After a review of the disadvantages of linear models for estimating the probability of academic success from previous school records and admission test results, the use of a probit model is proposed. The model is illustrated with admissions data from the Ecole des Hautes Etudes Commerciales in Montreal. (Author/BW)

Building on Bloom's, and subsequent educational taxonomies, a larger, synthetic, theoretical basis, called the process hierarchy theory, is developed. Its relationship to general systems theory and its metatheoretical context are described. A general methodology for empirically testing aspects of the theory using mathematical modeling is explored.…

A model of subtraction development and the computing difficulties and research issues suggested by the model are outlined. Demands of simultaneous processes, difficulties with informal subtraction, and the impact on the counting-up procedure are discussed. (MNS)

Proposes a quadratic programming, least squares solution to Carroll's weighted unfolding model with nonnegativity constraints imposed on weights. It can be used to test various hypotheses about the weighted unfolding model with or without constraints. (RC)

Described is a "studio" procedure utilized at The University of Michigan for teaching mathematical modeling. (SL)

This paper addresses the developments of a class of fifth-grade children as they worked modeling problems during the first year of a 3-year longitudinal study. In contrast to usual classroom problems where students find a brief answer to a particular question, modeling activities involve students in authentic case studies that require them to…

The Archdiocese of Indianapolis has been using the Sander's value-added model to determine if they have had gains in student achievement in language arts, mathematics and reading. The article summarizes the method to make this determination and the results from three years of testing using the CTB McGraw-Hill Terre Nova test. The archdiocese has…

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…

In three lectures, Benjamin D. Wright of the University of Chicago introduces the Rasch model and its basic concepts. The first lecture, March 30, 1994 discusses the model created by Georg Rasch, a Danish mathematician, which Dr. Wright initially saw as merely a way to make raw scores into measures. Eventually, the model developed into a…

This working paper contains the overheads used in a seminar designed to introduce some basic concepts of statistics to nonstatisticians. The seminar has been presented on several occasions. The first part of the seminar, and the first set of overheads, deals with the essentials of statistics, including: (1) population, sample, and inference; (2)…

With a construct-centered reliability analytical approach the reliability analysis should crystallize the multi-traits or constructs that the test specialists developed to measure from student performance and then estimate the degree of fit between the theoretical expectations of test developers and the performance exhibited by students. This…

Methods of effectively teaching algebraic thinking in elementary schools as well as secondary schools is the topic of the following 19 papers. Papers include: (1) "Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by 'Algebrafying' the K-12 Curriculum" (J. Kaput); (2) "Developing a Coherent and…

The Progress in International Reading Literacy Study (PIRLS) is a large international comparative study of the reading literacy of young students. The student population for the U.S. 2001 PIRLS (hereafter simply referred to as PIRLS) was the set of all fourth-graders in the United States, corresponding to the grade in which the highest proportion…

This paper discusses the Lens Model' approach to the analysis of subject performance in multiple-cue judgment tasks embedded in probabilistic environments. (Author/RK)