I could use your advice. A 7th grade student has asked what math he should be taking next year and I would appreciate your opinions. I apologize in advance for the long post - feel free to skip the details and start in with your advice if you are so inclined.
This student is currently using an web-based independent study program as he is ahead of his grade and his school offers no other math options. This program (ALEKS) seems to work well for him and he has progressed through pre-algebra and algebra 1 and is now in geometry. The student tells me he expects to complete geometry, algebra 2, trig and pre-calc by the end of this school year or at the latest the end of next summer.
My advice has been to take a proof-based geometry course in 9th grade and calculus in 10th. There is no rush and I don't see any benefit to racing into calculus. The ALEKS geometry does not focus on proofs and it looks like the student will complete this class in about a month.
If you agree with my advice for 9th and 10th, what do you recommend for 8th grade? (If you don't, please comment!) I was thinking of a distance learning version of AP Statistics (perhaps through Northwestern's CTD program) complemented by an Art of Problem Solving class (perhaps Advanced MATHCOUNTS/AMC 8) and/or computer language class.
This is obviously a student who enjoys math and is willing to work independently. But not so independent that he could pick up a book and focus on that as his learning - he needs guidance and checkpoints. My reason for suggesting a proof-based geometry course in 9th is that he would be able to take this in a class with a real live math teacher. I don't have direct experience but it seems to me that this is a type of math where the student would really benefit from the interaction of a class.
So what do you suggest? What am I missing? If this student was you what would you want for yourself?