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Measuring Up: Prototypes for Mathematics Assessment
Introduction

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Measuring Up: Prototypes for Mathematics Assessment
Goals for School Mathematics
The 1989 NCTM report Curriculum and Evaluation Standards for School Mathematics identifies five broad goals for students' study of mathematics:
To value mathematics. Students must recognize the varied roles played by mathematics in society, from accounting and finance to scientific research, from public policy debates to market research and political polls. Students' experiences in school must bring them to believe that mathematics has value for them, so they will have the incentive to continue studying mathematics as long as they are in school.
To reason mathematically. Mathematics is, above all else, a habit of mind that helps clarify complex situations. Students must learn to gather evidence, to make conjectures, to formulate models, to invent counterexamples, and to build sound arguments. In so doing, they will develop the informed skepticism and sharp insight for which the mathematical perspective is so valued by society.
To communicate mathematics. Learning to read, to write, and to speak about mathematical topics is essential not only as an objective in itself — in order that knowledge learned can be effectively used — but also as a strategy for understanding. There are no better ways to learn mathematics than by working in groups, teaching mathematics to each other, arguing about strategies, and expressing arguments carefully in written form.
To solve problems. Industry expects school graduates to be able to use a wide variety of mathematical methods to solve problems. Students must, therefore, experience a wide variety of problems that vary in context, in length, in difficulty, and in method. They must learn to recast vague problems in a form amenable to analysis; to select appropriate strategies for solving problems; to recognize and formulate several solutions when that is appropriate; and to work with others in reaching consensus on solutions that are effective as well as logical.
To develop confidence. The ability of individuals to cope with the mathematical demands of everyday life — as employees, as parents, and as citizens — depends on the attitudes toward mathematics conveyed by school experiences. One of the paradoxes of our age is the spectacle of parents who recognize the importance of mathematics yet boast of their own mathematical incompetence. Mathematics can neither be learned nor used unless it is supported by self-confidence built on success.

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Measuring Up: Prototypes for Mathematics Assessment
Measuring What's Worth Learning
The spotlight of educational reform continues to sweep across the stage of mathematics. First curriculum, then teaching, and now assessment have come under intense professional and public scrutiny. Amid deteriorating public confidence in the quality of American education, the mathematical community is addressing multiple challenges to articulate and implement effective standards in the key arena of testing, assessment, and accountability.
In the center of the assessment stage are three elements contesting for leadership. Conventional testing offers comfortable short-response tests on traditional content that are taken by millions of students every year. Reformers, including authors of the two K-12 Standards documents from the National Council of Teachers of Mathematics (NCTM), call for fundamental change — different in content, in format, and particularly in spirit. To this well-rehearsed contest of traditionalist vs. reformist has now been added a third movement arriving from outside the educational community: the political call for assessment of progress towards our nation's new standards in mathematics education.
In the decade since publication of A Nation at Risk, the United States has moved a long way toward a new consensus for education. Talk of national standards, once taboo, is now commonplace; so too is talk of alternative school structures