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Measuring What Counts: A Conceptual Guide for Mathematics Assessment
CHANGES INMATHEMATICS AND INMATHEMATICSEDUCATION
The mathematics taught in school must change in support of the way mathematics is used in our society.
Since 1900, the growth of the mathematical sciences—in scope and in application—has been explosive.5 The last 40 years have been especially productive, as advances in high-speed computing have opened up new lines of research and new ways mathematics can be applied. Problems in economics, social science, and life science, as well as large-scale problems in natural science and engineering, used to be unapproachable through mathematics. Suddenly, with the aid of computers and the new tools provided by research, many of these problems have become accessible to mathematical analysis. Applications derived from data analysis and statistics, combinatorics and discrete mathematics, and information theory and computing have greatly extended the definition and reach of the mathematical sciences.
An explosion in the way mathematics is used in society mirrors the explosion in mathematics itself. Today we encounter uses of mathematics in every corner of our lives. Graphs, charts, and statistical data appear on television and in newspapers. The results of opinion polls are reported along with their margins of error. Lending institutions advertise variously computed interest rates for loans. We listen to music composed and performed with the aid of computers, and we watch the fantastically detailed pictures of imaginary worlds that computers draw. Computers also do a host of ordinary tasks. They scan bar codes on purchases, keep track of inventories, make travel reservations, and fill out income tax forms. The citizen's need to perform simple calculations may have decreased, but there has been a dramatic increase in the need to interpret, evaluate, and understand quantitative information presented in a variety of contexts.
Although some people do not need or use highly technical mathematics in their daily jobs, many others do. The complexity of daily life requires that we all be able to reason with numbers. Any car or home buyer ought to understand how interest rates work even though a computer may be doing the calculation. Anyone building a house or redecorating a room should be able to make and read a scale drawing. Newspaper readers and television viewers