These results clearly showed that the early school mathematics experience in the United States ignores many of the actual capabilities of young children. At the same time, reports from international studies showed U.S. students learning much less mathematics in grades K-6 than students in many other countries. Teachers and other adults are a very important part of that experience. Children begin school with quite a lot of knowledge and intuition on which to build. One important task for the K-6 curriculum is to help children make the gradual transition from intuition and concrete operations to abstractions and symbol processing skills.
Excellent instruction is very important.
It should provide rich contexts and accommodate a variety of learning styles. Reforms often fail because they do not take into consideration the working lives of teachers. The new curriculum should be practical and manageable and it should include suggestions and procedures that make teachers' lives easier, at least in the long run. The new curriculum should include practical routines to help build the arithmetic skills and quick responses that are so essential for building number sense, estimation skills, and flexibility in a problem-rich environment. Thinking with mathematics becomes as natural as thinking with language Features of Everyday Mathematics Everyday Mathematics establishes a framework for dialogue about mathematics between teacher and children and among children themselves.