by Lee V. Stiff, NCTM President 2000-2002

*NCTM News Bulletin*, April 2002

*Principles and Standards for School Mathematics* is a comprehensive and coherent set of goals for improving mathematics teaching and learning in our schools. It is designed to be a resource and guide to teachers, developers of instructional materials and textbooks, professional development leaders, teacher educators, and administrators and policymakers, to name a few. It reflects our best thinking about content and pedagogy based on a combination of research, best practice in mathematics education, and experiences and observations of literally hundreds of mathematics teachers in the United States and Canada.

The vision of NCTM is a high-quality mathematics education for every child. The six principles found in *Principles and Standards for School Mathematics* are critical to the success of the Standards and this vision. The six principles are not unique to mathematics teaching and learning, but they must exist within any school that seeks to reap the full benefit of NCTM *Standards*-based instruction. The six principles--equity, curriculum, teaching, learning, assessment, and technology--can affect curriculum development, individual mathematics lessons, teacher assignments, professional development opportunities, and much more. Teachers can grow in their understanding and implementation of these principles over time. Consequently, we must offer opportunities for such growth through professional development.

*Principles and Standards for School Mathematics* consists of content and process standards that identify what we value in school mathematics. It states what students should know and be able to do. It describes how content and process standards grow across four grade bands, i.e., grades pre-K-2, 3-5, 6-8, and 9-12. It has taken great care to explain what we mean by *Standards*-based mathematics in terms of the content--number and operations, algebra, geometry, measurement, data analysis and probability--and the processes of mathematics--problem solving, reasoning and proof, communication, connections, and representation. It also takes great care not to prescribe a menu from which curricular choices might be made. But, in the evolution of implementing the *Standards,* has the time come to provide greater clarity of what *Standards*-based curricula might look like?

Realizing NCTM's vision for school mathematics requires strong systems of local, state and provincial, and national support. Obtaining support depends on many complex factors, not the least of which is the clear articulation of what the *Standards* represent and how we know when they have been effectively implemented.

For example, to what mathematics will students have access? Curricular options often determine the mathematics students have the opportunity to learn. Consequently, should mathematics curricula promote tracking, allowing students to move by different paths through a school's mathematics program, or should mathematics curricula promote advanced study in fewer courses rather than exposure to many different ones? Or should mathematics curricula have supplementary opportunities built into them to accommodate selected students? Is one approach to curriculum development better than the others? Can any curriculum be a *Standards*-based curriculum? Which approach should be promoted among parents, administrators, and policymakers?

Selecting curricular materials, textbooks, and mathematics programs that reflect the *Standards* has proven challenging for many teachers, mathematics supervisors, and administrators. Decisions about selecting appropriate materials may include an attempt to match *Standards*-based prescriptions with actual materials. Publishers can be helpful in highlighting some connections, but concrete correlations are not easily made. Without clear connections between proposed new programs and *Principles and Standards for School Mathematics*, obtaining support from parents, community leaders, and policy makers for *Standards*-based materials may be jeopardized.

Students must have an opportunity to learn high-quality mathematics. In elementary school, it's at least an hour per day. In middle-grades and high school, it's a full year of mathematics in each year. In all cases, the clear articulation of what mathematics students should learn will help teachers devise a scope and sequence of study. Such a scope and sequence will help parents understand the path that instruction will take over the course of a year. This should help them better understand *Standards*-based instructional materials.

Assessment has emerged as a critical aspect of any mathematics curriculum. Tests must be aligned with instructional goals. Furthermore, it is vital that the alignment is made to the satisfaction of teachers, administrators, parents, and policymakers. Agreement on a scope and sequence of mathematics instruction is an important step in guaranteeing that tests do not overshadow curricular goals and appropriate mathematics instruction or ongoing student growth in mathematics learning.

*Principles and Standards for School Mathematics* is a catalyst for continuing improvements in mathematics education. It is time to expand the expectations of each grade band associated with each content standard into a scope and sequence that teachers can use to implement the *Standards* more effectively. It is likely that more than one scope and sequence is appropriate, but at least one NCTM curriculum should be created.

The time has come for NCTM to provide NCTM curricula to help teachers meet the challenges represented by implementing *Standards*-based mathematics programs. Once more, NCTM must lead the way to achieve a high-quality mathematics education for every child.