We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

High academic standards are an important first step in ensuring that all Alaska's students have the tools they need for success. These standards reflect the collaborative work of Alaskan educators and national experts from the nonprofit National Center for the Improvement of Educational Assessment. Further, they are informed by public comments.…

Arguing that the teaching of stochastic processes should reflect the experience and reality of the student, the author urges concentration on fundamental ideas. The development of intuition should be encouraged, and to this end continuity in teaching and a spiralled curriculum are important. (SD)

A Bayesian solution is suggested to the problem of jointly estimating "k is greater than 1" binomial parameters in conjunction with the problem of testing, in a Bayesian sense, the hypothesis "H" of parametric homogeneity. Applications of the estimates are illustrated with several types of data, including ophthalmological…

The author describes a new graphing algorithm for computing probabilities, and presents problems for these algorithms for use in the classroom. (SD)

Queuing theory is explored by considering a simple example and by simulation with a computer. Sample BASIC computer programs are included. (DT)

The purpose of this paper is to present problems (and solutions) from the areas of marketing, population planning, system reliability, and mathematics to show how a computer simulation can be used as a problem-solving strategy in probability. Examples using BASIC and two methods of generating random numbers are given. (Author/MP)

Features and tools to outline and shape the long-term learning process for ratio are presented, with examples. Ratio-anticipating activity and creating visual models and schemes are stressed, with the basis for a theory of teaching and learning ratio presented. (MNS)

The purpose of this paper is to derive explicit estimates of the parameters of a latent structure model when the skills represented by the test items are hierarchically related. Two special cases are described, which may be used as an approximation to the Dayton and Macready model and also provide initial estimates in an iterative estimation…

Induced probabilities have been largely ignored by educational researchers. Simply stated, if a new or random variable is defined in terms of a first random variable, then induced probability is the probability or density of the new random variable that can be found by summation or integration over the appropriate domains of the original random…

The logit methodology provides a unique way of examining input-output relationships for social systems where the principal output of the analysis is a probability of some action or state. (Author)

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…

Included are probability models for various strategies that contestants on the television game show, "Let's-Make-a-Deal," might use when given the option to stick with their original choice of three unopened doors or switch to the unopened door after one of the other two doors has been opened. (JJK)

This book shows the advantages of Rasch measurement (G. Rasch) for school district testing programs. The results of Rasch methods are contrasted with conventional statistics for assessing student responses to basic skills testing. Chapter 1 shows how the Rasch probability-based method produces measures that are more useful for students, parents,…

Procedures for obtaining student samples for the National Assessment of Educational Progress (NAEP) and deriving survey weights for analysis of survey data are described. Sample designs are economically and operationally feasible, and weighting procedures result in increased precision of estimates as they account for the probabilities of student…