Implementing the Standards: Let's Focus on the First Four

In this paper we express a concern that there is a treasury of \advanced" mathematical ideas and experiences that are natural and accessible to children in grades K-4, and yet appear nowhere in the standard contents of the mathematics curriculum for these grades, including the NCTM Standards. We argue: (1) that Standards 1-4 (mathematical reasoning, problem solving, communication and making connections) are the most signiicant of the NCTM Standards and cannot be realized without an expanded mathematics content agenda; (2) that the project of implementing Standards 1-4 is intrinsically connected to the issue of mathematical science popularization, and is well-served by approaches that include manipulative, experiential, and open-ended topics based on deep mathematics; (3) that literature and literacy provide useful and powerful metaphors for understanding the important issues in mathematics education reform. In the project of enriching the mathematics content agenda for grades K-4 there is an especially important role for the wealth of concrete topics and mathematical models of modern discrete mathematics and computer science.