A math curriculum should be well articulated across the grades. In a coherent curriculum, mathematical ideas are linked to and build on one another. Math instruction should prepare students for continued study and for solving problems in a variety of school, home, and work settings. Foundational ideas like place value, equivalence, proportionality, function, and rate of change are important because they enable students to understand other mathematical ideas. Mathematical thinking and reasoning skills are important because they serve as a basis for developing new insights and promoting further study.
Effective teaching requires knowing and understanding mathematics and pedagogical strategies.
Teachers also need to create an intellectual environment where serious mathematical thinking is the norm. Students not only need to learn mathematics, they need to understand what they learn. Students learn more and learn better when they can take control of their learning by defining their goals and monitoring their progress. Using tests to certify students' attainment is not enough. Assessment should be an integral part of instruction that informs and guides teachers as they make instructional decisions.