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Database Project United States of America

There is no national curriculum in the United States. 

Each of the 50 states has its own standards that specify the mathematical knowledge and skills that students are expected to learn in each grade (K-8) or grade band or course (9-12) (it depends on the state). 
The question of how to teach the standards, i.e. the question of implementation, is the question of curriculum, and this is chosen by each school district.  There are roughly 18,000 public school districts in the US, and as well students may be in a private school or be home-schooled.

Each state lists its own standards somewhere on a state website.  (There are also standards for other disciplines such as language arts.) For an analysis and comparison of the different state standards, there is a report "The State ot State Standards Post-Common Core, Fordham Institute, 2018";  this document is an analysis and expresses professional judgments, rather than a collection of the actual standards.

b) National Associations:

The US National Commission on Mathematics Instruction, organized through the US National Academies, is the US body charged with interacting with ICMI.  The website is here.  

There are also professional organizations of math teachers, such as the NCTM, as well as of mathematicians (AMS, MAA, SIAM are the largest).

If you have further questions, please contact the US Country representative which can be found here.