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MEASURING WHAT COUNTS

A POLICY BRIEF

MATHEMATICAL SCIENCES

EDUCATION BOARD

NATIONAL RESEARCH COUNCIL

NATIONAL ACADEMY PRESS
WASHINGTON, DC
1993



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Measuring What Counts: A Policy Brief MEASURING WHAT COUNTS A POLICY BRIEF MATHEMATICAL SCIENCES EDUCATION BOARD NATIONAL RESEARCH COUNCIL NATIONAL ACADEMY PRESS WASHINGTON, DC 1993

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Measuring What Counts: A Policy Brief NATIONAL ACADEMY PRESS 2101 Constitution Avenue, NW Washington, DC 20418 NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce M. Alberts and Dr. Robert. M. White are chairman and vice chairman, respectively, of the National Research Council. The Mathematical Sciences Education Board was established in 1985 to provide a continuing national capability to assess the status and quality of education in the mathematical sciences and is concerned with excellence in education for all students at all levels. The Board reports directly to the Governing Board of the National Research Council. International Standard Book Number 0-309-04986-5 Copyright 1993 by the National Academy of Sciences. All rights reserved. Permission for limited reproduction of portions of this policy brief for educational purposes but not for sale may be granted upon receipt of a written request to the National Academy Press, 2101 Constitution Avenue, NW, Washington, DC 20418. Copies of the policy brief and the complete report may be purchased from the National Academy Press, 2101 Constitution Avenue, NW, Box 285, Washington, DC 20055. Call 800-624-6242 or 202-334-3313 (in the Washington Metropolitan Area). Printed in the United States of America

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Measuring What Counts: A Policy Brief CONTENTS     Preface   vii     Mathematics in Today's World   4     Assessment in Today's World   5     Assessment in the Service of Education   6     The Content Principle   8     The Learning Principle   10     The Equity Principle   12     Obstacles and Challenges   13     Benefits from Improved Assessment   15     Looking to Tomorrow   16     Study Group on Guidelines for Mathematics Assessment   19     MSEB Members   20 The contents of the entire report, from which this policy brief is extracted, are reproduced on pages iv and v.

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Measuring What Counts: A Policy Brief 1 A Vision of School Mathematics 15   Changes in Mathematics and in Mathematics Education 17   What Mathematics Should Be Learned 18   How Mathematics Should Be Taught 21   Who Should Learn Mathematics 23   Current Efforts at Reform 24 2 A Vision of Mathematics Assessment 29   The Role of Assessment in Reform 30   Principles for Assessing Mathematics Learning 32   Educational Principles in Context 34 3 Assessing Important Mathematical Content 41   Designing New Assessment Frameworks 41   Developing New Assessment Tasks 47   Scoring New Assessments 56   Reporting Assessment Results 61 4 Assessing to Support Mathematics Learning 67   Assessment in Support of Learning 69   Assessment in Support of Instruction 78   Assessment in Support of Teachers 83 5 Assessing to Support Equity and Opportunity in Mathematics Learning 91   Developing Assessments to Increase Equity 92   Interpreting Assessment Results 97   Using Assessments to Communicate New Expectations 99   Using Assessment Results to Support Opportunity 104

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Measuring What Counts: A Policy Brief 6 Evaluating Mathematics Assessment 117   The Content Principle 118   The Learning Principle 125   The Equity Principle 129   Generalization 132   Evidence 133   Costs and Benefits 136   Postscript 139   Commissioned Papers 147   Effects of Mandated Testing on Instruction 149   Design Innovations in Measuring Mathematics Achievement 175   Legal and Ethical Issues in Mathematics Assessment 201   Study Group on Guidelines for Mathematics Assessment 225   MSEB Members 226

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Measuring What Counts: A Policy Brief PREFACE Calls for standards in education have been echoing across the nation for several years, especially since political leaders of both parties decided to adopt bipartisan national goals for education. Standards without appropriate means of measuring progress, however, amount to little more than empty rhetoric. To stay the course and achieve the national goals for education, we must measure the things that really count. Since 1989 mathematics has led the national movement toward establishing standards for curriculum, teaching, and assessment, with publication of several significant reports authored by the National Council of Teachers of Mathematics (NCTM), the National Research Council, and the Mathematical Sciences Education Board (MSEB). Measuring What Counts further advances this national discussion by establishing crucial research-based connections between standards and assessment. It demonstrates the importance of three key principles—on content, learning, and equity—for any program of assessment that aims to support the national educational goals. The intent of Measuring What Counts is not to offer immediate practical advice, but to lay out a conceptual framework that will help those who are struggling with the urgent need to develop new assessments that align properly with the national standards for mathematics education. Its message is quite simple, but its implications are profound: Assessment in support of standards must not only measure results, but must also contribute to the educational process itself. Experience reveals enormous gaps between current assessment practice and new goals for mathematics education. It is clear from the recent history of failed reform that when assessment is

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Measuring What Counts: A Policy Brief separated from curriculum and instruction, teaching becomes distorted, thus diminishing learning. Experts agree that for education to be effective, curriculum, instruction, and assessment must harmonize for their mutual support. Both internal (teacher-based) and external (district-or state-based) assessment must support improved learning. However, the path from general agreement to specific assessments is far from clear. We are embarking on a new venture, guided by the principles of content, learning, and equity. Success at this venture will require years of exploration by thousands of practitioners working with mathematics education specialists and measurement experts to achieve a more effective balance of assessment in practice. It will also require leadership and support from policymakers at every level of government. All reform is evolutionary. As society changes, the targets and goals for education change. Assessment is our primary tool for monitoring progress and making midcourse corrections. The principles of assessment set forth in Measuring What Counts provide a solid conceptual basis for current efforts to improve assessment and lay the groundwork for more detailed assessment standards to be published by the NCTM. This policy brief is based on a lengthier report, Measuring What Counts: A Conceptual Guide for Mathematics Assessment, which was developed by National Research Council's Study Group on Mathematics Assessment over a period of two years. Members of the study group faced many significant hurdles posed by their differing professional perspectives, by the rapidly changing context of educational assessment, and by the challenges posed by the new Standards for school mathematics. We owe each of them a special thanks for persisting in this formidable task to reach consensus on the key principles enunciated in the two reports. We are indebted as well to authors of the three commissioned papers published with the full volume, to provide additional background on several core issues addressed by the study group. Like all reports of the National Research Council, the policy brief and the full volume of Measuring What Counts were extensively reviewed—first by outside experts in early draft form, then by the MSEB Committee on Policy Studies at several key stages, and, at the final stage, under the careful protocol of the NRC's Report Review

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Measuring What Counts: A Policy Brief Committee. We thank these many reviewers for their insightful and knowledgeable comments. Financial support for work of the study group and preparation of Measuring What Counts was provided by the U.S. Department of Education and the National Science Foundation. We gratefully acknowledge the support of these organizations. Hyman Bass, Chairman Mathematical Sciences Education Board

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