> That allows more able (or more motivated) learners to move ahead of the meager expectations of the United States curriculum, [...], an improvement that is long overdue.
I suspect that a greater focus on advancing rapidly through the curriculum would be a mistake, no matter how well-intentioned.
If we're talking about mathematics applied to everyday life, what's missing are the fundamentals that you're supposed to complete by fifth or sixth grade but most people never really master.
If we're talking about preparation for a mathematically intensive course of higher education then I also don't see the rush. There's often a great disparity between the amount of mathematics "known" among the smarter math freshmen entering university. Some will have read ahead to the beginning graduate level and others will have more closely followed the curriculum's set pace. But given a pair of equally smart students of these two types, they will generally have achieved some level of parity in the extent of their knowledge around the middle of graduate school, their areas of specialization being equal.
The explanation for this phenomenon is surely complex. But I propose that there are two main reasons. The first is that when you race ahead you're likely to leave some gaping holes in your understanding--filling those holes means long, hard work as compared to the glamorous alternative of racing ahead to behold new and exciting mathematical vistas. The second reason is that you've become much better and faster at learning new areas of your subject by the time you get to that level, so it can be time efficient to put off learning until you're more truly ready for it.
What you say is both right and wrong. It is wrong because sometimes children already know the material and would like to move on to other things. On the other hand, letting people race ahead sets up certain unhealthy incentives for people not to properly master their subjects.
Yes, that is what I was trying to convey. The final part of mastering a subject often consists of hard, unglamorous work. Addressing your own weaknesses is never much fun, even if you know deep down that the pay-off will ultimately be worth it.
I suspect that a greater focus on advancing rapidly through the curriculum would be a mistake, no matter how well-intentioned.
If we're talking about mathematics applied to everyday life, what's missing are the fundamentals that you're supposed to complete by fifth or sixth grade but most people never really master.
If we're talking about preparation for a mathematically intensive course of higher education then I also don't see the rush. There's often a great disparity between the amount of mathematics "known" among the smarter math freshmen entering university. Some will have read ahead to the beginning graduate level and others will have more closely followed the curriculum's set pace. But given a pair of equally smart students of these two types, they will generally have achieved some level of parity in the extent of their knowledge around the middle of graduate school, their areas of specialization being equal.
The explanation for this phenomenon is surely complex. But I propose that there are two main reasons. The first is that when you race ahead you're likely to leave some gaping holes in your understanding--filling those holes means long, hard work as compared to the glamorous alternative of racing ahead to behold new and exciting mathematical vistas. The second reason is that you've become much better and faster at learning new areas of your subject by the time you get to that level, so it can be time efficient to put off learning until you're more truly ready for it.
The race is not to the swift, etc.