The major portion of the article establishes the basis for the stated rule - to divide by a fraction, turn it upside down and multiply. With this background, three justifications for the rule are given. Several possible errors in students' use of the rule are noted. (LS)

This paper describes an investigation of problem sequencing as part of a symposium presenting theoretical concerns and research findings regarding several diverse types of strategies for designing and presenting instructional materials. The first step involved analyzing a set of problems, to determine the knowledge (rules) required for solving the…

The arithmetic needed for complex calculation using an electronic calculator is explained and exemplified. Problems involving square roots, number theory, Fibonacci numbers, and electrical resistances are solved. (SD)

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)

PRESENTED IN THIS PAPER IS A SIMPLIFIED DESCRIPTION OF AN ALGORITHM FOR TRANSFORMATIONAL ANALYSIS OF ENGLISH SENTENCES. IT IS NEITHER ASSUMED NOR IMPLIED IN THIS ALGORITHM THAT ANY KIND OF PRIOR ANALYSIS (EITHER STRING OR CONSTITUENT ANALYSIS) IS REQUIRED AS A PREREQUISITE. IN ORDER TO DEFINE THE SET OF ALL TRANSFORMS, THE AUTHORS FIRST DEFINE A…

THIS PROJECT DEVELOPED A MANUAL TO BE USED BY TRANSPORTATION OFFICERS FOR COMPUTING SCHOOL BUS ROUTES. MATHEMATICAL TECHNIQUES WERE REVIEWED AND A COMPREHENSIVE STUDY MADE OF CRITERIA ELICITED FROM LITERATURE AND INTERVIEWS. QUESTIONNAIRES WERE MAILED TO SCHOOL AUTHORITIES TO RANK THE VARIOUS FACTORS INVOLVED. A COMPUTER PROGRAM WAS DEVELOPED FOR…

An algorithm is defined here as an unambiguous procedure which will always produce the correct result when applied to any problem of a given class of problems. This paper gives an extended discussion of the definition of an algorithm. It also explores in detail the elements of an algorithm, the representation of algorithms in standard prose, flow…

Heretofore, methods of claiming missing issues of serials publications have been ad hoc. The study describes four methods of claiming and analyzes the performance of three of the methods on 16 arrival patterns of serials. The arrival patterns, selected as workable examples from a random sample of the Kardex files at the University of Utah, were…

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)