Presents a synthesis of the nominal categories model of R. Bock (1972) and the choice model for mixed-effects analysis of rank-ordered data by R. Luce (1959). Shows that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates. Discusses relationships…

Several probabilistic models for subset choice have been proposed in the literature, for example, to explain approval voting data. We show that Marley et al.'s latent scale model is subsumed by Falmagne and Regenwetter's size-independent model, in the sense that every choice probability distribution generated by the former can also be explained by…

Few researchers have gone beyond case studies to examine characteristics of teachers who engage in research activities. Results from the authors' logistic regression models provide evidence that teaching in private schools, teaching in a midsize or large city, participating in professional development programs, and receiving support from the…

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

Geometric modeling provides graphic representations of real or abstract objects. Realistic representation requires three dimensional (3D) attributes since natural objects have three principal dimensions. CAD software gives the user the ability to construct realistic 3D models of objects, but often prints of these models must be generated on two…

Radical behaviorism considers private events to be a part of ongoing observable behavior and to share the properties of public events. Although private events cannot be measured directly, their roles in overt action can be inferred from mathematical models that relate private responses to external stimuli and reinforcers according to the same…

In this article, the authors identify and anecdotally describe three tutor archetypes: the pragmatist, the architect, and the surveyor. These descriptions, based on observations of remedial mathematics tutors at a land-grant university, shed light on a variety of philosophical beliefs regarding and pedagogical approaches to tutoring. An analysis…

This article examines how visual representations may mediate the teaching and learning of mathematics over time in Japanese elementary classrooms. Using the Zone of Proximal Development Mathematical Learning Model (Murata & Fuson, 2006; Fuson & Murata, 2007), the process of mediation is explicated. The tape diagram, a central visual…

This article details the results of a written test designed to reveal how education majors construct and evaluate histograms and frequency polygons. Included is a description of the mistakes made by the students which shows how they tend to confuse histograms with bar diagrams, incorrectly assign data along the Cartesian axes and experience…

Discusses the modelling of library circulation systems. (PF)

Bayesian techniques were developed for approximating the joint and marginal distributions of universe scores in single-facit-mixed-model designs with unknown covariance structure. Empirical results indicate that when compared with Cronbach's estimates, marginal means obtained through this procedure are substantially better predictors of subsequent…

When a linear structural equation model results in nonlinear procedures for solution, multiple (but finite) sets of solutions may be possible, even with population data. An example of a three-variable feedback system is given in which two sets of solutions may be generated. (Author/CTM)

One of the more surprising findings in the information sciences is the recurrence of a small number of frequency distributions. In this paper, these distributions are described, and a point of view is adopted that allows us to understand them as being different versions of a single distribution. (Author)

Characteristic curve approaches for linking parameters from the generalized partial credit model were examined for cases in which common (anchor) items are calibrated separately in two groups. Three of these approaches are simple extensions of the test characteristic curve (TCC), item characteristic curve (ICC), and operating characteristic curve…