The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry,…

This article presents a mathematical algorithm that relates student achievement with directly observable, quantifiable teacher and student behaviors, producing a modified form of the Walberg model. The algorithm (1) expands the measurable factors that comprise the quality of instruction in a linear basis of research-based teaching components and…

This document consists of three papers. The first, "A Parallel Model of (Sequential) Problem Solving," describes a parallel model designed to solve a class of relatively simple problems from elementary physics and discusses implications for models of problem-solving in general. It is shown that one of the most salient features of problem…

This paper argues that the introduction of the scientific method in the very rich environments of the natural sciences or human sciences may disguise the process and create difficulties for students because of the multiplicity of variables involved, whereas the variables present in a mathematical context can be readily manipulated and their…

This three-part article introduces a population dynamics model of an information processing system. The first part describes the general model and defines the terms used, the second describes the functional relationships between components, and the third explores the hypothesized emergence of increasingly complex, hierarchical information systems.…

Discusses the development of a mathematics attitude model guided by the analysis of mathematical life-history interviews, Vygotsky's developmental theories, and research on attitudes toward mathematics. Explores implications for curriculum planning and development. (Contains 36 references.) (MDH)

This study examined the internal/external (I/E) frame of reference model of self-concept (Marsh, 1986) with higher education students in Hong Kong (n=274). Structural equation models relating English and math achievement (both requirements for university entrance) to English and math self-concepts replicated the I/E model in that paths leading…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

Previous studies were conducted with 14- to 15-year-old students on the nature of the processes they used to solve tasks given the incorrect/buggy/mal-rules. The computer-based Leeds Modelling System (LMS) was implemented and a database of examples, correct and incorrect, or mal-rules had been established which was sufficient to diagnose the…

This essay provides commentary on the place of mathematics in the study and practice of educational administration. The incidence of mathematical topics in the writing of the field is explored, and their isolation from each other and from the body of literature is pointed out. Possible areas of synthesis are sought from the traditional use of…

Reports on a research development model designed to improve the teaching and learning of mathematics in the Dominican Republic. The model drew heavily upon the Missouri Mathematics Project. Discusses innovations in curriculum development, classroom instruction, and inservice teacher training. Includes statistical tables on student achievement and…

The study tested a structural equation model of community college enrollment patterns of White and Hispanic males and females and the invariance of parameter estimates among subgroups. High school preparation in mathematics and science (M/S), M/S attitudes, M/S enrollment patterns, parent education, encouragement, and high school grades were…