The vision for mathematics education described in Principles and Standards for School Mathematics is highly ambitious. Achieving it requires solid mathematics curricula, competent and knowledgeable teachers who can integrate instruction with assessment, education policies that enhance and support learning, classrooms with ready access to technology, and a commitment to both equity and excellence. The challenge is enormous and » meeting it is essential. Our students deserve and need the best mathematics education possible, one that enables them to fulfill personal ambitions and career goals in an ever-changing world.
Since the release in 1989 of the Curriculum and Evaluation Standards for
School Mathematicsfollowed in 1991 by the Professional
Teaching Standards for School Mathematics and in 1995 by the
Assessment Standards for School Mathematicsthe National Council
of Teachers of Mathematics (NCTM) has remained committed to the view that
standards can play a leading role in guiding the improvement of mathematics
education. As an organization representing teachers of mathematics, NCTM
shares with students, school leaders, and parents and other caregivers
the responsibility to ensure that all students receive a high-quality
mathematics education. All interested parties must work together to create
mathematics classrooms where students of varied backgrounds and abilities
work with expert teachers, learning important mathematical ideas with
understanding, in environments that are equitable, challenging, supportive,
and technologically equipped for the twenty-first century.
The Need for Mathematics in a Changing World
In this changing world, those who understand and can do mathematics will
have significantly enhanced opportunities and options for shaping their
futures. Mathematical competence opens doors to productive futures. A lack
of mathematical competence keeps those doors closed. NCTM challenges the
assumption that mathematics is only for the select few. On the contrary,
everyone needs to understand mathematics. All students should have the opportunity
and the support necessary to learn significant mathematics with depth and
understanding. There is no conflict between equity and excellence.
Principles and Standards calls for a common foundation of mathematics
to be learned by all students. This approach, however, does not imply
that all students are alike. Students exhibit different talents, abilities,
achievements, needs, and interests in mathematics. Nevertheless, all students
must have access to the highest-quality mathematics instructional programs.
Students with a deep interest in pursuing mathematical and scientific
careers must have their talents and interests engaged. Likewise, students
with special educational needs must have the opportunities and support
they require to attain a substantial understanding of important mathematics.
A society in which only a few have the mathematical knowledge needed to
fill crucial economic, political, and scientific roles is not consistent
with the values of a just democratic system or its economic needs.
The Need for Continued Improvement of Mathematics Education
The vision described at the beginning of this chapter is idealized.
Despite the concerted efforts of many classroom teachers, administrators,
teacher-leaders, curriculum developers, teacher educators, mathematicians,
and policymakers, the portrayal of mathematics teaching and learning in
Principles and Standards is not the reality in the vast majority
of classrooms, schools, and districts. Evidence from a variety of sources
makes it clear that many students are not learning the mathematics they
need or are expected to learn (Kenney and Silver 1997; Mullis et al. 1997,
1998; Beaton et al. 1996). The reasons for this deficiency are many: In
some instances, students have not had the opportunity to learn important
mathematics. In other instances, the curriculum offered to students does
not engage them. Sometimes students lack a commitment to learning. The
quality of mathematics teaching is highly variable. There is no question
that the effectiveness of mathematics education in the United States and
Canada can be improved substantially.
Standards can play a central role in the process of improvement. The
previously released NCTM Standards (NCTM 1989, 1991, 1995)
have influenced state standards and curriculum frameworks (Council of
Chief State School Officers 1995; Raimi and Braden 1998), instructional
materials (U.S. Department of Education 1999), teacher education (Mathematical
Association of America 1991), and classroom practice (Ferrini-Mundy and
Schram 1997). As with any educational innovation, however, the ideas of
the Standards have been interpreted in many different ways
and have been implemented with varying degrees of fidelity. Sometimes
the changes made in the name of standards have been superficial or incomplete.
For example, some of the pedagogical ideas from the NCTM Standardssuch
as the emphases on discourse, worthwhile mathematical
» tasks, or learning through problem solvinghave been
enacted without sufficient attention to students' understanding of mathematics
content. Efforts to move in the directions of the original NCTM
Standards are by no means fully developed or firmly in place.
