Reply #14: It's a common misconception

[LWolf]

and dysfunction to decide that students who can perform an operation or solve a problem by following an example are ready to move up the ladder.

It's especially common when teaching the gifted, who can race through the generally low-level activities happening in their class. Too often, instead of taking them deeper, they are rushed forward before they should be.

That's a problem with math education that has been around for generations. There is more emphasis on memorizing facts and rote procedures than on understanding math at that fundamental level. It, like everything else, is exacerbated in the "standards and accountability" culture that "raises standards" by dropping curriculum down grade levels, instead of adding that emphasis on concepts, and then pouncing with high-stakes tests.