I've mentioned before here that I have taught college, high school, and elementary school. Also adult remedial education. The findings here are well known and have been for a long time, they come up all the time in the placement exams used in community colleges. Most people can do addition, subtraction and some multiplication. Fractions, long division, and everything that follows is a complete void for the majority of american adults.

Their conclusions are wrong though. It's not that they weren't taught fractions well enough. It's that the educational system is broken. Kids start doing badly in math at fifth grade. The reason is that's the age where they are old enough to start to realize on some level their time is being wasted, the schools are exhausting and the materials probably useless. Too much time is spent in school pandering to the slowest student. Classes are no longer segregated by ability. Fast students become bored, slow students never catch up, and the rest just misbehave or check out mentally.

To fix the problem, you don't need to push fractions and long division (which, true, most elementary school teachers do not really understand) harder, you need to prevent the students from burning out and losing interest by age 10.

We don't see these results in adults in other countries because they don't burn out their students at such an early age.

The US schools are unlikely to reform for bureaucratic and political reasons. Some argument will be contrived to link fractions to pay, or require higher salaries and funding in order to teach fractions properly. Perhaps yet more computers in the classroom will be proposed as the answer: truckloads of iPads for everyone! This will not solve the problem though.

If you want your kids to learn math properly, tools like Khan Academy are good, especially their web based hierarchical exercise software. This allows students to proceed at exactly the pace they need, independently of every other student.

If you are starting from the beginning, use a sensible curriculum like the Singapore Math series. By fourth grade though you should have a teacher who understands math better than the average american to assist students with it as needed. This is not possible to have in most school districts and is not going to change since people are unwilling to basically burn the schools to the ground and start over (fire everyone and requiring teachers to pass competency exams before rehiring, also eliminate 90% of bureaucracy and rules that impose restrictions on teaching). So things will continue as they are in the schools.