Methods and indices based on item response theory (IRT) for detecting and diagnosing aberrant response patterns are reviewed. These indices are divided into three groups: (1) residuals-based; (2) likelihood-based; and (3) ratio of covariances-based (extended cautions). For each index, the determination of its sampling distribution as well as its…

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

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…