I just posted the following Quora answer to the question “What are the problems with math education today?”
One of the issues with math education that is rarely considered, is a question of “what should be learned”? While I echo other respondents who say that there is not consensus on the goal of math, if we at least assume that one important part of mathematics is how it can be used, then there are scientific methods of determining which particular parts of math are important to know for a particular context (nation, career, etc.), but I have seen little in the way of research on this, and less in the way of using the research that is available.
For example, in the U.S., not a single state nor the Common Core State Standards require students to know what a Trillion means before they graduate high school (Walker 2011), yet they are supposed to know scientific notation and imaginary numbers before graduation… Something seems amiss with this set of priorities.
Walker, J. J. (2011). Missing a “Trillion”: How do we know if we are teaching the right things? SSRN eLibrary. doi:10.2139/ssrn.2194853