Individual fifth grade classrooms in five schools of differing socioeconomic levels were used in a study to analyze the reaction of the school to the experimental format, the adequacy of the test instrument, and the differential effects of the experimental treatments. Students were instructed in one of two experimental addition algorithms,…

Beginning with the results of Girschick on the asymptotic distribution of principal component loadings and those of Lawley on the distribution of unrotated maximum likelihood factor loadings, the asymptotic distributions of the corresponding analytically rotated loadings is obtained. The principal difficulty is the fact that the transformation…

One hundred seventy-six seventh grade students underwent a recorded interview where each was given a set of computational exercises and asked to say aloud his thinking as he worked them. The most frequently used strategies in computations with whole numbers and fractions are described in detail, an analysis of the nature of wrong answers is…

This guide continues instruction of the three guides in SE 012 723 and of the two guides included in SE 012 724. Counting skills, appreciation of pattern and order, and understanding of place value are extended to numbers up to one million, and the associative, commutative and distributive laws are made explicit. Manipulation of equations is…

When two methods of transforming numbers from one base to another were taught sequentially, the first interfered with learning of the second. (SD)

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (MP)

Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

The method described here converts a given problem in a base other than ten to a related problem in base ten, solves the related problem in base ten, and converts the answer back to the original base. Limitations are discussed. (MP)

The patterns of the coefficients in the expansion of (x + y +z)n are discussed, and a recursive property is developed as a generalization of the Pascal triangle. (MP)

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

An algorithm for the calculator is given for determining the day of the week for any date. An instructional sheet, a worksheet, and a BASIC program are included. (MP)

A straight forward process for working in fractions on any calculator is presented. The method involves converting a decimal back into a fraction in its lowest terms. (MN)

Algorithms are developed and presented for the addition and multiplication of positive rational numbers using only their repeating decimal representation. (MN)

Calculators are a big help in extending classroom activities and this article took a look at how the students of tomorrow might use them. (RK)