I'm asking you, What could we do?
It always makes me laugh a little when I hear or read the question, How do children learn mathematics?
Regardless whether the question is explicit or implicit, my first reaction is to ask back (usually to a piece of paper or to my computer screen), How do children learn how to drive?
Actually, it is this reaction--this thought--that makes me laugh, because what seems to be meant by the first question is, How do children naturally learn mathematics, without the aid (or with the very minimal aid) of teaching or culture or environment? So when I replace mathematics in the question with how to drive, then that question--the real question--sounds, appropriately, ridiculous: How do children learn how to drive without the aid (or with the very minimal aid) of teaching or culture or environment? They don't.
Now, obviously there are a thousand points one could quibble with here. One might argue that I have misrepresented the "real" question--that teaching or environment or culture is taken into account but what is truly sought after is how those factors fit with students' potential (or proclivities or "reasoning," whatever). Or one might laugh back and call my comparison ridiculous because learning mathematics is simply nothing like learning how to drive. Or one might argue that transplanting the phrase how to drive into the first question doesn't make it ridiculous at all--that there is, indeed, a set of skills/abilities/proclivities/etc. that makes us naturally capable of driving. Et cetera, et cetera.
But even though those considerations crowd my brain, I still laugh whenever I hear that question: How do children learn mathematics?
Maybe it's just a dumb question. I mean, really, what could we do fundamentally differently in education if we ever got an answer to that question--the real question?
Regardless whether the question is explicit or implicit, my first reaction is to ask back (usually to a piece of paper or to my computer screen), How do children learn how to drive?
Actually, it is this reaction--this thought--that makes me laugh, because what seems to be meant by the first question is, How do children naturally learn mathematics, without the aid (or with the very minimal aid) of teaching or culture or environment? So when I replace mathematics in the question with how to drive, then that question--the real question--sounds, appropriately, ridiculous: How do children learn how to drive without the aid (or with the very minimal aid) of teaching or culture or environment? They don't.
Now, obviously there are a thousand points one could quibble with here. One might argue that I have misrepresented the "real" question--that teaching or environment or culture is taken into account but what is truly sought after is how those factors fit with students' potential (or proclivities or "reasoning," whatever). Or one might laugh back and call my comparison ridiculous because learning mathematics is simply nothing like learning how to drive. Or one might argue that transplanting the phrase how to drive into the first question doesn't make it ridiculous at all--that there is, indeed, a set of skills/abilities/proclivities/etc. that makes us naturally capable of driving. Et cetera, et cetera.
But even though those considerations crowd my brain, I still laugh whenever I hear that question: How do children learn mathematics?
Maybe it's just a dumb question. I mean, really, what could we do fundamentally differently in education if we ever got an answer to that question--the real question?