You might want to be careful about how long you avoid requiring your daughter to show her work.
Our son used computer-based independent study (EPGY & ALEKS) for math from 4th through 7th (pre-algebra), and so other than fruitless prodding from me, he was never asked to show his work. As many parents here undoubtedly experience, he didn't *need* to show his work to get correct answers. And for those rare instances when he did add some scribbling, he was usually incorporating multiple steps into one line.
His first formal classroom instruction was when he took Algebra I as an 8th grader. And guess who demanded that students show all the steps! Although he could still do *most* of the work in his head, his reliance on brute force for the multi-step problems just wasn't cutting it. Unfortunately, he did not have the necessary discipline and so was plagued with careless errors.
Like your daughter, my son is lightning fast (99.8% Processing Speed on WISC). Anything that requires him to slow down (e.g. showing all that stinking work) really frustrates him. After a lower-than-expected score on the CTY SCAT and later the SAT, he clearly needed to force himself to slow down and neatly show his work so that he could reduce the careless errors. (I received some great suggestions and support back in February:
http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/148869/1.html)
I am totally on board with his teacher's demand that he show all the steps. More than once, he's missed out on partial credit when he provided a wrong answer and failed to show the steps he used (which were usually correct).
Additionally, just five minutes thumbing through a college calculus book let my son see how ridiculously easy his "hardest" problems are now compared to the typical stuff he'll face in calculus.
Dandy
