Offers an alternative instructional method of constructing cubes based on the use of linking smaller cubes to form triangles. Offers learners insight into algebra by clearly exposing the underlying structure of the problem-solving process. (ASK)

Presents an approach to explaining a relation, a - b = -(b - a), that is difficult for algebra students to understand. The approach came about as a result of discussions with students in which they provided many novel explanations. (DDR)

Hypermedia provides an easy-to-use option for adding visualization, via the computer, to the classroom. Some examples of this medium are presented, including applications in basic linear algebra and calculus, and a tutorial in electromagnetism. (Author)

Illustrates use of rule space as a tool for cognitive analysis of students' mathematical behavior. The rule-space approach is explained and used to classify students according to two methods for solving linear algebraic equations in one unknown and diagnose their knowledge states on this topic. (Author/MDH)

Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)

Discussed is a method of approximating the roots of a quadratic that allows the discovery of relationships between parabolas and circles and between the use of geometry and algebra. Included are the procedure and justification of the method. (KR)

Students who study algebra are more likely to attend college than those who don't. A major hurdle for students in studying algebra is the transition from arithmetic to algebra. In response to overcoming this hurdle, the College Board and Educational Testing Service has developed "Algebridge," a teaching supplement that integrates…

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

Described are ways that specific concepts from abstract algebra can be programed using the software package features of the Ada Programming Language, which is the primary language of the Department of Defense. Included are typical programs with their respective outputs. (JJK)

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

Discusses the interconnection among the various modes of the TI-92 calculator (geometry, data graphing, function graphing, and algebra) and how the power of visualization is extended to provide multiple approaches to complex problem situations. Provides a graphing problem with illustrations and results. (AIM)

Describes an experimental course in which the programming language ISETL served as a tool for exploring concepts in abstract algebra, and identifies instructional strategies that facilitate the successful use of ISETL. Offers informal observations regarding the effectiveness of this approach. (13 references) (Author/MKR)

Argues that the vast majority of adults have no use for the specialized mathematics taught in high schools and required by colleges--algebra, geometry, or calculus. Suggests that colleges should accept applicants who have studied percents, formulas, logic, computer commands, and basic statistics. (TE)

Investigates the probability of winning the largest prize at Bingo through a series of five simpler problems. Investigations are conducted with the aid of either BASIC computer programs, spreadsheets, or a computer algebra system such as Mathematica. Provides sample data tables to illustrate findings. (MDH)

Discusses a method of implementing the computer algebra system DERIVE for diagnosis and remediation of basic difficulties in mathematics. Learning activities for junior high school students were developed, each directed at a different area of difficulty. The basic strategy implemented in these activities is replicating and completing examples.…