Speed and accuracy in adding a colunm of one addend numbers directly down a column was compared to adding by looking for combinations which add to ten. Ninety-two fourth-grade subjects learned one of these two methods for one week and then learned the other method the following week. Using timed tests after each treatment, it was found that the…

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

Presented are the results of a study conducted to develop algorithms for ordering and organizing data that can be presented in a two-dimensional matrix form. The purpose of the work was to develop methods to extract latent data patterns, grouping, and structural relationships which are not apparent from the raw matrix data. The algorithms…

Large-scale, on-line information storage and retrieval systems pose numerous problems above those encountered by smaller systems. A step toward the solution of these problems is presented along with several demonstrations of feasibility and advantages. The methodology on which this solution is based is that of a posteriori automatic classification…

This Noun Reference Dictionary is divided into two sections: nouns derived from verb roots and those not so. The following features are noted in each entry: (1) class index; (2) occurrence in idiomatic expression; (3) part of speech; (4) declinability; (5) occurrence with prefixes "B,""K,""L," and "M," or…

This document comprises the second part of the pure nominal section of the Noun Reference Dictionary. See AL 002 267 for the first part, and AL 002 269 and AL 002 270 for the verb root-nominal sections. ED 019 668 and AL 002 296 contain a description of the project. (DO)

The purpose of this study was to determine differences in achievement of fifth-grade students in 16 classes taught two of four mathematical algorithms by one of four instructional strategies. Computational skills and ability to extend the algorithm were tested. The instructional strategies were: pattern, algebraic, pattern followed by…

On the basis of analytical and observational work during Phase 1 of this project, an experiment was developed to test the effects of systematic variations in the level of the independent variable "instructional cue" (I.C.). The first phase of the research consisted of the development of a precise operational definition of the variable. This was…

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…