may have an even greater effect on children’s proficiency than is the case with reading.
An important recent change in American education is the increased emphasis on ensuring that all children achieve a basic level of competence in reading during the course of elementary school. Success in school also depends on establishing good mathematical competence in the early elementary grades, yet mathematics instruction has not received the same sustained emphasis. Schools generally lack a mathematics specialist corresponding to the reading specialists who provide instruction and assist children having difficulties with the subject. Many school districts have revised their schedules and their curriculum programs to ensure that adequate reading instruction is given in the elementary grades; mathematics instruction has yet to receive similar attention. The recommendations we give at the end of this report attempt to take into account the progress made in homes and at school in achieving reading proficiency.
The mathematics to which U.S. schoolchildren are exposed from preschool through eighth grade has many aspects. However, at the heart of preschool, elementary school, and middle school mathematics is the set of concepts associated with the term number.8 Children learn to count, and they learn to keep track of their counting by writing numerals for the natural numbers. They learn to add, subtract, multiply, and divide whole numbers, and later in elementary school they learn to perform these same operations with common fractions and decimal fractions. They use numbers in measuring a variety of quantities, including the lengths, areas, and volumes of geometric figures. From various sources, children collect data that they learn to represent and analyze using numerical methods. The study of algebra begins as they observe how numbers form systems and as they generalize number patterns.
We have focused much of this report on the domain of number. Most of the controversy over how and what mathematics should be taught in elementary and middle school revolves around number. Should children learn computational methods before they understand the concepts involved? Should they be introduced to standard algorithms for arithmetic computation, or should they be encouraged to develop their own algorithms first? How much time should be spent learning long division or how to add common fractions? Should decimals be introduced before or after fractions? How proficient do children need to be at paper-and-pencil arithmetic before they are taught