When I grew up, it was the end of the Cold War and in America's attempt to "beat the Russians" mathematics education was given tons of funding. As a result, I was able to take a math elective course at a pretty young age with a college professor. In my prep school, Chapin, it was a given that most students graduated 8th grade knowing Algebra I. While I think we can do better than even that, the dumbing down of mathematics education all over the country can now be seen quickly by simply asking the typical 9th grader what math class they are in.
The situation is not so simple though. We cannot simply introduce more complex math topics in younger grades. It won't "fix the problem." We must also a) look to how other countries that are teaching math effectively are doing it and b) craft meaningful PBL assignments that create a culture of inquiry in math. Everything from the terrific project by Andrea Layman for 4th graders teaching them fiscal responsibility by working with local banks to realworldmath.org's PBL assignment using Google Earth to teach math having students look into access to drinkable water across the globe. These projects can start by being done a couple a year and eventually interwoven into the curriculum completely. Our students need to see the relevance to the use of mathematical principles if we want more of them to be math literate.
Just as we cultivate a strong sense of reading and literacy in schools, American schools need to become fixated and even obsessed with mathematics education at the highest level. This will mean seriously looking at some of the math we are currently doing and sometimes discarding it. Certainly some of the math that might have been relevant years ago may no longer be needed (and some may be needed even more). In fact, I would suggest looking at higher math and reviewing what skills, what knowledge students need to be able to bring to the table to do that math well and focusing on this first. We may find the order of how we teach math might also need to be altered. (This is already being done with common core math and Singapore math, but I am skeptical how.) Certainly computer based math needs to be taught at an earlier age (by this I mean calculator math). Estonia is investing a lot in it, but has seen little results on the TIMSS as of yet, so I am not jumping on their bandwagon so fast. We may find even older math curricula (like from the 1800's) to be better than today. I'm open and willing to entertain all ideas, but the current system is not producing real results among Americans in mathematics like it can and should.
I'd love to hear from upper level math teachers and college professors on the topic as well as practitioners of math in the professional fields. How do you think we should change math in this country? What can we learn from other nations programs that are clearly more successful? How can we craft a better learning environment in schools that fosters serious mathematics education that is relevant and rigorous?
If you'd like to see what graduating 5th graders in china can do click here: http://nycpublicschoolparents.blogspot.com/2008/06/sample-of-summer-math-problems-in-china.html
Info on Estonia's use of Computer Based Math https://www.computerbasedmath.org/computer-based-math-education-estonia.html