"Life is open book."
With the advent of widely accessible, inexpensive (or even free) computational tools and Computer Algebra Systems (TI-89, Wolfram|Alpha, etc.), much of what traditionally comprises a high school math curriculum can now easily be done by almost everyone. Factoring polynomials, solving inequalities, graphing linear equations, differentiation and integration -- these are the types of skills high school math students spend most of their time learning, and yet all of it can be done for free by anyone with a web browser.
What does this mean for the high school math curriculum? On the one hand, we could leave it more-or-less the same, insisting that today's student learn what we learned decades ago, while banning or carefully regulating the use of these new tools. On the other hand, we could embrace the tools and the opportunities they create to spend more math class time on different topics and skills, perhaps focusing more on analytic and synthetic problem solving and less on mechanical symbolic manipulation -- but at the risk of students never learning some basic foundations.
So how about it? Binomial coefficients? The angle-addition formulas for trig functions? The conditions under which a function has an inverse? Basic computer programming? Keeping in mind that the vast majority of high school students do not go on to become professional mathematicians, what should the high school math curriculum consist of?
Btw, I post this question (inspired by this discussion) here because this is a community of thoughtful mathematicians. I recognize this discussion may belong in a different forum, but I don't what/where that forum is. Any suggestions are welcome.