Potential instructional uses of the computer for expanding middle school mathematics programs are described. Content areas which are represented include geometry, number theory, computation, consumer education, and probability. (Author/JN)

Three questions dealing with hypothesis testing are presented. Activities that can be best worked with calculators as tools are detailed and suggestions for extensions of these problems are given. (MP)

Stage-state analysis of the life course is presented as useful in identifying types of life courses and their relative frequency, in estimating the likelihood of moving from a given state through a sequence of future states, and in analyzing routes and processes connecting initial states with potential outcomes. (Author/DB)

Examined developmental and individual differences in tendencies to favor analytic over heuristic responses in three tasks (inductive reasoning, deduction under belief bias conditions, probabilistic reasoning) in children varying in age and cognitive ability. Found significant increases in analytic responding with development on first two tasks.…

Discussed are the use of probability simulations in a mathematics classroom. Computer simulations using regular dice and special dice are described. Sample programs used to generate 100 rolls of a pair of dice in BASIC and Logo languages are provided. (YP)

Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)

This is the position statement of the National Council of Supervisors of Mathematics describing the essential mathematical competencies that citizens will need to begin adulthood in the twenty-first century. Twelve components of essential mathematics, the learning environment, technology, evaluation, and extension of the essentials are described.…

A study investigated whether the decision making of pharmacists and pharmacy students could be modified by providing computer-generated information on probabilities for efficacy and adverse reactions for antihypertensive agents, using case scenarios. Pharmacists were more likely than students to be influenced by probability information.…

Reanalyzed data from a study on respite care's effects by focusing on the linear relationship between amount of respite use and probability of nursing home placement at the end of the treatment period. Results indicate a significant negative relationship between the amount of respite use and nursing home placement. (RJM)

Discussion of expert systems and computerized adaptive tests describes two versions of EXSPRT, a new approach that combines uncertain inference in expert systems with sequential probability ratio test (SPRT) stopping rules. Results of two studies comparing EXSPRT to adaptive mastery testing based on item response theory and SPRT approaches are…

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)

Explored are the distributions of residual components in two model systems. A system of components with exponentially distributed lifetimes and the two-dimensional "leaf model" in which objects fall on a plane with positions independent and normally distributed are discussed. Included are the definition, application, computations, and theorem. (KR)

Surveys in which one can observe--after sample selection--that each sample member belongs to one or more aggregations are considered. A formula for the probability that a given aggregation contains at least one sample member is applied to eighth grade data from the National Educational Longitudinal Study of 1988 (NELS:88). (TJH)

Two frame-of-reference rater training approaches were compared for effects on reliability and accuracy of cutoff scores generated by 21 raters using Angoff methods on tests taken by 155 undergraduates. Both approaches result in higher interrater reliability and more accuracy than does a non-frame-of-reference method. (SLD)

Applies chaos theory to complex social organization, beginning with a mathematical definition of chaos. Shows how a nonlinear equation might be used to describe organization. The conclusion section identifies three approaches to analyzing chaos in social organization: metaphorical analysis, mathematical modeling, and data collection. (36…