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)

Presents the Fibonacci sequence in a format that is readily implemented using the table and list features of the Texas Instruments TI-82 graphing calculator or a spreadsheet. Includes questions and investigations that can be explored using these tables and lists. (MKR)

Shows how five points determine the formula of a conic section and uses the determinant as a computational device to find the coefficients in the formula. Uses symbolic, numerical, and graphical techniques. (Author/MKR)

This paper considers the problem of variables, in particular parameters, analyzes how these concepts are presented in textbooks, comments on paradigms of exercises in which parameters intervene, and points out difficulties encountered by students. Discusses results of teacher interviews concerning their dealing with parameters in class.…

Presents a summary report of the Algebra Working Group's discussion subgroup on secondary algebra at the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. Three appendixes include the reactions to the keynote addresses in this issue. (MKR)

Three experiments investigated the ability of 79 college students to solve similar algebra word problems. Data indicate that students are able to perceive and use similarities in such problems at the level of a conceptual structure. A training session to explain relevant structural principles was effective in improving performance. (SLD)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Data from students in grades 8-10 in suburban schools were presented to show that errors in formulating algebraic equations are not primarily the result of syntactic translation, as has been assumed in the literature. A theory of cognitive models is offered as an explanation for the errors. (Contains 37 references.) (MLN)

Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)

Discusses the objectives, organization, assessment, student reactions, and evaluation of an abstract algebra course in which small-group instruction was used. Concludes that better understanding is achieved and the students assimilate more concepts using this method, although the pace is slower than that in a traditional classroom setting.…