Temporal discounting refers to the decrease in the present, subjective value of a reward as the time to its receipt increases. Results from humans have shown that a hyperbola-like function describes the form of the discounting function when choices involve hypothetical monetary rewards. In addition, magnitude effects have been reported in which…

This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

Applications in engineering, science and technology within undergraduate programmes can be difficult for students to understand. In this paper, new results are presented which go some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications. The study is based on student responses to…

Critiques a two-dimensional model for identifying scenarios of future development of education, describing the concepts of "dimension" in mathematics of space and "opposite" in logic. Asserts the model does not deal with dimensions and has no opposites between the end points of the model's two "dimensions" and…

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of 'cart-pendulum' electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts…

This article is a discussion of some geographical problems related to geographic and population centers of the U.S. The focus is on modeling, using concepts from calculus.

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a…

Traditional college algebra courses focus almost exclusively on power functions such as y = x[superscript 2] and y = x[superscript 3] rather than the more general y = x[superscript p]. However, it is the more general form that is the basis of the mathematical models that arise throughout the natural sciences in a host of unexpected and highly…

A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…

This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north-south pole orientation of the two magnets. The attraction or repelling force induced by the…

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present…

The question of how to estimate school and teacher contributions to student learning is fundamental to educational policy and practice, and the three thoughtful articles in this issue represent a major advance. The current level of public confusion about these issues is so severe and the consequences for schooling so great that it is a big relief…