...if the school challenges only on achievement, an underachiever may be missed... careless mistakes.
You've nailed it. It's as though the gifted brain seeks challenge and thrives on complexity, turning "on" in the presence of a challenge worthy of its potential, "off" for routine, mundane, mind-numbing repetition. These kids may pick up on higher level concepts, almost able to see the patterns and finish the teacher's sentences, or they may ask unusual questions about applying what they are learning, different ways or methods which may work for solving the problem, finishing a story, etc... they may seem truly out-of-step and be forced to "hide" their thought processes in the classroom. They need their families to be a soft place to land, a place where they can receive validation and affirmation.
Teachers may sometimes over-rely on these kids to answer questions when the rest of the class is lost, and even to tutor other students. Teachers may also sandbag these students, making an example of them by calling on them in class while the child is working ahead in attempt to keep their mind engaged and active without disrupting the class, talking with others, etc.
Even the best behaved, most composed, outwardly compliant, and self-disciplined gifted students may exert tremendous effort to remain so, often by learning to keep their mind occupied: They may be multi-tasking, strategizing, and making mental connections while monitoring the class or performing rote tasks.
Rather than being assessed for the reach of their depth/breadth of knowledge, comprehension, and their ability to explain things in other terms which builds a bridge of understanding for students the teacher was unable to make things clear to... they may often be assessed according to a careless mistake on the simplest of items.
They may receive low placement and pacing, and be locked-in and labeled for careless errors, beginning a downward negative spiral in performance/achievement and self-esteem. These kids may be at risk for dropping out of school and society. This is why we advocate for gifted kids: They simply deserve a chance, an opportunity to learn at a level of challenge worthy of their potential.
Despite careless mistakes. Here is an interesting article from the Maryland Coalition for Gifted and Talented Education (MCGATE) about one individual's preconceptions and even misconceptions in identifying gifted kids
http://mcgate.org/103/, and an article from Duke TIP mentioning careless errors and underachievement
http://tip.duke.edu/node/723. Many more articles may found with search engines.
