Mathematical Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education

By Deborah Loewenberg Ball | Go to book overview

Chapter One
INTRODUCTION

The United States needs to substantially improve the teaching and learning of mathematics in American schools. A growing number of Americans believe not only that the future well-being of our nation depends on a mathematically literate population but also that most adults are weak in mathematics, with some groups disproportionately worse off. The basic level of mathematical proficiency needs to be raised substantially, and the gaps in proficiency across societal groups need to be eliminated.

Despite years spent in mathematics classes learning about fractions, decimals, and percents, many well-educated adults, for example, would respond incorrectly to the following question:

If the average salaries of a particular group within a population are 16 percent less than the average salary of the entire population, and one wants to give the individuals in that group a raise to bring them up to parity, what should the raise be—16 percent, something more, or something less?1

Although they may have been taught the relevant calculation skills, what most American adults remember from school mathematics are rules that are not grounded in understanding. Many adults would be unable to answer this problem correctly or even to attempt to reason through it. Proficiency in formulating and solving even relatively simple percent problems is not widespread.

____________________
1
Although 16 percent may seem to be the obvious answer, it is not correct. For example, if the average salary is $40,000, then the salaries of the underpaid group are 16 percent of $40,000 ($6,400) less than the average salary—i.e., $33,600. If one had assumed that 16 percent of the lower salary was the required raise, the raise would have amounted to only $5,376 ($33,600 x 0.16)—clearly, not enough to make up the $6,400 difference between the higher and lower salaries. Instead, one needs to determine what percentage of $33,600 equals $6,400. A simple calculation ($40,000 divided by $33,600) reveals that $40,000 is approximately 19 percent more than $33,600, so the raise required to bring the lower salaries up to par with the higher ones would be a bit more than 19 percent.

-1-

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