Middle school and college students were assessed on percentage. Better students in each group were given word problems involving percentage and asked to think aloud as they solved problems. College students made more use of strategies for control and monitoring of their own procedures. A three-stage model for problem solving is then hypothesized.…

Suggests ways in which mathematical models can be presented and developed in the classroom to promote discussion, analysis, and understanding of issues related to energy consumption. Five problems deal with past trends and future projections of availability of a nonrenewable resource, natural gas. (Contains 13 references.) (MDH)

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Presented is the solution to the problem of calculating the probability of winning or losing a game played by moving a counter from the center of a hexagonal grid according to the number shown after the toss of a die. The exercise is an example of an interesting mathematical investigation. (MDH)

Describes the New Mexico High School Supercomputing Challenge, a year-long project sponsored by New Mexico Technet, Los Alamos National Laboratory, and other statewide institutions that engages high school students, teachers, and professionals in complex scientific problem-solving that include written reports, mathematical models, and…

The concept of Arithmetic Story Grammar is introduced. Arithmetic Story Grammar maintains that any equation containing a single operand tells, in and of itself, a complete story with a setting, plot, theme, and resolution. Multiple-operand equations differ from their single-operand siblings only in the number of actions undertaken and the number…

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

Some diverse fields in which the effects of mental representations have been noticed are first discussed, largely through illustrations of differing problem-solving experiences. Then the LAKOS Project (Logical Analysis of Cognitive Organizational Structures) at the University of Osnabruck is described. A central concern is the specification of a…

A work-scheduling model for Corrections Officers at State Correctional Institutions is described. This is a real-life model that was developed to deal with a problem of unacceptably large expenditures for overtime work by state prison guards. The problem involves more than 200 constraints and more than 800 variables. It is felt the model can be…

Models of the motion of an object through space are discussed. The material begins with the simplest view possible in which gravity is the only force examined. Discussion progresses to an examination of the drag force, which is the resistive air force of the wind. Suggestions for further improvements are made at the conclusion of the presentation.…

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

A general process for testing the feasibility of applying alternative mathematical or statistical models to the solution of a practical problem is presented and flowcharted. The system is used to develop a plan to compare models for test equating. The five alternative models to be considered for equating are: (1) anchor test equating using…

This paper discusses goal programming, a computer-based operations research technique that is basically a modification and extension of linear programming. The authors first discuss the similarities and differences between goal programming and linear programming, then describe the limitations of goal programming and its possible applications for…

This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…

An approach to teaching the exponential function using discrete methods, rather than continuous analysis, is presented. A model for simple geometric growth is explored, with a computer program given. (MNS)