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"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.

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    Please set this to community-wiki if it does not get voted to close... (subjective yada-yada?) I liked Theo Gray's little rant when I first read it, though. :)2010-08-23
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    To a large extent, I think the premise is false--the *skills* (generally meaning symbolic manipulations) that can be replaced with CAS are not the core of secondary school curricula today. Further, the notion that secondary school curricula today are the same as they have been for the past decade or two or three is just not true. There is a somewhat cyclical nature to curricula on a national level in the U.S., but even within that, there are shifts, and local variance in the U.S. is very high (and then there's international curricula).2010-08-23
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    On the other hand, there is the persistent accusation that things are getting "dumbed down" even more, every year. Having been off academia for quite a while, it might be great if answers to this question can address that, or better yet, the ones fresh from or are still in the "affected" levels can chime in (under the presumption that since you hang around here, you have an idea on what is or isn't missing in your education).2010-08-23
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    ...and probably the lesson I most want to be hammered home to students: don't (blindly) trust the computer/calculator. Verify, verify, verify!2010-08-23
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    Statistics. it was an optional class in my HS, but if there is anything in math that is used more often and more maliciously to defraud people and persuade the public opinion I can't think of it. People should be aware of the limitations and the meaning of statistical results.2010-10-30
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    Most high school students-outside of the occasional public school class with a passionate teacher and some private schools most Americans can't even afford to go on the tour of-in America can barely ADD AND SUBTRACT in 2012. That tends to make questions like this superfluous,Alex. : (2012-05-03
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    @Mathemagician1234 Perhaps you're right. But I'm the head of the math department at one of those can't-afford-to-take-the-tour private schools, so it's my job to ask these kinds of questions. I welcome any help I can get.2012-05-03

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