I do think the most important kinds of high school math are logical thinking, and also statistics (so as to be able to be wary of false claims in advertising and in news reports). Applications to real life, like mortgages, taxes, and running a business are also things worth teaching to all students. I'm less convinced that knowing how to deal with an unknown quantity x is valuable for the students whose future will clearly never include a math-based career. It used to be thought that traditional Euclidean geometry with axioms and proofs is the best way to teach logical thinking. I'm not convinced that this trickle-down based approach is best; perhaps addressing logical thinking directly through real-world problems is better. I do agree with Gene (below) that we do need to try many different approaches, since amidst all the debate, nobody really knows the best methods to use the resources available (which vary widely among school districts, anyway) to get the best results -- without actual experience in trying said methods. I don't know if free market competition is the way to find the best ways. It might be; certainly free market competition has led to a great deal of valuable innovation in certain cases. But on the other hand, privatization (e.g., of prisons) has also often led to the contract being awarded to the lowest bidder, resulting in very low quality of the services provided. SO ... I would conclude that among the many different approaches I mention in my first paragraph, privatization should be one of them, but care should be taken to avoid the low bidders who are likely to provide poor services. --Dan Gene wrote: << The dismal state of math and science public education shows that the current process is a failure, and its deterioration over several decadesindicates that the system is incapable of self-repair. The tragedy is that students who might have become mathematicians and scientists are frustrated and discouraged by a system that is geared towards the dumbest of the dumb. There is no "one size fits all" solution. Only by breaking the public education monopoly, and opening up education to competition will we discover the best processes. . . .

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Sometimes the brain has a mind of its own.