(no subject)
I am having a really hard time understanding how something "can't be explained."
A speaker this morning at the NCTM (National Council of Teachers of Mathematics) gave a cute example of a kid's interpretation of the prompt, "Write a story problem whose answer is 5*(7+3)". The kid wrote,
Tim went to the candy store to bye (sic) some chocolate bars. He knows that if he calculates 5*(7+3) in his head, he'll know how many chocolate bars to buy. What's the answer?
The speaker went on to conclude that the teacher would have a hard time explaining to the kid why his story doesn't quite fit expectations, and that moreover, understanding must be "enacted", and that this just can't be explained.
But wouldn't an ideal teacher be able to explain? More generally, can't almost anything be explained? I guess I understand on some level that people with tetrachromatism wouldn't really be able to explain how they perceive color differently than I would. And I would be loathe to explain my mathematics research area to someone, but this is more a matter of time and patience (on my part and the potentially totally bored hypothetical other) than it is a matter of inability to articulate the concepts. Ultimately, I am bothered by the notion that there are mathematical and intellectual concepts that we shouldn't bother to try to articulate the conventions of. It smacks of lazy elitism.
Last summer at the ICME (International Congress of Mathematics Education), I saw a talk explaining some dichotomies in education. That's the euphemized description; a blunter description might be, "a talk where the speaker explained why people argue all the time." One line along which people fight is "metaphors for teaching." On one extreme end, there are the "enacted" people who think that transmission of knowledge is implicit can can't be made explicit; on the other extreme, there are people (like me, I suppose) who think that things in teaching are "statable", that concepts can be made explicit. Even though I believe that there are things like practice and getting faster/more automated that can't be substantially improved by hearing someone explain stuff to you, I do think that good explanations are almost always possible, and that we should struggle to explain as much as we can rather than trying to identify things we cannot explain.
A speaker this morning at the NCTM (National Council of Teachers of Mathematics) gave a cute example of a kid's interpretation of the prompt, "Write a story problem whose answer is 5*(7+3)". The kid wrote,
Tim went to the candy store to bye (sic) some chocolate bars. He knows that if he calculates 5*(7+3) in his head, he'll know how many chocolate bars to buy. What's the answer?
The speaker went on to conclude that the teacher would have a hard time explaining to the kid why his story doesn't quite fit expectations, and that moreover, understanding must be "enacted", and that this just can't be explained.
But wouldn't an ideal teacher be able to explain? More generally, can't almost anything be explained? I guess I understand on some level that people with tetrachromatism wouldn't really be able to explain how they perceive color differently than I would. And I would be loathe to explain my mathematics research area to someone, but this is more a matter of time and patience (on my part and the potentially totally bored hypothetical other) than it is a matter of inability to articulate the concepts. Ultimately, I am bothered by the notion that there are mathematical and intellectual concepts that we shouldn't bother to try to articulate the conventions of. It smacks of lazy elitism.
Last summer at the ICME (International Congress of Mathematics Education), I saw a talk explaining some dichotomies in education. That's the euphemized description; a blunter description might be, "a talk where the speaker explained why people argue all the time." One line along which people fight is "metaphors for teaching." On one extreme end, there are the "enacted" people who think that transmission of knowledge is implicit can can't be made explicit; on the other extreme, there are people (like me, I suppose) who think that things in teaching are "statable", that concepts can be made explicit. Even though I believe that there are things like practice and getting faster/more automated that can't be substantially improved by hearing someone explain stuff to you, I do think that good explanations are almost always possible, and that we should struggle to explain as much as we can rather than trying to identify things we cannot explain.