Conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly, but must be inferred from fallible or incomplete data. For example, responses to mental test items may depend upon latent aptitude variables, which modeled in turn as functions of demographic effects in the population. A…

A subtraction algorithm for numbers having several digits is described. The algorithm requires that, for digits in the same place, the smaller is always subtracted from the larger. (SD)

A new subtraction algorithm is described and illustrated. Research by the author has shown the method to be easier for low achievers, as well as useful as enrichment for average students. (SD)

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…