on how hard the trick is, you may work on it for days or weeks* before seeing any sign of progress. But then, one day it starts to work. Then you want it to work better, and still nothing you do seems to have any effect. But if you keep working
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Actually, what *is* second grade algebra? I remember learning multiplication and division. I think. Maybe we were discussing the differences between circles and squares. I didn't even hear the word algebra until 7th grade, in the context of "pre-algebra".
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I am fond of comparing the way I learn things in juggling with the way I learn things on the piano. On the piano, there seems to be a theorem that as tempo -> 0, practice -> theory. If you're frustrated by not being able to play something at full speed, you can always find a tempo where it's doable. Then you can start working your way up to full speed gradually.
In juggling, slowing down helps a little, but eventually you get to the point where trying to keep the pace slow becomes just as difficult as doing the trick. I think this makes progress in juggling proceed in a much more punctuated series of plateaus. Invariably, when you first start practicing a trick, it just falls apart and gravity takes over. Depending on how hard the trick is, you may work on it for days or weeks* before seeing any sign of progress. But then, one day it starts to work. Then you want it to work better, and still nothing you do seems to have any effect. But if you keep working ( ... )
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