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…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

Engineering students use spatial thinking when examining diagrams or models to study structure design. It is expected that most engineering students have solidified spatial thinking skills during K-12 schooling. However, according to what we know about geometry learning and teaching, spatial thinking probably needs to be explicitly taught within…

This module applies linear algebraic methods to solve the following problem: If an object in a three-dimensional coordinate system is first rotated about a given axis through the origin by a given angle, and then rotated about another axis through the origin by another angle, there is a straightforward way to calculate the combined result of the…

Differences found in men's and women's attitudes towards mathematics, and differences in demonstrated abilities and experiences in mathematics classes are detailed. The sample used includes 479 pupils from 22 classes in 11 urban and suburban schools, with approximately 49% of the students female. The instruments used to collect data included…

This is one of a series of reports summarizing the results of the second mathematics assessment conducted by the National Assessment of Educational Progress (NAEP). Nine, 13- and 17-year-olds were assessed during the 1977-78 school year. The assessment measured achievement in various content areas at four levels of cognitive processes: knowledge,…

This "minimum teaching essentials" bulletin presents the minimum in basic skills and knowledge which must be taught to students in grades 9-12 in the subject areas of algebra, geometry, and mathematics fundamentals. Each subject area is prefaced with a section on work study skills to be used by students. (APM)

This bibliography is an effort to sort through the mathematical literature that is available. It categorizes the books into the main strands found in most elementary mathematics curricula or scope and sequence charts. Those strands are: sets and numbers; measurement and geometry; and graphs, functions, and probability. These are supplemented in…

AN EXPLORATION OF THE INTERACTION BETWEEN PROGRAMED TEACHING DEVICES AND INDIVIDUAL CHARACTERISTICS OF HIGH SCHOOL STUDENTS WAS UNDERTAKEN. THERE WERE FOUR PARTS -- PREPARATION OF MATERIALS ON GEOMETRY, THE ESTABLISHMENT OF CRITERION MEASURES, PRELIMINARY PILOT EXPERIMENTS, AND THE MAIN EXPERIMENT. THE MAIN EXPERIMENT WAS PERFORMED IN 27 CLASSES…

This mathematics curriculum guide was developed in response to the need for an updated regional mathematics guide identifying common student performance expectations of the professional staff. The expectations, stated as instructional objectives, have been organized into two major components: (1) an overall "Mathematics Comprehensive Program…

This collection is comprised of 63 objectives and corresponding sample test items for evaluation of students in grades K-8. Correct answers or criteria for judging the adequacy of student responses are provided. Major categories in the collection are: (1) preparing to use the metric system--decimal and fractional notation; (2) measurement--length,…

One-hundred twenty packages of computer programs, each package dealing with a single mathematical topic, are developed. Each package consists of three programs; the first gives the student a problem set, the second allows students to check answers, and the third composes a test. Topics range from addition of non-negative integers and other…

The curriculum guide for secondary level, career-oriented General Mathematics Part 2, correlates performance objectives in basic mathematics with career-oriented concepts and activities. The material is designed to lead the student in a systematic development that provides for continuous progress. The guide is in outline format, providing a…

This is the fifth in a series of technical research reports by Harvard Project Zero which study artistic creation and comprehension as a means toward better art education. The three papers in this report all concern the bearing of projective geometry on the perceptual processes by which pictures are "read" for spatial information. The…

This manual was designed for use by teachers using the School Mathematics Study Group's (SMSG) special text series for low achievers in grades 7 and 8; it covers chapters 10 through 18 of that series. The manual begins with introductory material describing characteristics of low-achieving students and suggested instructional approaches. Testing…