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Standards Overview


Realizing the Vision 

Standards 2000 Project  



We live in a mathematical world. Whenever we decide on a purchase, choose an insurance or health plan, or use a spreadsheet, we rely on mathematical understanding. The World Wide Web, CD-ROMs, and other media disseminate vast quantities of quantitative information. The level of mathematical thinking and problem solving needed in the workplace has increased dramatically.

In such a world, those who understand and can do mathematics will have opportunities that others do not. Mathematical competence opens doors to productive futures. A lack of mathematical competence closes those doors.

Students have different abilities, needs, and interests. Yet everyone needs to be able to use mathematics in his or her personal life, in the workplace, and in further study. All students deserve an opportunity to understand the power and beauty of mathematics. Students need to learn a new set of mathematics basics that enable them to compute fluently and to solve problems creatively and resourcefully.

Principles and Standards for School Mathematics describes a future in which all students have access to rigorous, high-quality mathematics instruction, including four years of high school mathematics. Knowledgeable teachers have adequate support and ongoing access to professional development. The curriculum is mathematically rich, providing students with opportunities to learn important mathematical concepts and procedures with understanding. Students have access to technologies that broaden and deepen their understanding of mathematics. More students pursue educational paths that prepare them for lifelong work as mathematicians, statisticians, engineers, and scientists.

This vision of mathematics teaching and learning is not the reality in the majority of classrooms, schools, and districts. Today, many students are not learning the mathematics they need. In some instances, students do not have the opportunity to learn significant mathematics. In others, students lack commitment or are not engaged by existing curricula.

Attaining the vision laid out in Principles and Standards will not be easy, but the task is critically important. We must provide our students with the best mathematics education possible, one that enables them to fulfill personal ambitions and career goals in an ever changing world.

Principles and Standards for School Mathematics has four major components. First, the Principles for school mathematics reflect basic perspectives on which educators should base decisions that affect school mathematics. These Principles establish a foundation for school mathematics programs by considering the broad issues of equity, curriculum, teaching, learning, assessment, and technology.

Following the Principles, the Standards for school mathematics describe an ambitious and comprehensive set of goals for mathematics instruction. The first five Standards present goals in the mathematical content areas of number and operations, algebra, geometry, measurement, and data analysis and probability. The second five describe goals for the processes of problem solving, reasoning and proof, connections, communication, and representation. Together, the Standards describe the basic skills and understandings that students will need to function effectively in the twenty-first century.

The ten Standards are treated in greater detail in four grade-band chapters: prekindergarten through grade 2, grades 3–5, grades 6–8, and grades 9–12. For each of the Content Standards, each of the grade-band chapters includes a set of expectations specific to that grade band.

Finally, the document discusses the issues related to putting the Principles into action and outlines the roles played by various groups and communities in realizing the vision of Principles and Standards.


Realizing the Vision

Overhead Principles and Standards for School Mathematics acknowledges that there are significant challenges in realizing the vision for improving mathematics education. For example, How can all students have access to high-quality mathematics education? How can teachers learn what they need to know? Are assessments aligned with instructional goals? The Principles provide a useful perspective in addressing these difficult issues.

Many groups and individuals need to be involved in attaining the vision described in Principles and Standards, including teachers, mathematics teacher-leaders, school and district administrators, institutions of higher learning, mathematicians, professional organizations, parents and other caregivers, politicians, business and community leaders, and students. Principles and Standards can help all these people engage in constructive dialogue about mathematics teaching, curriculum, and assessment. It is a means for developing a shared commitment to the improvement of mathematics education.

A strong system of support is needed at both the local and national levels in order to make the vision of Principles and Standards a reality. Teachers must continually update their professional knowledge, both of mathematical content and of pedagogy. Teacher-leaders should strive to shift the conversation among their colleagues from just "activities that work" to a critical analysis of their practice. School, district, and state or province administrators must establish effective structures that support students' learning and teachers' professional growth.

The teaching of mathematics can be controversial. Today's mathematics classrooms look quite different from classrooms of twenty years ago. Outreach to parents and others in the community is essential. Choices of instructional materials need to be based on a community's agreed-on goals for mathematics education. Parents and caregivers should know why an extensive and rigorous mathematics education is essential for their children and what options are available. Students must take responsibility to engage seriously with mathematics. Community members need to understand the changing goals and priorities of school mathematics and must be involved in the process of improving mathematics education.

Though the challenge posed by Principles and Standards is great, there are good reasons to be optimistic. A substantial body of research on teaching and learning is now available that can guide the teaching of mathematics. Many strong communities of practice already exist among teachers, administrators, and others. Powerful organizations are supporting efforts to improve mathematics instruction. If teachers work together with the many other groups that influence mathematics education, all children can receive the solid grounding in mathematics that they will need in the twenty-first century. It is our hope that Principles and Standards will serve as a catalyst for the continued improvement of mathematics education.


Standards 2000 Project

With the release of Curriculum and Evaluation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics (NCTM) moved to the forefront of efforts to improve mathematics education in the United States and Canada. The document marked a historically important first step by a professional organization to articulate extensive goals for teachers and policymakers in a school discipline. Since its release, the Curriculum and Evaluation Standards has provided focus, coherence, and new ideas to mathematics education.

In 1991 the NCTM, which is an international organization of teachers and others committed to excellence in mathematics teaching and learning for all students, published Professional Standards for Teaching Mathematics, which described the elements of effective mathematics teaching. Assessment Standards for School Mathematics, which appeared in 1995, established objectives against which assessment practices can be measured. Together, these three documents have given focus, coherence, and new ideas to efforts to improve mathematics education.

NCTM recognized that its Standards would need to be periodically examined, evaluated, and revised to remain relevant. In 1995 its Board of Directors appointed the Commission on the Future of the Standards to recommend how NCTM might proceed in updating its existing Standards documents. As a result, the Standards 2000 project was begun in 1997, with the appointment of a Writing Group to produce an updated Standards document and an Electronic Format Group to produce an electronically enhanced version of that document.

The Commission obtained input from many different sources to revise the Standards. The Writing Group consulted extensive collections of curriculum materials, state and provincial curriculum documents, research publications, policy documents, and international frameworks and curriculum materials. Association Review Groups, a set of "white papers" commissioned by NCTM's Research Advisory Committee, and conferences sponsored by the National Science Foundation and the Eisenhower National Clearinghouse furnished additional input.

The Writing Group finished a draft version of the new document in October 1998, and many groups and individuals reviewed the printed draft and its electronic edition on NCTM's Web site. The Writing Group substantially revised the document on the basis of the many hundreds of reactions received in response to the draft.

The resulting book, Principles and Standards for School Mathematics, is a single resource that can be used to improve mathematics curricula, teaching, and assessment. Principles and Standards is also available in an electronic edition on CD-ROM and on the World Wide Web at The electronic edition of Principles and Standards has a rich array of examples to illuminate and extend the ideas presented in the printed text. Icons in the margins of the printed text indicate relevant electronic examples.


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