side note:
What has interested me most is some of the kids who constantly score high in a competition setting are not on a crazy accelerated course. They will have Honors Algebra 1 in 8th grade at a minimum everyone there will.
This sounds right. It is certainly possible to do very well in competitions without acceleration or preparation. (I know.) The good competitions may have a range of problems from not so hard to extremely difficult, but intentionally designed so that advanced knowledge typically can't help, though it may help to know some things not emphasized in school. There are some relevant articles here.
http://www.artofproblemsolving.com/Resources/articles.php?page=calculustraphttp://www.artofproblemsolving.com/Resources/articles.php?page=discretemathhttp://www.artofproblemsolving.com/Resources/articles.php?page=pc_competitionsThat said, strong maths students should not be held back from acceleration, and acceleration is much easier these days with the internet.
