Recall of multiplication number facts is a major educational objective in elementary grades, yet some children never acquire total mastery. A microcomputer multiplication number facts training program was developed which incorporated programmed instructional features including feedback, positive reinforcement, vanishing, branching and pairing.…

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 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.…

Examined is the notion of "representation" as it is used in mathematics education. The first section explains what appears to the current "received view" of representation within mathematics education. The second section describes the constructivist view of representation, especially as this view is related to Piaget's theory. The third section…

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

This booklet designed for students in grades 4-8 provides 52 activities, including puzzles and problems. Activities range from simple to complex, giving learners practice in finding patterns, numeration, permutation, and problem solving. Calculators should be available, and students should be encouraged to discuss solutions with classmates,…

This report examines the most recent middle school data from the National Assessment of Educational Progress (NAEP) to investigate how selected dimensions of instructional practice are related to higher-order learning of middle-grade students. In particular, the paper: (1) outlines the theoretical basis for prescribing middle level instructional…

The purpose of this project was to produce an integrated program that effectively improves adult literacy, affects employment, enhances employability, and provides career adaptability. The goals directing these efforts were to design a series of modules for teaching reading, writing, and math, and to provide adults with basic employment skills.…

The teaching of problem solving begins the moment a child first enters school and the senior high school plays a major role in the development of this skill since a number of students terminate their formal education at the end of this period. This book combines suggestions for the teaching of problem solving with activities, problems, and…

This paper offers a framework for examining the role of subject matter knowledge in the teaching of mathematics. Starting with a brief review of the history of efforts to investigate the role of subject matter knowledge, the paper continues with an in-depth look at what "subject matter knowledge of mathematics" might mean. An approach to…

This report reviews Apple computer courseware in business education, library skills, mathematics, science, special education, and word processing based on the curricular requirements of Alberta, Canada. It provides detailed evaluations of 23 authorized titles in business education (2), mathematics (20), and science (1); 3 of the math titles are…