I continue to be troubled by the amount of symbolic manipulation in a typical Algebra 2 course. Once a student has completed Algebra 1 and Geometry, shouldn't there be another option for them if a math/science field is not in their future? What would that look like? What else could we teach if we weren't so focused on the path to Calculus?
I'd be careful about trying to identify students for whom a math/science field is not in their future. At the college I work at, about half of our math majors do not intend to major in math or science when they arrive, but discover during their first few semesters that math is actually much more interesting than they had assumed. In the last five years, I've advised math majors who originally intended to major in photography, music, creative writing, anthropology, history, literature, psychology, political studies, and philosophy.
When high-school students don't take Algebra 2, it almost entirely closes off any possibility that they might go to college and study math or science. I agree that there are certainly some students who would be better served by a high-school math course that focused more on quantitative reasoning, but "closing the door" on students who might one day go into science is quite troubling.
At the very least, I would hope that the majority of college-bound students would take an Algebra 2 course. I would even say that it makes sense for most college-bound students to take Precalculus.
I've always thought we should teach students more statistics. Including "uses and abuses" thereof. Serious statistics does require calculus, of course, but I'd throw a non-calculus-based statistics course into the standard HS curriculum, if I were in charge of the world. Statistics is important for all citizens, to be able to understand a lot of what is reported in the news. I would consider it more useful than Algebra II for most students. (However... I also agree with the arguments that we don't want to assume which students don't have higher math in their future.)
A very reasonable question. If the aims of high-school math were purely educational, and if we really knew who might eventually be in STEM fields or not, there'd certainly be many other mathematical topics more interesting, intellectually substantive, aesthetically engaging, etc., than more-of-the-same symbol pushing in Algebra II.
However, in the current state of affairs at many U.S. colleges and universities, "calculus" (often of a cook-book genre) is used as a "filter" for nearly everyone, regardless of eventual major and interests. Thus, the game as it is currently played would often penalize those who'd deviated. This is unfortunate, yes.
NO! Absolutely not!
This answer became resoundingly clear to me when I moved from learning high school and undergraduate math in the U.S. to teaching high school maths in South Africa. The differences in the way maths is taught in the two countries is astonishing, yet the outcomes (at least for good students going to good schools) is more or less comparable. Let me highlight two of the most important differences between the two curricula:
The South African curriculum is standardized nationally. There is overall significantly less room in South Africa for textbook writers, schools, or teachers to decide what content should or shouldn't be taught. Though the U.S. is slowly becoming more standardized with the rise of Common Core standards, I suspect that teachers and curriculum organizers in the U.S. still have much more latitude to teach what and how they want than in South Africa
The most interesting part of South Africa's mathematics education system, however, is their alternate math curriculum called "Mathematical Literacy."
- Maths lit is required through grade 12 for all students not taking the higher grade maths.
- Its purpose is to ground students in "life related applications" and "enable learners to develop the ability and confidence to think numerically and spatially in order to interpret and critically analyse everyday situations and to solve problems." (From p. 19 in the following document: http://www.education.gov.za/LinkClick.aspx?fileticket=25TyZ4RTmKc%3D&tabid=246&mid=594)
- Maths lit has been criticized widely in South Africa for not being rigorous enough. Indeed, South Africa scores among the very worst in its maths scores, an unfortunate and lasting legacy of apartheid. Nevertheless, I believe that while maths lit might not be done correctly in South Africa, I'm wide open to the idea that mathematics can be taught and learned in many different ways.
I believe that the math needs of folks are different (just ask different people when they last computed a derivative or integral...). The hard problem is to find out what each one really needs, and offer personalized curricula... Mostly I believe the resources just aren't there to do this.