I have wondered how the science curriculum should be changed for gifted math students, the vast majority of whom will not become mathematicians.

The Avid Academy in California recommends http://www.avidacademy.com/courses that a physics course be taken in 8th grade after Algebra I is taken in 7th, followed by AP Physics B in 9th grade, AP Chemistry in 10th, and AP Physics C and AP Biology in 11th and 12th, in either order. Usually physics is taken only in 11th grade in the U.S., perhaps because students do not have the math background for it in earlier grades.

The EPGY Online High School lists Sample Courses of Study with a focus on humanities, math/science, or advanced math at
http://epgy.stanford.edu/ohs/samplestudycourses.html . Like Avid Academy, its math/science track also has students taking AP Physics B in 9th grade.

My perspective:

I'm a physical scientist by avocation and training, as is my spouse, and we've both been post-secondary educators in those disciplines as well...

plus our DD is a high school student at the moment, and has definitely got substantial math and science ability/interest.

Her acceleration in math seems to be about right, and this is probably an area where she is more like EG rather than purely PG. That is, she has to work at anything beyond Geometry, though we still find areas of intuitive understanding of concepts and she certainly learns much more rapidly than other classmates.

With that said, I think that the EPGY model has a lot to recommend it, here.

DD could (maybe 'should') have, IMO, taken AP Physics B this past year, while she was taking Algebra II. I would probably hold off on AP Physics until after a student has completed Geometry, simply because so many courses up to that point either skim or don't cover the geometry concepts presented in the texts at all. That material is useful in Physics, even in algebra-based physics, IMO.

I don't necessarily think that taking AP physics this early is the right move for all mathematically gifted students, some of whom may well prefer as less practical/applied approach to things.

For mathy kids with a more theoretical bent, I'd probably enrich mathematics with statistics, modeling, or economics instead after Algebra I, Geometry/Algebra II.

My daughter is not one of the 'theoretical' kind; she did not enjoy Economics with its modeling, but really relished her semester of introductory high school physics as a 9th grader. She's a more 'applied math' mathy kid.

Does that help?

Very interesting topic - thanks, as usual, for bringing it up!

It's on my mind these days too, mostly because ds13 just set his probable course of study in high school in consultation with the heads of the math and science departments at the high school he will attend this fall.

Years ago, I followed what I have long assumed was the common path in high school: Biology, Chemistry and Physics, in that order. But the math and science heads advised ds to take AP Physics B in 9th, AP Physics C in 10th, AP Chem in 11th, and AP Bio in 12th. (Their advice was based partly on the fact that he took Bio in 7th and Chem in 8th via CTD.)

I thought maybe his path was atypical because his math sequence is unusual -- he's aiming to take a joint AP Calc BC - AP Physics C course in 10th. But the science head actually said he thinks this science sequence makes a lot of sense on its own terms, because he thinks of biology as the most complex or interdisciplinary of sciences (sorry, I can't remember his exact choice of words).

So it was very interesting to read that EPGY and Avid Academy recommend a similar course of study.