There has been considerable interest in mathematical understanding. Both those attempting to build, and those questioning the possibility of building intelligent artificial tutoring systems, struggle with the notions of mathematical understanding. The purpose of this essay is to show a transcendently recursive theory of mathematical understanding…

This book is intended for middle-grade mathematics teachers who are searching for a wide variety of appropriately challenging and motivating problems with which to supplement regular textbook offerings. The 125 problems presented were found in the "Arithmetic Teacher" from 1975 to 1990. References are given both to the articles that contain these…

The purpose of this study was to investigate the effect of an eclectic thinking processes model on the logical reasoning abilities of students in grades six through twelve. The experimental school consisted of 159 students whereas the control school had 111 students. The Group Assessment of Logical Thinking (GALT) was administered to the sample as…

This computer-assisted curriculum is intended to be used to enhance a vocational mathematics/applied mathematics course. A total of 32 packets were produced to increase the basic mathematics skills of students in the following vocational programs: automotive trades, beauty culture, building trades, climate control, electrical trades,…

A large and representative 10% sample of classrooms consisting of 1,587 students from a mid-western province in Canada was administered a standardized achievement test battery. This battery consisted of four tests, Reading, Mathematics, Written Expression, and Using Sources of Information. Gender and rural-urban differences in achievement and…

This study compares and contrasts the following variables on the types of attributions (ability, effort, environment, and task) students make for their performance in algebra: attributions by gender and gender identification; attributions by level of math anxiety and self esteem; attributions by experience in competitive activities; and…

The status of high school students' mathematics and science preparation and the existence of gender inequities in such courses were investigated in this study of Rhode Island secondary schools. A stratefied random sampling of districts was taken to include schools demographically representative of the state's population. Course enrollment data…

This volume contains the papers and comments from the Workshop on Mathematics Education, a special session of the 15th Conference on Stochastic Processes and Their Applications, held in Nagoya, Japan, July 2-5, 1985. Topics covered include: (1) probability; (2) statistics; (3) deviation; (4) Japanese mathematics curriculum; (5) statistical…

With the help of widely available microcomputers, it is possible to demonstrate certain statistical phenomena which students of statistics are usually expected to take on faith. Two demonstrations are described. In the first demonstration, three common types of sampling (simple random, biased, and stratified-random) are used to compare statistics…

This study tested the hypothesis that the relationship between self-image and achievement would show different developmental patterns for boys and girls, particularly with regard to the relationship between self-image and mathematics and science achievement. Subjects were selected from two successive sixth grade cohorts in two predominantly white,…

This study presents composite profiles of teachers who were interviewed in order to assess how they are being affected by the challenges and opportunities presented by computer technology use. In-depth interviews were held with 76 teachers from 10 sites around the country, and the interview data were analyzed to identify themes and to construct…

This is a series of research projects that can be used for enrichment of the high school mathematics curriculum. It is suggested that the topics are either not found in the standard curriculum or represent a more indepth study of standard topics. The areas considered are: applications of the microcomputer in mathematics; the fourth dimension and…

This paper is an attempt to draw on the thinking of a group of secondary school geometry teachers who are participants in the Laboratory Sites Study of the Educational Technology Center (ETC) at Harvard University. The purpose of the Lab Sites Study is to understand the process of implementing technology-enhanced guided exploration in school…

This paper is a discussion of algebraic factoring. It is suggested that factoring is frequently presented in textbooks and by teachers without specifying one of the great values of this technique; that is, finding some of the factors of any number that can be generated by a particular polynomial. Concrete examples can help students understand the…

The Second International Mathematics Study investigated the status of the curriculum, achievement, and instructional practices at grades 8 and 12 in about 20 countries. The introductory first chapter explores the need for change in mathematics programs. Chapter two describes the achievement of U.S. students compared to others. At grade 8, U.S.…