The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for…

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)

Concerns about students' difficulties in statistical reasoning led to a study which explored year 11 (14 to 16 year-olds) students' ideas in this area. The study focussed on sampling variability, probability, descriptive statistics and graphical representations. This paper presents and discusses the ways in which students made sense of sampling…

Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…

This publication is designed to aid schools in planning a course of study for students in Course III Mathematics in New York State schools. This guide continues the developmental program begun in Course I. It is intended to serve as the Regents syllabus for the third year of the academic sequence for a New York State Regents diploma. This document…

Expert systems can be used to aid decision making. A computerized adaptive test (CAT) is one kind of expert system, although it is not commonly recognized as such. A new approach, termed EXSPRT, was devised that combines expert systems reasoning and sequential probability ratio test stopping rules. EXSPRT-R uses random selection of test items,…

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

The Comprehensive School Mathematics Program (CSMP) is described as a complete elementary mathematics curriculum that provides a natural place for probability and statistics. The CSMP approach of innovative, pictorial techniques is summarized here, with emphasis on methods and activities seen as proven successful through the enthusiastic reception…

The real problems of contextual analysis concern the conceptualization of contextual effects, the kinds of data with which to estimate them, and the selection and implementation of appropriate statistical techniques. This paper focuses on detection; specifically, an approach to contextual analysis based on the estimation and interpretation of a…

Our department has redesigned its electrical and computer engineering programs by adopting a learning methodology based on competence development, problem solving, and the realization of design projects. In this article, we show how this pedagogical approach has been successfully used for learning probabilities and their application to computer…

This book contains the tenth chapter of a pilot mathematics sequence for the seventh and eighth grades. The content of the sequence is to serve as a vehicle for the development of relevant computational skills, mathematical reasoning, and geometric perception in three dimensions and is to reflect the application of mathematics to the social and…

Exploratory research with large numbers of variables and even larger numbers of relationships is likely to result in frequent Type II errors; that is falsely accepting an incorrect null hypotheses. There are three ways of reducing Type II errors: (1) choosing a lower significance level, which then increases the probability of Type I error; (2)…

Because it is a true score model employing item parameters which are independent of the examined sample, item characteristic curve theory (ICC) offers several advantages over classical measurement theory. In this paper an approach to biased item identification using ICC theory is described and applied. The ICC theory approach is attractive in that…

A probabilistic hypothesis testing procedure to assess the fit of hypothesized hierarchical structures for test item data is discussed. Statistical procedures are presented which are useful for evaluating the fit of data of a certain class of probabilistic models. These models apply to sets of dichotomous (O,1) responses for which there are…

Research supported by a grant form the U.S. Office of Education, Bureau of Research