Two attempts to adjust state mean Scholastic Aptitude Test (SAT) scores for differential participation rates are examined. Both attempts are rejected, and five rules for performing adjustments are outlined to foster follow-up checks on untested assumptions. National Assessment of Educational Progress state data are determined to be more accurate.…

Describes an activity to solve an applied problem using a random-number-based simulation. Provides objectives, prerequisites, directions, extensions, answers, a computer program, and worksheets for the activity. Six references are listed. (YP)

The evolution of ideas about the concept of chaos is surveyed. Discussed are chaos in deterministic, dynamic systems; order in dissipative systems; and thermodynamics and irreversibility. Included are logistic and bifurcation maps to illustrate points made in the discussion. (CW)

Three correlation matrices (PEARSON, POLYCHORIC, and TOBIT) were used to obtain reliability estimates on ordered polytomous variable models. A Monte Carlo study with different levels of variable asymmetry and 400 sample correlation matrices demonstrated that the PEARSON matrix did not perform as well as did the other 2 matrices. (SLD)

Presents an example of a proof to the mathematical problem of the sum of the cubes of the digits. Provides a Pascal program to search for these results. (MVL)

A simple algebraic model relating the mean achievement in a class to the students' ability range is presented. Agreement between the model and data on the relationship between mean achievement and class size is described. Data concerning opinions of 15 primary school through university teachers quantitatively support the model. (TJH)

Outlines differences between classical statistics and exploratory data analysis. Provides examples in the use of the exploratory techniques. (YP)

Identifies and discusses the overlap between mathematics and physics at different educational levels. Presents some examples of the overlap and some suggestions for teachers. (YP)

A probabilistic item response theory (IRT) model is developed for pair-comparison design in which the unfolding principle governing the choice process uses a discriminant process analogous to Thurstone's Law of Comparative Judgment. A simulation study demonstrates the feasibility of estimation, and two examples illustrate the implications for…

Introduces "The Bouncing Ball Project" made for teaching mathematics through practical mechanics. Describes four activities in the project: what is bounciness; drop height and rebound height; timing the bounces; and extension activities. Provides many worksheets, graphs, and a list of five other projects. (YP)

A technique and mathematical model--the "Catch Model"--for identifying a face previously seen are presented. Three experiments, involving a total of 38 American and 30 Israeli college students, supported the model for identification of a target face. Practical implications are discussed. (SLD)

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

Analyzes the decision to network a collection of microcomputers into a local area network (LAN) based on cost factors. A mathematical model of the decision-making process is proposed that identifies an indifference point where the choice between a network and a stand-alone environment is equally attractive. (10 references) (LRW)

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

Presents mathematical models to determine whether seven-game baseball playoff series are significantly fairer than five-game series. Compares the results obtained from the models to actual playoff results. (MDH)