Good points amylou, ColinsMum. As usual I blathered on without much structure, but I think one key point is this: math students eventually have to learn how to take in prepackaged information, and do that efficiently and with as full an understanding as possible. It's like reading comprehension, but math-model comprehension. I don't think we'd get very far in any scientific field if people weren't well trained in communicating with each other.

We've also seen some posts here on how early math frustration led to an abandonment of math as an interest. But barring that, I'm guessing that one could be fairly inefficient with lots of bottom-level arithmetic concepts and procedures, or even fail to understand completely why they work as they do, and still be able to think abstractly at a high level very well.

Striving to increase my rate of flow, and fight forum gloopiness. sick