Gee, all this terrible struggle over what can and can't get from some K-12 school. What a WASTE. Huge misunderstanding.

Bronx High School of Science? How about instead Stanford, MIT, Harvard, Princeton?

How to do that? Well, big secret (don't tell anyone!): How do professors at research universities stay up to date so that they can do leading edge research? Do they take refresher courses at the Bronx High School of Science? Not likely! Do they take courses at all? Essentially no.

So, what the professors do is just study the best materials and go to some seminars. In simple terms, students can do much the same starting with, say, high school ninth grade material and continuing on. If get very far in academics, then just MUST work and learn fully independently or nearly so, so might as well just start doing that ASAP, especially to get around all the terrible struggles of K-12.

Bluntly, nearly no US K-12 teacher knows any material that is worth any student struggling over. So, get THROUGH the K-12 material and get on to college level material, ASAP.

So, for a student who wants the best education in K-12 and later, first, get the basics, the prerequisites for college material, and then study the best college material. "The basics" are just high school math and science together with good skills reading and writing English. History, belle lettre literature, music, etc., maybe fun and nice but for academic success close to irrelevant.

So, in K-12 years, ASAP get into fractions, exponents, compound interest, areas and volumes. Then do first year algebra, plane geometry, second year algebra, trigonometry, solid geometry. Do general science, chemistry, biology, physics. For the science, will do it all again and much more thoroughly again anyway, essentially several times more, so don't get all perfectionistic for the first pass.

Then start on college material -- first up, calculus of one independent variable and then several independent variables, heavy on intuition, light on proofs. Watch the best Internet lectures -- IMHO, Khan Academy is NOT good enough. Use several of the best regarded texts; to find those, ask some college students, TAs, or profs or look at the Web sites of calculus courses at the best universities and see what texts they are using. Likely buy the texts used -- calculus hasn't much changed in decades, highly recommended old texts should be fine and cheap! Do the homework problems and check answers in the back of the book.

Maybe wander onto a college campus or have a family friend who is a college prof and get the tests for the calculus course, take those, and beg a calculus TA or prof to grade the results.

Continue with math and science the same way -- best materials, with some informal contact with a college.

Once get to college junior level material, at some research universities, start attending public research seminars. Typically won't understand more than 10% of the material but WILL get lots of keywords that can motivate and direct studies. Maybe meet a prof or two who will volunteer to grade some homework, say, in math, physics, maybe let you have some copies of tests and grade your solutions. Also many graduate school departments publish their qualifying exams -- they are good and important sources of exercises.

When have good reason to feel confident, take the SAT aptitude tests and the STEM field subject matter tests AND then the same for the GREs. Right, still in K-12 but taking the GRE to show that you are ready for graduate school.

If really want to seal the deal, blow away the college admissions committees, publish some papers, a few should do, in good quality peer reviewed journals.

Then apply to college, maybe using some of the contacts you got from attending the research seminars. So, a friendly prof might just contact the college admissions committee and ask that you be admitted with full scholarship.

So, you enter as a college freshman but start on your Master's and maybe are a TA or research assistant for a prof.

Look, for academics, the real goal is likely not very visible at the Bronx High School of Science or any K-12 place. The real goal is in three words, research, research, and research. For that, get into a good research university, do well learning the prerequisites, attend seminars to see what some of the current research topics are, work with good profs, and do publish some good research.

If want some additional concentration on bio-medical and get an MD, fine. It's also possible to go for a law degree. Or can continue in main line STEM field academics and be a professor at a research university. Or, sure, can do what, say, A. Viterbi did and go for entrepreneurship and, then, get your name on an engineering school!

Does independent study work? It certainly did for me: I got a Ph.D. in applied math and was a college prof. Starting with first year algebra, class time was mostly a waste of time, and I learned nearly all the material, especially the good material I learned well, from independent study. My preparation for the graduate school qualifying exams, my Ph.D. research, my other, published research -- all from essentially just independent study. That's what research professors do -- learn what they need to know and then do their research, both essentially independently.

At least at one time, the math department at Princeton stated on their Web site that no courses were offered for preparation for the qualifying exams, that the courses were introductions to research by experts in their fields, and that students were expected to prepare for the qualifying exams on their own. So, the Princeton math department regards independent study as essential.

One of the best lessons I learned in math was in high school plane geometry: The teacher was the most offensive human I ever saw. So, in class, I just put my head down and slept. Then after school, I read the lesson material quickly and then looked at the exercises. I started with the last, most difficult ones and did them all until I got to the trivial ones. Then I turned to the back of the book for the more difficult supplementary exercises and did ALL of them, never let even one go. So, on the state test, I did well!

I continued to learn math that way: E.g., I never took freshman calculus, instead, got a good text and taught myself, much as I learned high school plane geometry and for a course started on sophomore calculus and did well.

E.g., as a senior, I got a famous, challenging text in topology and gave a prof a lecture a week, for each chapter, one lecture on the material and one more with solutions to the exercises.

It's not just me: Bluntly, if go very far in academics, just MUST be good at independent study. So, might as well get started in high school material, and if do that then can f'get about all the struggles with Bronx High School of Science, Dalton School, etc. Again, the K-12 teachers don't know anything worth struggle. Want to struggle a little? Okay, on YouTube, watch the lectures on quantum mechanics from MIT. Or, for a mathematician giving an introduction to bio-medical research, watch the Eric Lander lectures -- on YouTube, from MIT.

Bronx High School of Science? F'get about it. Again, get the good stuff from, say, Stanford, MIT, Harvard, Princeton, etc. Done. Any questions?