This guide was prepared to assist in determining the mathematics that should be included in drafting, electricity, electronics, and machine shop programs. Information for the guide was obtained by asking teachers from every postsecondary vocational school in Kentucky to respond to a questionnaire listing mathematics competencies for their…

High school students (N=213) of various ability levels enrolled in first-year algebra classes were presented lessons concerning geometry concepts. The lessons were varied according to the degree of complexity of the examples that were presented. Students then were tested over their understanding of the concepts. The test questions ranged from…

This study investigated young children's ability to solve probability problems and studied the cognitive processes proposed by Piaget and Inhelder as necessary to solve probability problems. The effects of tutorial and self-discovery training were measured and discussed. Results from 168 first-graders in five training conditions indicated that:…

The purpose of this study was to investigate whether homework affects second grade mathematics achievement. The study involved two classes of on-grade-level students and involved a unit on place value. The results indicated that the achievement of the experimental group, which was given homework, was better than the achievement of the control…

The use of telecommunications to enhance local educational opportunities, especially in science and mathematics, was the subject of two hearings before a Senate committee. Eleven persons made presentations and/or submitted written statements at the first hearing: (1) Joseph Duffey, University of Massachusetts at Amherst; (2) Andy Turner,…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the first term of a one-year course. The complete course is divided into 12…

This yearbook responds to the growing recognition among mathematics educators of the importance of teaching and learning estimation. It makes a strong case for the importance of estimation in such domains as numerosity, computation, and measurement. An important theme is the interdependency between the process of estimating in a particular domain…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

The Mathematics Curriculum and Teaching Program (MCTP) is a joint initiative of the Curriculum Development Centre and the Directors of Curriculum of the States and Territories of Australia. The program seeks to improve the teaching of mathematics in grades K-10. This manual contains guidelines for people who have a responsibility for the…

The purpose of this study was to assess children's and adults' quantitative understanding of fractions in a new and potentially definitive way, and to determine whether this understanding was related to fraction computational skill. Thirty-seven seventh graders and 32 adults (college students) participated in the study. A computation task was used…

The purpose of the basic skills component of this project was to improve the reading and mathematics skills of 2085 junior high school and middle or extended elementary school students who were assigned to transition teachers for help. The target population for the Mathematics Teacher Resource Development consisted of teachers who (1) needed…

In the fall of 1980 the Pittsburgh Board of Education embarked on a program of change and improvement for all public schools in the city. A comprehensive needs assessment was conducted by groups with broad school and community interests. The need to improve student achievement in basic skills was identified as the priority. The Monitoring…

This teacher resource material was written from the perspective that it is possible to improve number fact learning in the primary grades, and in remedial situations beyond those years, in ways that: (1) will help children learn all facts; (2) will emphasize the process as well as the answer; and (3) by capitalizing upon natural extensions of…

Children appear to interpret the "equals" sign as an operator ("adds up to") not a relational ("the same as") symbol--e.g., viewing equations like 13 = 7 + 6 or 8 = 8 as senseless. This study, a natural experiment, examined the effects of long-term instruction emphasizing a relational definition of "equals."…

This document is designed to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. The approach used is to: (1) develop the material in terms of full-rank factorizations and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) include…