Extending the teaching of multiplication facts at the seventh grade level

Researchers in the field of mathematics education discovered dissatisfaction with the revised mathematics curricula instigated after World War II. These curricula, intended to familiarize students with the concepts and the basis of the numeration system, failed to improve computational skills to the expected level. It may have been that the bases of the concepts as taught in the "new math" were not thoroughly understood, but merely memorized and used as tools. The material used in this experiment was developed to allow the students to use the concepts of structure currently being taught. To extend and generalize them with an improvement of computational accuracy and to increase the speed of the computations while emphasizing the structure of the numeration system were the primary goals of this study. The explanation given during the lessons demonstrated how the digits were placed, and the discovery method enabled the students to understand why with expanded notation the long multiplication process could be eliminated. The experimental lessons included the extension of the multiplication table through the twenties, squaring two-digit numbers, multiplying any pair of two-digit numbers, and tests of divisibility by primes as an aid in calculating with fractions. Two seventh grade classes from each of the three junior high schools were used in testing these additions to the curriculum. One class from each school was placed in the control group and one in the experimental group. Each of these six classes was taught at regular intervals for nine lessons. ..