Measuring Up: Prototypes for Mathematics Assessment (1993)

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.