But the two things aren't mutually exclusive: gifted children can both learn how to solve complex problems and accelerate through the standard curriculum.
I'd go so far as to say (at least in my own experience with myself, my DH, and our DD-- all of us HG+)-- that such children rarely
learn math in any other way.
Without challenge, there is no real engagement, mentally speaking. It's like trying to "learn" from standing in line at the department of motor vehicles otherwise.
I estimate that, had we followed her natural arc developmentally, that she would probably have been well-prepared and intrigued by algebra and geometry at about age 8-9. Instead, school ruined her. Well. I say "ruined" but I
have watched this process in action, let's just say, and the results have been striking.
We've joked that we gave her school a curious, engaged 6yo with a two hour attention span and they gave us a 14yo with a twenty second attention span and cynical, perfectionistic, avoidant outlook on life(gallows humor, obviously).
She's "learned" that the "right" answer isn't about a process, and that if at first you don't succeed, it's because there is something Very Wrong and that it is Probably With You, But Could Be With The Problem-- best to give up.
So I
do think that this is partly to blame on how schools think that all children MUST learn mathematics. We should have intervened when they forced her to spend 3 y 'learning' stuff that she knew before she was even four years old. She was at one time like Marnie's DS.
