This publication contains revised versions of the major papers presented at a research conference on the learning and teaching of algebra. The papers and discussions focused on four major themes: what is algebra and what should it become, in light of continuing technological advances; what has research told us about the teaching and learning of…

A training procedure was developed to improve (or to encourage) the construction of a meaningful problem representation by mentally retarded and learning disabled children. Children are taught to use an external visual representation for arithmetic word problems, in which the meaning of the problem is reflected. The construction of this visual…

This document is intended to describe several software learning environments in an order that parallels a reasonable sequence of use by students. It also describes a planned an designed, but not yet implemented, extension of these environments from the discrete to the continuous case. Each of the implemented environments was developed in…

This paper discusses the overall design of the PIXIE Intelligent Tutoring System, and more specifically a series of recent enhancements. The original system has been implemented to involve three separate phases: the offline, or model generation phase; the online, or tutoring, phase; and the analysis phase. The offline phase, which is completed…

Twin aims--to advance theory and to improve practice in science, mathematics, and computing education--guided the Educational Technology Center's (ETC) research from its inception in 1983. These aims led ETC to establish collaborative research groups in which people whose primary interest was classroom teaching and learning, and researchers…

This book which treats the central issues facing mathematics teaching today, provides both a picture of current practice and innovation and a state of the art review of research in mathematics education. The first section, "Innovations," provides an overview of new technologies, new forms of assessment, and new curriculum developments.…

Some mathematics educators feel that too little geometry is taught in elementary schools. This may have serious effects as many students arrive in the traditional high school geometry course without essential backgrounds in informal geometry. The result of this lack of preparation is often lower scores on standardized tests. In this situation,…

This study summarizes data collection activities associated with the first two years of a large scale project involving teachers of science and mathematics with computers. The innovation being implemented in the project is that of using computer based strategies directly in the teaching of science and mathematics in the classroom and laboratory.…

Suggests one possible way to combine the technological facility of the computer with students' natural abilities for concept formation. Describes the software the "Geometric preSupposer." (PK)

Proposes to modify the procedure proposed by Abelson and diSessa to produce a polygonal path with vertices that lie exactly on an ellipse. Provides a detailed proof. Implements a limiting process to produce the best possible approximation to any ellipse for any given screen resolution. (CW)

Seven research conclusions concerning computers in elementary schools are presented. A summary conclusion suggests that researchers have been unable to detect improvement in mathematical skills, although some evidence suggests that students using computers acquire attributes related to success in mathematics. (PK)

Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

In this paper we report on two complementary research results. In the first we describe a tool that allows different modes of synchronous distance teaching of mathematics. In the second we report the preliminary results of a pilot study conducted using this tool to teach geometry, both with school students aged 14-15 and with undergraduate…

Preservice teachers do not feel prepared to teach mathematics using technology (Smith & Shotsberger, 2001). To address this issue, we have developed a tool-based categorization of mathematics software and used it to instruct preservice teachers. Changes in thinking that occurred as a result of the course are analyzed primarily using repertory grid…

The paper commences by reviewing some of the issues currently being raised with respect to the use of technology in undergraduate mathematics teaching and learning. Selected material from three research projects is used to address a series of questions. The questions relate to the use of symbolic manipulators in tertiary mathematics, to…