Some of the major results of future goals of an automatic program synthesis project are described in the two papers that comprise this document. The first paper gives a detailed algorithm for synthesizing a computer program from a trace of its behavior. Since the algorithm involves a search, the length of time required to do the synthesis of…

This study investigated two methods used to teach multidigit multiplication to fourth-grade students: the lattice method and the distributive method. Classes from four schools were randomly assigned so that the two treatment groups contained two each or urban, rural and inner city classrooms. A series of 15 lessons was prepared for each treatment…

The teacher's guide for the second unit of this SMSG series covers the two chapters in Unit 2 of the student text on algorithms and flow charts and on problem formulation. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed,…

It is argued that many investigators utilize the Tucker and Messick (1963) Model with no intention of looking for individual differences or, after utilizing the model, draw improper inferences. An example is given illustrating the difficulties which result from improper use of the model. Several proper methods are outlined. (Author)

A new basic algorithm is discussed that may be used to do factor analysis by any of these three methods: (1) unweighted least squares, (2) generalized least squares, or (3) maximum likelihood. (CK)

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)