<p>As long as your school district is footing the bill, I agree with those suggesting EPGY, especially if it is proof-intensive. Our son finished Calc BC as a sophomore and could have taken a college class, but couldn't fit it into the schedule around his high school classes and activities. His school offered multivariable that year for a handful of kids with a teacher who basically let the students muddle through on their own, and the next year he took an evening linear algebra class at community college. He got something out of both of those classes, but no experience doing proofs until his first year of college.</p>
<p>I think that even more than the accelerated math, I'd suggest your son accelerate in physics, if that is his ultimate passion. My son has been discouraged in college not by the difficulty of the physics classes but by how many he has to churn through before he gets to what he considers the "fun" stuff. He gets discouraged by profs who say it will be six years of classes before he can understand their research, and hates the idea of having to do labs to reproduce experiments everyone already knows the answer to. If he'd had the opportunity to accelerate through physics, the way he was able to in math, I think the world might have had another physicist rather than what seems likely to be another Wall Street analyst. :)</p>
<p>Sly Si- just thought I'd plug ARML, too. I had a great time on a not-very-competitive ARML team, and I learned a ton from the incredibly gifted kids!</p>
<p>Like Marite's son, mine was an 8th grader in a class of seniors. I think it depends on the personality of the student as to whether that would be a problem...my son was kind of low key, and became comfortable with the older kids. They came to accept the fact that math came easily to him, and were extremely nice to him. I think the ease of a younger student fitting in also depends on how the teacher handles it.</p>
<p>
[quote]
For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer. That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. This is not to say that high school students should not learn calculus they should. But more importantly, the gifted, interested student should be exposed to mathematics outside the core curriculum, because the standard curriculum is not designed for the top students. This is even, if not especially, true for the core calculus curriculum found at most high schools, community colleges, and universities.
[/quote]
From "The Calculus Trap" by Richard Rusczyk.</p>
<p>NYmom,</p>
<p>Mathcounts, ARML, USAMTS, AMC/AIME/USAMO all build skills at the precalculus level and are all great oportunities for the gifted math student. Building sophisticated problem solving skills will be of much greater value to a gifted high school student and future physicist than will completing multivariable calculus and linear algebra.</p>
<p>Interesting points, my$0.02. My son did the exact standard curriculum you describe (two multivariable courses and linear algebra), but his passion and future is with science, not math. I can see for the kind of student you describe, your suggestions make sense.</p>
<p>my$0.02 and others, Thank you for clarifying something that I had been only vaguely aware of. My son, after the weekend he spent at MIT last fall taking 2-hour classes in subjects like Group Theory and Number Theory, complained that he wasn't learning this material in school. I explained that there were very few HS or MS offering math outside of the usual track (algebra, geometry, calculus, etc.), and that the kids he met who knew more than he did were getting it on their own. My son is very interested in accelerating through the regular courses, because he has a burning desire to understand basic physics and he needs calculus for that, but he also seems to have an interest in the other subjects, and I want to make sure he has an opportunity to learn them. </p>
<p>My son is probably going to be a physicist or other scientist rather than a pure mathematician. But I'm a physicist myself, having done (formally) only the regular math track, and I can see the value of the other mathematical fields. I've had to plow through a couple of them n my own in order to solve problems I had, and formal training as well as practice in solving the kinds of problems that appear on math exams would have been immensely valuable to me. </p>
<p>This has all been very helpful. I find CC the best resource for these kinds of issues. Thanks to everyone who commented.</p>
<p>I think that the out-of-the box problem solving approach of math competitions and summer math programs such as PROMYS, Mathcamp, ROSS, etc... will be very helpful to a prospective physicist.</p>
<p>Yes, marite, I agree. I'm leaning toward having him go faster and deeper through the regular curriculum via EPGY and do the competitions/summer programs on the side.</p>
<p>My S was initially self taught - no tutors, no online courses - through 5th grade. His teachers pushed for him to start taking classes at the high school, which he did in the 6th grade. One of my concerns was that he had never learned math in a classroom setting prior to going to the high school. While I had some concerns about him accelerating him so quickly, I thought it was important for him to learn how to learn math in an actual classroom. He had to learn to take notes, keep materials organized, and to show his work in writing. This was initially a challenge for him, especially since he was used to doing everything in his head, but these skills are invaluable in college classes.</p>
<p>Because of his acceleration, he had exhausted the high school curriculum by the 9th grade. He took several college classes throughout high school, but took no math classes at all his junior year. Instead he took AP Physics and increased his involvement in the math competitions everyone has talked about. Now that he's in college, he says that his math competition experience really helps him in both his math and physics classes. The speed and creativity he developed through competitions has been better preparation for physics than the more advanced classes some of his classmates took in high school. He's able to solve very tricky problems on problem sets and exams very quickly. </p>
<p>As every "math mom" here will tell you, every high ability kid is different. You have to make decisions based on what's best for him and what's available in you community.</p>