A sophomore-level course in applications of mathematics was designed to introduce students to the diversity of situations in which mathematical models are used. The course precedes the study of the calculus, and is composed of a sequence of modules. A problem-solving approach is used. (SD)

Undergraduate and graduate students are often confused about several aspects of modeling physical systems. Describes an approach to address these issues using a single physical transport problem that can be analyzed with multiple mathematical models. (DKM)

Explains an application of mathematical modeling within a school setting as well as progressive use of graphing calculators in mathematical modeling. Analyzes students' performances in the process of problem-solving using the problem of baton-passing in relay races. Discusses students' use of their mathematical knowledge and ideas when they used…

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Discusses a team-oriented formal testing method used in a mathematical modeling course taught during the Alma College intensive spring term. Asks the question, If a collaborative teaching method is used, how does one assess students' acquisition of problem-solving and mathematical-thinking skills? (Author/MM)

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)

Polynomial algorithms are presented that are used to solve selected problems in test theory, and computational results from sample problems with several hundred decision variables are provided that demonstrate the benefits of these algorithms. The algorithms are based on optimization theory in networks (graphs). (SLD)

A model for solving very large item selection problems is presented. The model builds on binary programming applied to test construction. A heuristic for selecting items that satisfy the constraints in the model is also presented, and various problems are solved using the model and heuristic. (SLD)

This paper deals with a teaching approach aimed to help students become aware of targeted techniques of significance in problem solving. The teaching approach is to present a series of tasks that all can be solved by applying the same technique. Two levels of prompting are used; first for the students to realize solutions without necessarily being…

A study on sampling errors of variance components was conducted within the framework of generalizability theory by P. L. Smith (1978). The study used an intuitive approach for solving the problem of how to allocate the number of conditions to different facets in order to produce the most stable estimate of the universe score variance. Optimization…

The way that graphs can be used to make calculations that are commonly used by institutional researchers is described using specific examples, and the technique of constructing computational graphs (and nomographs) is outlined. It is shown that once a calculation involving several variables has been represented by a computation diagram or a…

Four problems in which elementary mathematics can be used in constructing models are described. (SD)

The similarity between two apparently dissimilar problems is explored. Pascal's triangle is involved. (SD)

The mathematics of the game "Instant Insanity" is described in terms of graph theory, a part of combinational mathematics. (SD)