The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

The fraction 16 over 64 has a well known, interesting property. If one incorrectly cancels the sixes, a correct answer of 1 over 4 is obtained. This is an example of a lucky fraction. In this article, the author presents several examples of lucky fractions and proves two interesting properties of these fractions. This article provides students the…

We developed four separate scenarios focusing on the connections between mathematics, biology, and social sciences. This structure facilitated the coordination of faculty from seven academic departments on campus. Each scenario had students from different majors build mathematical models, gather information from their respective disciplines, and…

Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

This paper revisits the demonstration of Lenz by dropping magnets down a non-magnetic tube. Recent publications are reviewed and ideas for undergraduate laboratory investigations are suggested. Finally, an example of matching theory to observation is presented. (Contains 4 tables, 5 figures and 3 footnotes.)

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…

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…

Presents a generalization and improvement for the definition proposed by E. Dzhafarov (2001) for selectiveness in the dependence of several random variables on several (sets of) external factors. This generalization links the notion of selective influence with that of conditional independence. (SLD)

Presents a version of the nonlinear mixed-effects model that allows random effects only on the linear coefficients, and in which nonlinear parameters are not stochastic. Highlights the flexibility of the model and illustrates features through two examples. (SLD)

Presents a method for estimating the random coefficients model using covariance structure modeling and allowing one to estimate both fixed and random effects. The method is applied to real and simulated data, including marriage data from J. Belsky and M. Rovine (1990). (SLD)

This paper explores the use of spreadsheets to develop an exploratory environment where mathematics students can develop their own understanding of the parameters of commonly encountered families of functions: linear, logarithmic, exponential and power. The key to this understanding involves opening up the definition of rate of change from the…