Quantitative algebraic and qualitative topological models can be used in the quest for simple explanations in the field of teaching and learning. The examples described cover such diverse topics as teacher anxiety and classroom control, process-product studies, aptitude-treatment interactions, the pace of instruction, the size of classes, and…

Analyzes the individual and collective activities of fourth grade students while trying to explain a school fellow's mistake in the use of a geometrical schema for the sunshadows phenomenon. Aims at detecting productive links between context-related argumentation and mathematical modeling as well as discussing their relevance for mathematics…

Reports on an instructional method designed to address the cognitive gaps in children's mathematical development where operational conceptions give rise to structural conceptions. Describes two experiments in teaching integers and conceptualizes modeling as the transformation of outside-school knowledge into school mathematics. (Contains 28…

Mathematically explains why the range of a projectile is most insensitive to aiming errors when the initial angle is close to 45 degrees, whereas other observables such as maximum height or flight time are most insensitive for near-vertical launching conditions. (WRM)

Uses a growth model involving an aggregate production function to measure social benefits from human capital improvements due to investments in Hong Kong higher education. Returns calculated using the production-function approach are significantly higher than those derived from the wage-increment method. Returns declined during the past 10 years.…

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…