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The mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. When today's students become adults, they will face new demands for mathematical proficiency that school mathematics should attempt to anticipate. Moreover, mathematics is a realm no longer restricted to a select few. *All young Americans must learn to think mathematically, and they must think mathematically to learn.* (*Adding It Up,* p. 1)

During the late 1980s and 1990s, events such as publication of the National Council of Teachers of Mathematics (NCTM) *Curriculum and Evaluation Standards* (NCTM, 1989), the formation of the National Education Goals Panel, and the call for high expectations for all students spurred demands for the improvement of mathematics teaching and learning. As educators struggled to implement changes or to understand what change might mean in their own systems, the Mathematical Sciences Education Board (MSEB) recognized the need to provide support for those involved in this struggle. So, the Board began work on a document that would provide guidance for educators and other stakeholders making crucial decisions regarding their mathematics programs.

During this time, a variety of groups and organizations produced reports about research findings and policy recommendations relating to mathematical content, effective teaching and learning, and assessment. To ensure that this array of information reached the field in a coherent fashion, MSEB directed its initiative toward helping educators understand how to use these new resources to address key issues related to improving mathematics education. The result *Improving Mathematics Education: Resources for Decision Making,* summarizes the major recommendations in eight documents related to mathematics education and provides an analysis of overlapping recommendations.

To find potential publications, the committee contacted representatives of national mathematics organizations, searched the Web for publications, and considered recent publications from the National Research Council (NRC), the

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1 Introduction
The mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. When today's students become adults, they will face new demands for mathematical proficiency that school mathematics should attempt to anticipate. Moreover, mathematics is a realm no longer restricted to a select few. All young Americans must learn to think mathematically, and they must think mathematically to learn. (Adding It Up, p. 1)
During the late 1980s and 1990s, events such as publication of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards (NCTM, 1989), the formation of the National Education Goals Panel, and the call for high expectations for all students spurred demands for the improvement of mathematics teaching and learning. As educators struggled to implement changes or to understand what change might mean in their own systems, the Mathematical Sciences Education Board (MSEB) recognized the need to provide support for those involved in this struggle. So, the Board began work on a document that would provide guidance for educators and other stakeholders making crucial decisions regarding their mathematics programs.
During this time, a variety of groups and organizations produced reports about research findings and policy recommendations relating to mathematical content, effective teaching and learning, and assessment. To ensure that this array of information reached the field in a coherent fashion, MSEB directed its initiative toward helping educators understand how to use these new resources to address key issues related to improving mathematics education. The result Improving Mathematics Education: Resources for Decision Making, summarizes the major recommendations in eight documents related to mathematics education and provides an analysis of overlapping recommendations.
To find potential publications, the committee contacted representatives of national mathematics organizations, searched the Web for publications, and considered recent publications from the National Research Council (NRC), the

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Department of Education, and other education organizations. The committee was looking for documents that were national in scope, addressed more than one aspect related to K–12 mathematics, and were accessible to educators working to improve mathematics education.
Eight documents form the basis for this report. The following documents are reviewed:
Principles and Standards for School Mathematics
Adding It Up: Helping Children Learn Mathematics
How People Learn: Brain, Mind, Experience, and School
Before It's Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21
st
Century
Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium
The Mathematical Education of Teachers
High Stakes: Testing for Tracking, Promotion, and Graduation
Every Child Mathematically Proficient: An Action Plan of the Learning First Alliance
The authoring groups for the reports in Improving Mathematics Education represent a range of constituencies and viewpoints. Four of the reports were produced by the National Research Council, whose report process is characterized by the deliberate inclusion of balanced viewpoints in committee composition and report review. A fifth report, Principles and Standards for School Mathematics, was produced by the National Council of Teachers of Mathematics, which used Association Review Groups to gather input to the report and reactions to a draft version. These Association Review Groups were convened by organizations representing different facets of mathematics and mathematics education. The NCTM process of seeking and incorporating diverse input was reviewed by an NRC committee and judged to be exemplary. An open process of public hearings and testimony led to a sixth report, which was produced by the Glenn Commission a body appointed by the United States Department of Education. After a lengthy process of review and commentary, The Mathematics Education of Teachers report was produced by the Conference Board on Mathematical Sciences, an organization of professional mathematical associations. The Learning First Alliance report was produced by a group that represents a broad consortium of public policy groups concerned about mathematics education.
This collection of works represents a variety of perspectives and opinions within the mathematics community but, because there are many and substantially different perspectives, it does not necessarily represent a full range of views. Each report represents a negotiated consensus achieved through the consideration of diverse perspectives.

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In addition to having different perspectives on improving mathematics education the eight documents differ in length, potential audience, and scope. For example, the document produced by the Learning First Alliance is not comparable in length or scope to the document produced by the National Council of Teachers of Mathematics. It is, however, significant in at least three ways: (1) it was a significant attempt by a group of those outside of the mathematics education community to address important issues related to improving what happens in mathematics classrooms; (2) it suggested steps the organizations represented by the Alliance might take in order to realize their recommendations; and (3) it served as resource for other groups that built on the thinking in the Learning First Alliance document to produce their own. As another example, the document produced by the Conference Board on Mathematical Sciences and published by the American Mathematics Society is content focused and primarily addresses university mathematics faculty who are in some way responsible for the mathematics preparation of prospective teachers. On the other hand, the document on teacher education published by the NRC is targeted at the wider audience of those who are responsible for preparing teachers. It describes in general the problems and issues related to teacher education and the teaching of science, mathematics, and technology, and it makes policy recommendations that call for restructuring teacher preparation and professional development programs.
Improving Mathematics Education has been designed to help inform stakeholders about the decisions they face, to point to recent research findings, and to provide access to the most recent thinking of experts on issues of national concern in mathematics education. The essence of the report is that information is available to help those charged with improving student achievement in mathematics. The documents cited above can guide those who make decisions about content, learning, teaching, and assessment.
The report is organized around five key questions:
What should we teach, given what we know and value about mathematics and its roles?
How should we teach so children learn, given what we know about students, mathematics, and how people learn mathematics?
What preparation and support do teachers need?
How do we know whether what we are doing is working?
What must change?
Each of the five main chapters in this report considers a key area of mathematics education and describes the core messages of current publication(s) in that area. To maintain the integrity of each report's recommendations, we used direct quotes and the terminology defined and used in that report. If the wording or terminology seems to need clarification, the committee refers the reader directly to the original document. Because these areas are inter

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Page 4dependent, the documents often offer recommendations related to several different areas. While the individual documents are discussed under only one of the components in Improving Mathematics Education, the reader should recognize that each document may have a broader scope. In general, the references in this report should serve as a starting point for the interested reader, who can refer to the original documents for fuller discussions of the recommendations and, in some cases, suggestions for implementation. Improving Mathematics Education is designed to help educators build a critical knowledge base about mathematics education, recognizing that the future of the nation's students is integrally intertwined with the decisions we make (or fail to make) about the mathematics education they receive.