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…

A technique for the numerical identification of bacteria using normalized likelihoods calculated from a probabilistic database is described, and the principles of the technique are explained. The listing of the computer program is included. Specimen results from the program, and examples of how they should be interpreted, are given. (KR)

Discussed are solutions to the problem "What is the expected number of rolls for the total first to exceed 6?" Several algebraic solutions are presented. A computer program which may be used to simulate this problem is included. (CW)

This paper provides a method for analyzing data consisting of event sequences and covariate observations associated with Markov chains. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. (TJH)

This article shows how the methods of survival analysis (also known as event history analysis) lend themselves to the study of the timing of educational events. Using examples from teacher attrition and student dropout research, survival methods are introduced for building statistical models of the risk of event occurrence over time. (Author/SLD)

This paper examines the contribution of parents' education and children's gender on parental expectations of their children's future education and the role of parental perceptions of their child's competencies in the formation of their expectations. A group of university and vocationally educated parents (N = 418) were asked to estimate the…

Revealing or visualizing the thinking involved in making clinical decisions is a challenge. A case study is presented with a visual implement for sharing the diagnostic process. This technique adapts the Bayesian approach to the case presentation. Pretest probabilities and likelihood ratios are gathered to obtain post-test probabilities of every…