School Mathematics Standards Research Articles

Illuminating NCTM's Principles and Standards for School Mathematics

The National Council of Teachers of Mathematics' Illuminations Project provides electronic resources to illuminate the Principles and Standards for School Mathematics and to improve the teaching and learning of mathematics for all students. This paper describes the types of resources that are available and discusses how the Principles and Standards document has guided work on the project. Organized around the six principles, this paper provides a vehicle for further discussion of the vision put forth in the Principles and Standards.

NAEP, TIMSS, and PSSM: Entangled Influences

This article examines the interaction of large‐scale mathematics assessments and standards efforts in the United States. In particular, it considers the (Principles and Standards for School Mathematics (2000) and the (Curriculum and Evaluation Standards for School Mathematics (1989) developed by the National Council of Teachers of Mathematics, the National Assessment of Educational Progress (NAEP) and the Third International Mathematics and Science Study (TIMSS). It traces possible influences the NAEP and TIMSS had on the development of standards, as well as the influence of the standards on the frameworks for these assessments, and speculates about the influence of the Principles and Standards for School Mathematics on future frameworks of the NAEP and the TIMSS.

Principles and Standards for School Mathematics and Teacher Education: Preparing and Empowering Teachers

Teachers and teacher educators play a critical role in the improvement of mathematics education. Recommendations for appropriate teacher support can be gained from examining the Teaching Principle in the document, Principles and Standards for School Mathematics (NCTM, 2000), as well as earlier recommendations from the Professional Standards for Teaching Mathematics (NCTM, 1991). This paper discusses implications of the recommendations for preservice teacher preparation, the continuing professional development of teachers, and mathematics teacher certification policy.

The Cyclical Relationship Between Research and Standards: The Case of Principles and Standards for School Mathematics

The link between standards and research may not be clearcut. However, in this article the authors argue that there is a notable relationship between standards and research, one that is cyclical in nature. Using the standards for school mathematics developed by the National Council of Teachers of Mathematics (NCTM) as a case in point, the authors examine how NCTM's standards have influenced the agenda for mathematics education research and stimulated research on the impact of those standards. In turn, this and other research played a significant role in the development of NCTM's new Principles and Standards for School Mathematics. The authors conclude with a discussion of ways in which the Principles and Standards may continue this cyclical relationship in coming years, potentially promoting investigation of new research areas and systematic research on the impact of standards.

Principles and Standards (2001): October 2001

Since the publication of NCTM's Principles and Standards for School Mathematics in April 2000, considerable discussion has taken place about “key messages” of the document. The breadth of the content of Principles and Standards may hamper attempts to identify messages about particular topics. In addition, many of the fundamental messages are not easily distilled into short phrases. In fact, when such messages are too succinctly articulated, the danger of oversimplification and misunderstanding arises. This misapprehension can be seen in a question that often emerges in discussions about elementary school mathematics and Principles and Standards. That is, what does Principles and Standards say about calculator use in elementary school?

Two Mathematicians' Perspectives on Standards: Interviews With Judith Roitman and Alfred Manaster

This article summarizes an interview in the spring of 2001 with professional mathematicians Judy Roitman, University of Kansas, and Alfred Manaster, University of California, San Diego. Both mathematicians were members of the Writing Group for the National Council of Teachers of Mathematics Principles and Standards for School Mathematics.

In My Opinion: October 2001

As the statement above shows, Principles and Standards for School Mathematics (NCTM 2000) calls for focused and cohesive school mathematics curricula. To create such curricula, we must make hard decisions about what topics to include and what to remove from the curricula. What, then, are the “big ideas” in mathematics for primary grades? The current crowded state of primary curricula is the result of our inability to make hard decisions. It is about time that we tackle this difficult issue.

Implementing and Using Mathematics Standards in North Carolina

North Carolina has a history of supporting and using national standards in structuring the state‐adopted mathematics curriculum framework. This focus is associated with increased achievement of North Carolina students. The connection of the 1989 revision of the framework to the 1989 National Council of Teachers of Mathematics standards seemed to increase acceptance of the framework by teachers, school boards, and the public; revisions since then have been explicitly responsive to evolving national standards. Plans for the next revision include attending to the Principles and Standards for School Mathematics. To inform leaders in North Carolina about the Principles and Standards, a symposium was held in September 2000. This symposium provided a model for making the Principles and Standards visible to different constituencies. It is also important to involve teacher education institutions in sharing the Principles and Standards with new teachers so that they enter teaching with a deep understanding of and appreciation for standards.

How Reform Secondary Mathematics Texts Stack Up against NCTM's Principles and Standards

This analysis of the five NSF–funded secondary mathematics curricula describes their alignment with the Process Standards and Content Standards in Principles and Standards for School Mathematics. Distinctive features and examples are included.

