Two models are presented. The first assumes that air resistance is proportional to the velocity of the falling body. The second assumes that air resistance is proportional to the square of the velocity. A program written in BASIC that simulates the second model is presented. (MP)

The problems involved in making reservations for airline flights is discussed in creating a mathematical model designed to maximize an airline's income. One issue not considered in the model is any public relations problem the airline may have. The model does take into account the issue of denied boarding compensation. (MP)

A simple teaching model, designed to show rapidly which are the principal factors in population growth and how they are related, is presented. The apparatus described allows students to play several different active roles. (MP)

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)

The use of mathematical modelling as a systematic framework for solving word problems is presented. Applications for typical elementary algebra and calculus problems are featured. (MP)

Ways are presented to help students develop precomputational fraction concepts and skills using a circular-region or "pie" model. (MK)

Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Outlines a possible framework for allowing teachers to explore how children learn mathematics. A mathematical modelling process and three domains, including content, process and pragmatic domain, are described. Twelve strategies for encouraging children to translate between the domains are suggested. (YP)

Presents a mathematical metaphor for the birth and decline of historical eras. Identifies conditions necessary for transition from one era to the next. Argues that each era is characterized by sigmoidal growth that declines to saturation. Suggests that only synergetic, innovative people can open new areas and criteria to issue in a new era. (DK)

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Describes a problem formulated by fourth-grade students about having more pizza for lunch, and the clarifying, predicting, modeling, simulating, comparing, and extending activities that occurred in addressing the problem from a probabilistic perspective. (MKR)

The recursive model presented here involves the study of drugs in the bloodstream and their subsequent elimination from the body. Both a basic and a more realistic model are presented and discussed in terms of an algebraic approach, a recursive approach, the graphical representation, and other extensions and connections particularly with models…

Discusses a misconception about the cycloid that asserts the final point on the path of shortest time in the "Brachistochrone" problem is at the lowest point on the cycloid. Uses a BASIC program for Newton's method to determine the correct least-time cycloid. (MDH)

Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)