The Role and Purpose of Standards
The introduction to the 1989 Curriculum and Evaluation Standards noted three reasons for a professional organization to formally adopt standards: to ensure quality, to indicate goals, and to promote change. One way in which standards documents help meet these goals is by shaping conversations about mathematics education. As with the previous NCTM Standards, Principles and Standards offers common language, examples, and recommendations to engage many groups of people in productive dialogue. Although there will never be complete consensus within the mathematics education profession or among the general public about the ideas advanced in any standards document, the Standards provide a guide for focused, sustained efforts to improve students' school mathematics education. Principles and Standards supplies guidance and vision while leaving specific curriculum decisions to the local level. This document is intended to
An Overview of Principles and Standards
Principles and Standards for School Mathematics builds on and consolidates messages from the previous Standards documents. The document is organized into four main parts:
The principles are statements reflecting basic precepts that are fundamental to a high-quality mathematics education. The discussions in chapter 2 elaborate on the underlying assumptions, values, and evidence » on which these Principles are founded. The Principles should be useful as perspectives on which educators can base decisions that affect school mathematics. NCTM's commitment to mathematics for all is reaffirmed in the Equity Principle. In the Curriculum Principle, a focused curriculum is shown to be an important aspect of what is needed to improve school mathematics. The Teaching Principle makes the case that students must have opportunities to learn important mathematics under the guidance of competent and committed teachers. The view of learning that is the basis for the document is taken up in the Learning Principle. The important roles of assessment and technology in school mathematics programs are discussed in the Assessment and Technology Principles.
Chapters 37 outline an ambitious and comprehensive set of curriculum standards for all students. Standards are descriptions of what mathematics instruction should enable students to know and dostatements of what is valued for school mathematics education. Each of the ten curriculum standards proposed in this document spans the entire range from prekindergarten through grade 12. Chapter 3 discusses each Standard in turn to convey its main ideas. In addition, these discussions give a sense of how the ideas encompassed in a Standard develop over all four grade bands, highlighting points at which certain levels of mastery or closure are appropriate. Chapters 47 present the Standards in detail for each grade band.
The first five Standards describe mathematical content goals in the areas of number and operations, algebra, geometry, measurement, and data analysis and probability. The next five Standards address the processes of problem solving, reasoning and proof, connections, communication, and representation. In each grade-band chapter, a set of "expectations" is identified and discussed for each Content Standard. The appendix displays the Content Standards and expectations in a chart that highlights the increasing sophistication of ideas across the grades. Each grade-band chapter discusses what each Process Standard should "look like" in that grade band and what the teacher's role is in supporting the development of that process.
The mathematical Content and Process Standards discussed in chapters 37 are inextricably linked. One cannot solve problems without understanding and using mathematical content. Establishing geometric knowledge calls for reasoning. The concepts of algebra can be examined and communicated through representations.
One purpose of this document is to offer teachers, curriculum developers, and
those responsible for establishing curriculum frameworks a way to focus
curricula. Focus is promoted through attention to the idea of "moving
on." School mathematics programs should not address every topic every
year. Instead, students will reach certain levels of conceptual understanding
and procedural fluency by certain points in the curriculum. Teachers should
be able to assume that students possess these understandings and levels
of fluency when they plan their mathematics instruction. Teachers and
policymakers can then fashion instructional programs and curricular frameworks
that develop progressively over the grades and that focus on important
Chapter 8 discusses what it will take to move toward the vision described
in the previous chapters. In particular, it discusses critical issues
» related to putting the Principles into
action and outlines the key roles played by various groups and communities
in realizing the vision of the Principles and Standards.
As We Move Forward
Attaining the vision described at the beginning of this chapter will require the talents, energy, and attention of many individuals, including students, teachers, school administrators, teacher-leaders, policymakers, parents and other caregivers, mathematicians, mathematics educators, and the local community. It will require that the vision of this document be shared and understood and that all concerned be committed to improving the futures of our children. The task is enormous and essential. All students need an education in mathematics that will prepare them for a future of great and continual change.