Shows how the phenomenon of instability in the solution of a system of linear equations can be analyzed both algebraically and geometrically. (KHR)

Describes a lesson taught in primary school based on the use of linking cubes. Shows how meaningful mathematics can be made accessible to children and how fundamental issues of variant and invariant properties might be developed. (KHR)

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)

Presents some funny stories that can be used to develop a mathematical method as a starting point for creating alternative approaches to solving traditional algebra word problems. (KHR)

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Examines whether the embodiment of a familiar geometric system facilitates better understanding of the vector-space concept than the embodiment of a variety of unfamiliar algebraic systems. Analyzes students' responses with description, final answer, and justification of answers. Provides six problems. (YP)

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)

Eighty-six college students studied solutions of simple and complex word problems and then used the examples to construct algebraic equations as the frequency of referral to example was recorded. Students did not always select the appropriate example, and ability to select appropriately did not interact with aptitude. (SLD)

A computer algebra system was integrated into instruction for two large classes of mathematics for business and the social sciences. Comparisons of student achievement and attitude showed no significant differences, but other implications of the study are discussed. (23 references) (LZ)

Undergraduates in an abstract algebra course were interviewed to see how they learned the concept of isomorphism. Analysis showed students used step-by-step procedures, exhibited various degrees of personification in their language, and chose properties they perceived as simpler. (MKR)

Presents a real-life example of mathematical modeling in which a medical company asks for help in solving a warehouse-inventory problem. Uses charts, graphs, and computers. (MKR)

Reports the results of a teaching experiment involving like terms and equations in algebra. Seventh-grade students (n=6) experienced difficulties in decomposing an additive term into a difference. (Author/MKR)

Presents a paper-folding method to develop a class repertoire of construction methods for the ellipse, hyperbola, and parabola using straws, rulers, dental floss, paper circles, and other household items. Uses the Geometer's Sketchpad software to complement the paper-folding process. (MKR)

Describes an activity designed to help students understand the concept of a variable and the process of gathering like terms or simplifying algebraic expressions using egg cartons and plastic eggs. (MKR)

Details the authors' investigation of journal writing in first-year algebra and unveils journal writing's connections with the National Council of Teachers of Mathematics Professional Standards for Teaching Mathematics. (MKR)