|A curriculum is more than a collection of activities: it must be coherent,
focused on important mathematics, and well articulated across the
Mathematics is a highly interconnected and
cumulative subject. The mathematics curriculum therefore needs to introduce
ideas in such a way that they build on one another. Instead of seeing
mathematics as a set of disconnected topics, students should perceive the
relationships among important mathematical ideas. As students build connections
and skills, their understanding deepens and expands.
The curriculum also must focus on important
mathematics--mathematics that is worth the time and attention of students and
that will prepare them for continued study and for solving problems in a variety
of school, home, and work settings. The relative importance of particular
mathematics topics is likely to change over time. Topics such as recursion,
iteration, and the comparison of algorithms have emerged and deserve increased
attention because of their relevance.
Students should have opportunities to learn
increasingly more sophisticated mathematical ideas as they progress through the
grades. They should not spend a significant part of their instructional time
reviewing mathematics content. A well-articulated curriculum is necessary for
teachers at each level to know what mathematics their students have already
studied and will study in future grades.