I think the history part and the practicality of math is so important, yet I still don't see much of this being taught. Just looking at the math textbooks recently as well, the content is very basic and repetitive in the early years when children are capable of learning more complex math skills.

Have only read the OP: From my own experience coming to a US high school from high school in Europe, I can only say: of all subjects, math was the most different, in the *way* it was taught. Like a completely 180 degree different approach. In my US high school, we were given a formula, which the teacher quickly explained, and then we were supposed to do hundreds of problems/calculations with it. There was no intrigue, no curiosity, no critical thinking, just using the formula. After days or weeks we received another formula. In my high school in Europe, we never knew where the teacher would lead us, he treated the subject as if we were the first ones to discover the problem and its solution, a lot of math history was involved -just hearing it-. The class arrived at the formula as if we had invented it, we were doing a few problems and moved on. We were several years ahead, content wise. That said, I could not do these calculations anymore, regardless of my US or European approach. Clearly though, I enjoyed the European one infinitely more!

Give young, smart, dynamic people an incentive to become math teachers. Right now, there are absolutely none. No money and no respect. Trust me, I was a star math teacher/tutor for Kaplan during college, and I loved teaching. As someone who both knows math and is a good communicator, I had a lot of options, however, and it would have made very little sense for me to have made that choice.

We waste years in elementary school math on memorizing multiplication tables, as if they consist of 100 discrete facts. 6x7=7x6... so focus hard on the commutative property, and cut the burden by half. The 5 and 10 tables are obvious once you understand the system. Squares should be taught graphically, so you can see what "square" (and cube) really mean.

But mostly American children learn "math facts" as if they are arbitrary. And from there, everything about math seems arbitrary.

MORE THAN HALF of the elem. teachers I've encountered have trouble dividing fractions, because someone taught them some voodoo "flip" thing they never understood, as opposed to the nice pizza-dog example above.

Pay math teachers more, showcase math heroes (see, it even sounds funny compared to "sports heroes"), and we'll get better.