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*.

*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.

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 standards.nctm.org. 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.