Did you even read the article, or did you read the subheading, which I will admit is a stretch, and immediately cast judgement? You used the strawman of a k-12/college student who learns something and quickly by practicing a particular method then forgets it. What about those who actually do learn this way? There are most certainly visual learners who can see concepts in their head -- a trait I admire personally.
>So many students in other cultures
Do you know every student? Every culture? Again, nothing but over-generalizations here. The article actually referenced the afterschool programs in Japan that had success.
Yes at some point you have to back and understand the why and the how, but solving equations and crafting proofs are actually two different skills in my opinion and I have met mathematicians that were stronger in either or both.
In any case, I think you are missing the point of this author. I think the authors strongest argument which is building that foundation, or "innate ability" and he argues that comes through memorization and rote learning. Quoting, "building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success" I don't think he just pulled that out of his butt. If you take the time to practice like the author did where it becomes engrained into your mind, you are in fact learning effectively.
Besides all this, what is mathematics anyways? Is it not a language? Does it not have "letters" (variables, operators, symbols), does it not have a grammar? Does it not have "parts of speech?" (an equation must have a left side, and a right side), Is it not used to communicate to others?
In any case, certainly not a terrible read in any way.
>So many students in other cultures
Do you know every student? Every culture? Again, nothing but over-generalizations here. The article actually referenced the afterschool programs in Japan that had success.
Yes at some point you have to back and understand the why and the how, but solving equations and crafting proofs are actually two different skills in my opinion and I have met mathematicians that were stronger in either or both.
In any case, I think you are missing the point of this author. I think the authors strongest argument which is building that foundation, or "innate ability" and he argues that comes through memorization and rote learning. Quoting, "building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success" I don't think he just pulled that out of his butt. If you take the time to practice like the author did where it becomes engrained into your mind, you are in fact learning effectively.
Besides all this, what is mathematics anyways? Is it not a language? Does it not have "letters" (variables, operators, symbols), does it not have a grammar? Does it not have "parts of speech?" (an equation must have a left side, and a right side), Is it not used to communicate to others?
In any case, certainly not a terrible read in any way.