Wilcox has described three probability models which characterize a single test item in terms of a population of examinees (ED 156 718). This note indicates indicates that similar models can be derived which characterize a single examinee in terms of an item domain. A numerical illustration is given. (Author/JKS)

Presents a method for carrying out the desired reduction which eliminates all ambiguities and trial-and-error. This method, which works with any properly constructed representation of any of the continuous points groups, is based upon the cosine form of the character for the arbitrary rotation operation. (HM)

Presents an undergraduate physical chemistry question and its acceptable solution. This question, presented to share exam questions with other teachers, shows the analogy between molecular kinetics and population dynamics. (HM)

An approach is described for teaching formulation of mathematical models to undergraduates with no modeling experience. Instruction is based on observation of successful patterns of behavior. (MP)

An attempt was made to validate for sentence type items a mathematical model for inventory response. Data were gathered from subjects responding under candid and under faking sets. In the former case only limited support for the model was found, but in the latter it seemed highly relevant. (Author/RC)

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

Presents new proofs of the Pythagorean theorem while exploring examination questions. Briefly reviews the work of Elisha Scott Loomis, a mathematician who amassed 320 different proofs of the theorem. (DDR)

Presents a mathematical model of the development of reaching behavior in infants, along with the results of two experiments that showed that infant movements could be decomposed into the underlying submovements using a principled method; and the angular error in infant reaches matches the form and magnitude of error assumed by the model. (MDM)

Generalizations of L. A. Goodman's RC(M) association model (1991 and earlier) are presented for three-way tables. These three-mode association models use L. R. Tucker's three-mode components model (1964, 1966) to represent the three-factor interaction or the combined effects of two- and three-factor interactions. (SLD)

A Monte Carlo study evaluated the effectiveness of different factor analysis extraction and rotation methods for identifying the known population multiple-indicator measurement model. Results demonstrate that exploratory factor analysis can contribute to a useful heuristic strategy for model specification prior to cross-validation with…

Proves a theorem about the invariance of the Lotka function under a transformation that maps numbers of authors as variables to number of collaborators as variables. A general approach to incorporate the average number of collaborators in a production function is discussed, leading to a general framework to model multirelational data. (Author/LRW)

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. (Author/SLD)

Notes that using spreadsheets to teach microeconomics principles enables learning by doing in the exploration of basic concepts. Introduction of increasingly complex topics leads to exploration of theory and managerial decision making. (SK)

Proposes a system to help at-risk students develop problem solving skills. Provides some teaching methods and evaluation ideas. (KHR)

Reports on middle school students' use of dynamic physical models to interpret functions. Includes student creations of symbolic variables and function equations. (KHR)