I've heard a good argument that algebra specifically should be moved the other way: teach it in elementary school, when kids are first exposed to arithmetic. I

I've heard a good argument that algebra specifically should be moved the other way: teach it in elementary school, when kids are first exposed to arithmetic. I think the core problem here is trying to teach all kids math in the same way. Not all kids are equally capable of learning math. Some smart kids can learn algebra in elementary school. There are plenty of students capable of going through the standard curriculum and finishing calculus by the time they are 13 or 14. For these students, the faster the better. Go into even a "good" second-grade math class and you will find some of these students, acing tests and completely bored with everything taught in class. On the other hand, some students will never be able to have a good understanding of pre-calculus. It doesn't matter if they take it when they are 17 or in college, they will never really get it. Or at least, there is no known teaching method capable of doing it. How can you possibly design an education program that takes this into account? You just can't teach all 15-year-olds the same math curriculum without wasting the time of many of the students, either it's too hard or too easy.