Spotlight on the Principles/Standards: Data in the Middle Grades: A Probability WebQuest

“Spotlight on the Standards” focuses on the grades 6–8 content and process standards found in NCTM's Principles and Standards for School Mathematics (2000). The articles compare NCTM's Curriculum and Evaluation Standards for School Mathematics, published in 1989, with the Principles and Standards relating to the middle grades and suggest ways that teachers might incorporate Standards-based practices into their instruction.

Introduction: Perspectives on Principles and Standards for School Mathematics

Introduction: Perspectives on <i>Principles and Standards for School Mathematics</i>

Families Ask: Understanding Mathematics and Basic Skills

Since the publication of Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and Principles and Standards for School Mathematics (NCTM 2000), many school districts and teachers have implemented new curriculum materials to achieve the vision of the Standards. In addition, many educators have adopted a constructivist viewpoint in their teaching practices, resulting in hands-on lessons for children and the use of real-life problems, visual and hands-on approaches, and invented strategies for solving problems. In the context of reform, however, parents and community members are prone to question whether their children will actually “learn the basics” when engaged in hands-on, real-life investigations.

Teaching Addition and Substraction Facts: A Chinese Perspective

In its Principles and Standards for School Mathematics, the NCTM suggests that fluency with basic addition and subtraction number combinations is a goal in teaching whole-number computation (NCTM 2000, p. 84). A mastery of lower-order skills instills confidence in students and facilitates higher-order thinking. The ability to automatically recall facts strengthens mathematical ability, mental mathematics, and higher-order mathematical learning. Without this automation, students have difficulty performing advanced operations.

Shape Makers

Summary Professional standards for school mathematics recommend that dynamic geometry programs such as the Geometer's Sketchpad can and should be used to enhance student learning of geometry. This article illustrates how a geometry computer microworld containing screen manipulable, dynamically transformable shape-making objects can promote the development of powerful geometric reasoning. Also described is the overall context and factors that should guide mathematics educators' design and use of instructional technology.

Links to Literature: May 2001

The phenomenal resurgence of children's literature in the marketplace has allowed teachers to help their students construct new knowledge by fostering the love of literature while teaching skills and knowledge. Principles and Standards for School Mathematics (NCTM 2000) recommends connecting mathematics with the real-world experiences of children. The authors chose Cook-a-Doodle-Doo! (Stevens and Crummel 1999) to provide students with opportunities for problem solving, estimating, predictive reading, and enjoyable eating.

Call for Manuscripts: Articles Related to Principles and Standards

The Editorial Panel is seeking manuscripts that help teachers understand Principles and Standards for School Mathematics, that connect these standards with those in the 1989 version, and that explore new ways of implementing them in classrooms.

Standards-Based Teaching: Alive and Well in Portugal

NCTM'S Professional Standards for Teaching Mathematics (1991) emphasizes that teachers are “the key” to changing mathematics teaching and learning. Given that mathematics reform movements have never brought about “large-scale changes in teachers' behavior and teaching practices” (Hitch 1990, p. 2), Willis (1992) lamented that “whether the standards will actually produce sweeping changes in the way mathematics is taught and learned in U.S. classrooms remains to be seen” (p. 1). With Principles and Standards for School Mathematics (NCTM 2000), we continue to ask the vital question, How can we induce teachers to implement the Standards?

NCTM’s Principles and Standards for School Mathematics: Implications for Administrators

The National Council of Teachers of Mathematics (NCTM) unveiled Principles and Standards for School Mathematics in April 2000. An extension of three earlier publications, Principles and Standards is a resource for anyone who makes decisions affecting mathematics education for prekindergarten through grade 12. This article highlights key points and discusses the importance of school administrators in realizing the vision set forth in the document.

A History of Mathematical Dialogue in Textbooks and Classrooms

Mathematical communication is an important goal of recent educational reform. The NCTM's Principles and Standards for School Mathematics (2000), continuing an emphasis on mathematical discourse from the 1991 Professional Standards for Teaching Mathematics, has a Communication Standard at each grade level. This article examines textbooks and classrooms from antiquity through the nineteenth century in search of historical precedents for mathematical communication in the form of dialogue between teacher and student. Although we have no way of knowing how prevalent this mode of teaching has been, interest in dialogue as a tool for helping students learn mathematics has been ongoing.

Principles and Standards (2001): March 2001

At the beginning of the twentieth century, David Eugene Smith wrote a book about teaching geometry. Although it was written for secondary school geometry teachers, his preface describing why he wrote the book is applicable for all grades. He said that his book “… stands for vitalizing geometry in every legitimate way; for improving the subject matter in such a manner as not to destroy the pupil's interest; for so teaching geometry as to make it appeal to pupils …” (Smith 1911, p. iv). At the beginning of the twenty-first century, the Principles and Standards for School Mathematics (NCTM 2000) gives us guidance in revitalizing geometry for elementary school students. In this article, we share some of its messages for teachers of prekindergarten through grade 5.