Discusses findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. Reveals four sources of mismatches that were significant in bringing about the occurrence of shifts in students' thinking. (Contains 16…

Math-education reformers encourage the incorporation of mathematical modeling activities into K-12 curricula. Many of the purported educational benefits derive from the authenticity of the activities-how well they reflect the everyday and occupational mathematical practices of adults. But a paucity in the literature of observational descriptions…

This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

A theory that there is a correspondence between Piagetian conservation operations and groups of symmetry transformations, and that these symmetry transformations may be used in explaining human problem solving behaviors, is developed in this paper. Current research in artificial intelligence is briefly reviewed, then details of the symmetry…

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

We explore the nature and consequences of teachers' problem solving through an example of a teacher's mathematical problem solving as it was occasioned by a student's mathematics. This illustration demonstrates the value of an interpretive framework that points to the mathematics of the classroom as a collective. Arising from this exploration is…

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

This study focused on determining the applicability of a mathematical modeling technique (goal programing) to state-level vocational education planning, using Missouri as a test case. Results indicate that such models may help the vocational planner solve problems that cannot be solved by more conventional methods. (SK)