[picomancer]

Basic algebra and geometry: Order of operations; simplifying expressions; solving quadratic equations by factoring; finding area and perimeter of shapes; the classic "garden problem" (maximize area of a rectangle given fixed sum of 3 sides); naming the Platonic solids; adding, subtracting, multiplying, and dividing complex numbers; logarithms; solving exponential equations.

I think probability, in particular Bayes' Theorem, and basic number theory should be covered in a high school curriculum for the college-bound as well. Including converting numbers between base 2, base 10, and base 16; solving linear congruences with small moduli by trial and error; finding gcd and lcm; prime factorization; determining whether a pair of numbers is relatively prime. Teaching the extended Euclidean algorithm in high school would be on my "nice-to-have" wishlist, but there's only so much classroom time available.

[transientbug]

Part of the problem for why this stuff isn't taught in high school as much is that (and I do say this with some hesitance, as an engineering student who has had a strong math education, imo) I feel most people would probably not benefit much from having that additional content added into the high school course. The other and more major issue I see is that universities seem to be (just from personal experience and hearing friends stories too) starting to want students to take most of their higher maths, that above basic algebra it seems sometimes, at the university. While you could argue that this is because they are greedy and want more money from forcing students to take more classes, I'd like to think that the reason why is because of how fragmented american high school math courses can be.

Personally, as an engineering student, I'd rather take most of my math classes here at my university because they tend to all be tied together (both with the math department and engineering department courses) well and I know that where I leave off in Ordinary Diff Eq, I will pick right back up from in Ord. Diff. Eq 2. Coming from having taken calculus and calculus 2 in high school and having entered straight to calculus 3 in university, I didn't have this comfort and in fact ended up missing some content between the classes as a result. There is also the issue of choice, and the limits of it within the context of high school curriculum.

Just my 2 cents against teaching additional stuff in high school (or probably addressing the wrong point within this comment). Also, I'm not sure (obviously) what its like across the nation, but at my high school at least these topics where all covered and taught to (nearly) all students: > Basic algebra and geometry: Order of operations; simplifying expressions; solving quadratic equations by factoring; finding area and perimeter of shapes; the classic "garden problem" (maximize area of a rectangle given fixed sum of 3 sides); naming the Platonic solids; adding, subtracting, multiplying, and dividing complex numbers; logarithms; solving exponential equations. [...] solving linear congruences with small moduli by trial and error; finding gcd and lcm; prime factorization;

[picomancer]

> most people would probably not benefit much from having that additional content added into the high school course

It would be great if we could switch from content to teaching actual mathematical reasoning. You can read a famous essay called "Lockhart's Lament" for more about this subject. But that's not something that's happening right now either in classrooms or on the standardized tests.

My point is that you have to teach something in high school, and it doesn't feel like the new SAT tests anywhere near four years' worth of content.

> linear equations; complex equations or functions; and ratios, percentages and proportional reasoning

"Linear equations" are a topic that can easily be taught in a month or less. "Complex equations or functions" is unclear, but I assume this means quadratic equations or maybe basic trigonometry -- probably a semester's worth or less. "Ratios, percentages and proportional reasoning" is really middle school level math -- or even elementary school level. It doesn't belong in a high school curriculum, except as review or remedial material.

So all of this content consumes less than a year of high school. I agree that maybe four years of intensive math coursework may be the wrong bar to set for the SAT, but is it setting the bar too high to expect college-bound seniors to know more than a single year worth of math content?

For that matter, only the best students should be expected to get a high score on the SAT; otherwise, the SAT score becomes meaningless. So I should re-phrase the question:

Is it setting the bar too high to expect the best math students among college-bound seniors to know more than a single year worth of math content?

[aet]

The suggested prep for the Math 2 subject test: More than three years of college-preparatory mathematics, including two years of algebra, one year of geometry, and elementary functions (precalculus) or trigonometry or both. I think the "put it on the subject test" is a powerful argument.

[United857]

Those are what the Subject Tests and (for calculus) AP Tests are for.

[dublinben]

In my experience, you should know most of those skills before high school anyway.