Teasing this out a little more, bullet points of my own:
If B learns math at a slower pace than A, then it can literally be the case that B will never understand math as well as A. At suitable slow (but common) learning paces, it can be impractical and unrewarding for B to study math. And I think there might even be large numbers of mentally normal human beings walking around for whom this pace is so slow that it’s misleading to call it a “learning pace” at all, e.g. too slow for progress they make one day to stick the next.
I’m sure that “math ability,” like anything else, is reducible, but in these kinds of brain-and-behavior cases it might “reduce” to thousands of different factors that don’t have much to do with each other. In that case it wouldn’t be very easy to give advice on how to be better at math, beyond “arrange each of those thousands of factors in a way favorable to math ability.”
Even if “math ability” has a more satisfying explanation than the kind in 2., so that it’s possible to give good advice on how to improve it, I think that this is not a solved problem. Specifically I still think that your proposed advice (“you simply haven’t bothered to update some aspect of your identity since childhood”) is no good.
In the meantime “lack of math ability” seems to me to be a perfectly good label for a real phenomenon, though I guess I agree with you that it is not an explanation for that phenomenon.
1. I disagree that a slower learning pace is less rewarding. On the contrary, learning is most rewarding when there is time to do it properly, and the frustration many people experience in school settings results from the pressure to (appear-to-) learn things more quickly than their natural pace.
(I owe to Michael Vassar the observation that there is something inherently contradictory and unrealistic about expecting people to learn calculus in a semester when they required five years to learn arithmetic.)
2. It might seem like it could be that complicated, but it turns out not to be. In practice (as revealed by teaching experience), “lacking math ability” usually reduces to something like “I flinch and run away when I realize that I will have to carry out more than two or three steps (especially if there is recursion involved), instead of just gritting my teeth and carrying them out.”
3. Most people don’t even try updating their identities; while on the other hand, I myself have updated my skill-related identities on a number of occasions, and it worked. (Math happens to be an example.)
4. It would be best to have a label that conveys more information about the cause(s) of the phenomenon.
Teasing this out a little more, bullet points of my own:
If B learns math at a slower pace than A, then it can literally be the case that B will never understand math as well as A. At suitable slow (but common) learning paces, it can be impractical and unrewarding for B to study math. And I think there might even be large numbers of mentally normal human beings walking around for whom this pace is so slow that it’s misleading to call it a “learning pace” at all, e.g. too slow for progress they make one day to stick the next.
I’m sure that “math ability,” like anything else, is reducible, but in these kinds of brain-and-behavior cases it might “reduce” to thousands of different factors that don’t have much to do with each other. In that case it wouldn’t be very easy to give advice on how to be better at math, beyond “arrange each of those thousands of factors in a way favorable to math ability.”
Even if “math ability” has a more satisfying explanation than the kind in 2., so that it’s possible to give good advice on how to improve it, I think that this is not a solved problem. Specifically I still think that your proposed advice (“you simply haven’t bothered to update some aspect of your identity since childhood”) is no good.
In the meantime “lack of math ability” seems to me to be a perfectly good label for a real phenomenon, though I guess I agree with you that it is not an explanation for that phenomenon.
1. I disagree that a slower learning pace is less rewarding. On the contrary, learning is most rewarding when there is time to do it properly, and the frustration many people experience in school settings results from the pressure to (appear-to-) learn things more quickly than their natural pace.
(I owe to Michael Vassar the observation that there is something inherently contradictory and unrealistic about expecting people to learn calculus in a semester when they required five years to learn arithmetic.)
2. It might seem like it could be that complicated, but it turns out not to be. In practice (as revealed by teaching experience), “lacking math ability” usually reduces to something like “I flinch and run away when I realize that I will have to carry out more than two or three steps (especially if there is recursion involved), instead of just gritting my teeth and carrying them out.”
3. Most people don’t even try updating their identities; while on the other hand, I myself have updated my skill-related identities on a number of occasions, and it worked. (Math happens to be an example.)
4. It would be best to have a label that conveys more information about the cause(s) of the phenomenon.
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