Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Demonstrates techniques for teaching quadratic equations. (KHR)

Discusses how to help students avoid some pervasive reasoning errors in solving cumulative percent problems. Discusses the meaning of ."%+b%." the additive inverse of ."%." and other useful applications. Emphasizes the operational aspect of the cumulative percent concept. (KHR)

Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

Responds to F. Uhlig's article on linear algebra that appeared in an earlier edition of this journal. (KHR)

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)

Shows how sequenced learning activities can help students build conceptual bridges from arithmetic to algebra. Focuses on understanding equivalent algebraic expressions, an area in which U.S. students scored poorly on the Third International Mathematics and Science Study (TIMSS). (YDS)

Describes the use of a purposefully designed set of problems borrowed from a variety of critical thinking activity books and selected to motivate, excite, and engage students in the learning process. Helps students develop a deeper, more conceptual understanding of mathematics by incorporating these problems into a beginning algebra course.…

Presents the technique of mind mapping and points out its special fitting as a pedagogical tool for mathematics education. Discusses possible applications of mind mapping in mathematics education together with their advantages and limitations. (Author/NB)

The values of a polynomial with integer coefficients can be computed using a graphing calculator, but it is impossible to see the formula itself. Suggests finding this formula from numerical data and describes the unusual way to solve this problem with one calculation only. (Author/NB)

Uses a counting book to discuss how primary-age students can begin to think about a meaning for the equals sign. Mathematical representations emerge from discussions between teacher and student. (Author/NB)

Describes three types of mathematics problems that are useful in promoting algebraic reasoning in the elementary school. (Author/NB)

Discusses social and intellectual factors in medieval Italian algebra; problems and methods, including operating on the unknown, quasi-equation problems, and giving-and-receiving problems; and the scope of algebraic methods. Considers implications for teaching. (43 references) (MKR)

Discusses algebra teaching by looking back into the history of algebra and the work of George Peacock, who considered algebra from two points of view: symbolic and instrumental. Claims that, to be meaningful, algebra must be linked to real-world problems. (18 references) (MKR)