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What's high achieving? Does it mean able to churn out ever-greater amounts of homework on time? Test at "A" level on all quizzes and exams?

If by high-achieving, you mean overeager, extroverted, people-pleaser, perfectionist, likes busywork etc., then no, programs should not be for high achievers (or not focused on them, at leadt) because that encourages unhealthy traits and hothousiing.

On the other hand, if a student happens to be able to do algebra and is ready to be in the honors algebra class, then I don't think IQ should matter -- it's their ability, and whether they're officially gifted or not, they need to be at their ability level.

At the same time, I don't think giftedness is exactly a "magic card" allowing kids to be able to do everything at a high level -- maybe some gifted kids at the same age just aren't ready for algebra, whether because of preparation or ability, and so that might not be the best choice.

I doubt anyone here would deny any student an appropriate learning environment, but I just want to say that I don't think it's right to decide, "Well, Susan, your parents took you to Kumon and now you'll be bored in Geometry....but your IQ is only 112. Julie has a 150 IQ and will be in the class instead, even though she didn't pay attention last year and isn't prepared for it." Not all gifted kids are geniuses and not all NT kids are incapable of advanced work.