Purpose: The purpose of this paper is to present a mathematical model that can be used as an educational tool to reflect the philosophical aspects of sustainability. Design/methodology/approach: This is a descriptive paper. Findings: Everyone carries a sustainability deficit. Therefore, opportunities to reduce this deficit abound. Education is an…

Multilevel models have come to play an increasingly important role in many areas of social science research. However, in contrast to other modeling strategies, there is currently no widely used approach for graphically diagramming multilevel models. Ideally, such diagrams would serve two functions: to provide a formal structure for deriving the…

The authors present a computational model that builds a holographic lexicon representing both word meaning and word order from unsupervised experience with natural language. The model uses simple convolution and superposition mechanisms to learn distributed holographic representations for words. The structure of the resulting lexicon can account…

The ultimate goal of physics education research (PER) is to develop a theoretical framework to understand and improve the learning process. In this journey of discovery, assessment serves as our headlamp and alpenstock. It sometimes detects signals in student mental structures, and sometimes presents the difference between expert understanding and…

In the United States, 21% of all energy is used in residential buildings (40% of which is for heating and cooling homes). Promising improvements in residential building energy efficiency are underway such as the Building America Program and the Passive House Concept. The ability of improving energy efficiency in buildings is enhanced by building…

The author explored whether 3 workplace conditions were related to teacher mobility decisions. The modeling strategy incorporated a series of binomial and multinomial logistic models to estimate the effects of administrative support, classroom control, and behavioral climate on teachers' decisions to quit teaching or switch schools. The results…

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…

A mathematical model of operant choice, the generalized matching law was used to analyze play-calling data from the 2004 National Football League season. In all analyses, the relative ratio of passing to rushing plays was examined as a function of the relative ratio of reinforcement, defined as yards gained, from passing versus rushing. Different…

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…

In the early 1990s, the National Science Foundation funded many research projects for improving statistical education. Many of these stressed the need for classroom activities that illustrate important issues of designing experiments, generating quality data, fitting models, and performing statistical tests. Our paper describes such an activity on…

The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In…

For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates,…