You are on to something here. The thing I'd contribute is that then we need teacher training to improve math teaching in the US. Math teaching in the US is often of poor quality, as teachers may not be trained well and are often not confident in their own mathematical ability. Curricula are often haphazard.

The US generally takes the approach that changing the curriculum or changing standards will change outcomes, but rarely invests in teacher quality, which would have very high impact (compare to Korea, Finland, etc.).