Several methods for the analysis of three-way data (data classified three ways) are described and shown to be variants of principal components analysis of the two-way supermatrix in which each two-way slice is strung out into a column vector. Direct fitting and fitting derived data are considered. (SLD)

The general transformation approach to time series analysis is extended to the analysis of multiple unit data by the development of a patterned transformation matrix. The procedure includes alternatives for special cases and requires only minor revisions in existing computer software. (SLD)

The concept of paradigm as disciplinary matrix and exemplar is applied to industrial education. It is suggested that research on the rapid and profound changes in the field must proceed within an explicit conceptual framework that takes into account the unique structure and dynamic nature of the field. (SK)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Describes methods for item construction for computer-based instruction (CBI). Use of a rational set generator (RSG) in presenting an adaptive sequence of items to the learner is described; a model matrix of a computer-based RSG is presented; concrete and defined concepts are discussed; and rule using is explained. (Four references) (LRW)

The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…

An example of scale invariance is provided via the LISREL model that is subject only to classical normalizations and zero constraints on the parameters. Scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. (TJH)

This fourth in a series of edited transcripts based on a conference at Utah State University compares Gagne's Conditions of Learning with Merrill's Component Display/Design Theory, and suggests a merging of the two. Topics discussed include content structures, learning hierarchies, learning theories, learner control, problem solving, cognitive…

Students can learn to make algebra, trigonometry, and geometry work for them by using matrices to rotate figures on the graphics screen of a graphing calculator. Includes a software program, TRNSFORM, for the TI-81 graphing calculator which can draw and rotate a triangle. (MKR)

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

Psychological tests often involve item clusters that are designed to solicit responses to behavioral stimuli. The dependency between individual responses within clusters beyond that which can be explained by the underlying trait sometimes reveals structures that are of substantive interest. The paper describes two general classes of models for…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

In an effort to increase the quality and quantity of service-learning assessment, this article provides a brief rationale for engaging in service-learning assessment and reviews a selection of available tools for doing so. The paper includes a matrix that lists cognitive outcomes, including critical thinking and problem solving, and the…

A structural meta-analysis was conducted to evaluate the fit of four different representations of the relations among RIASEC types, Holland's (1985, 1997) circular order model, Gati's (1991) three-group partition model, Rounds and Tracey's (1996) alternative three-group partition model, and Liu and Rounds' (2003) modified octant model, on 29…

Nonlinear factor analysis is a tool commonly used by measurement specialists to identify both the presence and nature of multidimensionality in a set of test items, an important issue given that standard Item Response Theory models assume a unidimensional latent structure. Results from most factor-analytic algorithms include loading matrices,…