The subject of mathematics is important for many other subjects, including physics. The questions we ask in physics often need a mathematical translation to be graphically interpreted and transformed. Students learn physics when interacting with physical questions; questions from physics also give insights and discoveries in mathematical problems.…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

The applications of a recently developed computer program for microcomputers in developing models in an institutional research environment are considered. The VISICALC program requires no user programming skills, is available for all major brands of microcomputers, and provides for easy exchange of information between users of different computing…

Discusses steps involved in model building and simulation: understanding a problem, building a model, and simulation. Includes a mathematical model (focusing on a problem dealing with influenza) written in the DYNAMO computer language, developed specifically for writing simulation models. (Author/JN)

Develops Volterra model for spread of information in group analytically and by simulation and compares characteristics of both methods. Topics of modeling, equilibrium, linearization, stability, error analysis, and parameter identification are incorporated in obtaining the solutions. (SK)

Relatively recent developments, ranging from microfilm catalogs to networked circulation systems, have the potential of removing much of the uncertainty from the routing of interlibrary loan requests. The opportunity of purchasing location and availability information changes the performance of a model interlibrary loan network. Data collected in…

Describes a computer application called HyperGami that permits users to design, explore, decorate, and study a variety of paper polyhedral models. Discusses the HyperGami interface and language, illustrates the construction of customized polyhedra, and describes results of middle school students' experiences using the system. (Author/AIM)

Discusses analytical design and experimental verification of a PID control value for a temperature controlled liquid delivery system, demonstrating that the analytical design techniques can be experimentally verified by using digital controls as a tool. Digital control instrumentation and implementation are also demonstrated and documented for…

To help mathematics educators realise the power of computer-based applications and modelling, this paper deals with four questions: (a) What implications does technology have for the range of applications and modelling problems that can be introduced? (b) In what cases does technology facilitate the learning of applications and modelling? (c) When…

Described is the notion of multiple alternative representations of mathematical reasoning, particularly as they relate to algebraic notation and the potential of computers to change representations. Features of a desirable notation for algebraic problem solving are described. This is followed by a description of the RAND Corporation's intelligent…

Describes a two-quarter sequence of graduate courses in numerical methods and modeling for chemical engineers. Rationale, course content, methodology, topic development, and such course requirements as homework and design projects are considered. Emphasis is placed on the treatment of numerical methods implemented in commercial software. (JM)

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

Discusses a mathematical model for mastery learning. The model includes measures of a motivational factor and the specific ability of a learner with respect to content being learned. The model also contains a variable reflecting prior learning. Assumptions/limitations are discussed, and research questions raised. (Author/JN)

Describes a one-dimensional model for an ideal gas to study development of disordered motion in Newtonian mechanics. A Monte Carlo procedure for simulation of the statistical ensemble of an ideal gas with fixed total energy is developed. Compares both approaches for a pseudoexperimental foundation of statistical mechanics. (Author/JN)

Describes the use of a microcomputer in studying a model experiment (Brownian particles colliding with thermal particles). A flow chart and program for the experiment are provided. Suggests that this experiment may foster a deepened understanding through mutual dialog between the student and computer. (SK)