A conceptual framework and heuristic model for considering the existence, magnitude, and consequences of context effects are presented through an extension of some generalizability theory concepts. Context effects are often misunderstood, and current measurement models have serious limitations for examining them. Their importance needs to be…

Three conceptual definitions of halo error are reviewed in the context of causal models of halo error. A corrected correlational measurement of halo error is derived, and the traditional and corrected measures are compared empirically for a 1986 study of 52 undergraduate students' ratings of a lecturer's performance. (SLD)

A model is presented for item responses when different subjects use different strategies, but only responses--not choice of strategy--can be observed. Substantive theory is used to differentiate the likelihoods of response vectors under a fixed set of strategies, and response probabilities are modeled via item parameters for each strategy. (TJH)

Criteria used in the equating process proposed in the literature are reviewed. The discussion begins by examining how equating is defined. The controversy over the best criterion, the utility of some, and whether a criterion is needed at all means that much work needs to be done in this area. (SLD)

Reviews the different types of models that can be used in groundwater modeling. Discusses the flow and contaminant transport models in the saturated zone, flow and contaminant transport in variably saturated flow regime, vapor transport, biotransformation models, multiphase models, optimization algorithms, and potentials pitfalls of using these…

A general structural equation model for measuring residualized true change and studying patterns of true growth or decline is described. This approach allows consistent and efficient estimation of the degree of interrelationship between residualized change in a repeatedly assessed psychological construct and other variables. (SLD)

A metrics and mapping framework is proposed to account for how heuristics, domain-specific reasoning, and intuitive statistical induction processes are integrated to generate estimates. Results of 4 experiments involving 188 undergraduates illustrate framework usefulness and suggest when people use heuristics and when they emphasize…

Aggregate data on grade-retention rates for grades 1 through 12 from 12 American states for 1979-80 and 11 for 1985-86 were examined for across-grade patterns. A negative growth exponential model appears to capture a basic underlying pattern of grade retention rates. (SLD)

Discusses the importance of history and original sources in motivating students to learn content. Describes how a simple question led to a fascinating quest through primary sources. Claims that once collected, these sources proved to be a treasure trove of material illuminating mathematics and mathematicians in an historical context. Contains 18…

Discusses the value of student-designed, in-depth, modeling projects in a differential equations course and how to prepare students. Provides excerpts from worksheets, a list of computer software for Macintosh that can be used in teaching differential equations, and an annotated bibliography. (Author/ASK)

Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)

Illustrates how a simple discontinuity in an individual's demand curve, or inverse-demand curve, affects the shape of market aggregate curves. Shows, for private goods, that an infinitesimal change in quantity can lead to large changes in consumption patterns; for collective goods, the analysis suggests a theory of coalition building. (DSK)

Introduces a model of differential equations for students--a very real overpopulation problem is occurring in the Ndumu Game Reserve in KwaZulu-Natal, South Africa, where one species of antelope, the Nyala, is crowding out another species, the Bushbuck. Constructs a competing species model to mathematically describe what is occurring in Ndumu.…

Adds a cropping or harvesting term to the animal overpopulation model developed in Part I of this article. Investigates various harvesting strategies that might suggest a solution to the overpopulation problem without actually culling any animals. (ASK)

Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete…