Discussed are various models proposed for the Moebius strip. Included are a discussion of a smooth flat model and two smooth flat algebraic models, some results concerning the shortest Moebius strip, the Moebius strip of least elastic energy, and some observations on real-world Moebius strips. (KR)

To develop students' abilities to reason with mathematics and apply mathematics to problem solving are abetted by building on their personal experiences, integrating the curricula, and designing learning activities that require students to write or speak about mathematics. Using an integrated approach is discussed and examples are included. (MNS)

Presents three teaching ideas: (1) investigating patterns in the sum of four numbers in a square array, no two from the same column or row; (2) using three-dimensional coordinates to generate models of three tetrahedra; and (3) applying the K=rs area formula for a triangle to other polygons. (MDH)

Examines the struggles of Kyle, a 30-year-old male, to overcome his innumeracy and to master the routine numerical tasks associated with daily life. Describes Kyle's arithmetic and problem-solving skills and the intervention program designed to develop his ability to solve everyday problems. (Contains 12 references.) (MDH)

Pragmatic and semantic problem solving are examined as processes that enhance acquisition of mathematical knowledge. It is suggested that development of mathematical cognition involves restructuring and that math teachers can help restructure children's knowledge systems by providing them with situations in which semantic and pragmatic problem…

The intuitive simplicity of probability can be deceiving. Described is a dialogue that presents arguments for conflicting solutions to a seemingly simple problem determining the probability of having two boys in a two-child family knowing that one child is a boy. Solutions contain multiple arguments and representations. (MDH)

Abstract ideas in linear algebra are illustrated at different levels of difficulty through the investigation of the solution to a well-known puzzle. Matrices are used to model the puzzle and the concepts of rank, underdetermined systems, and consistency are employed in the solution to the problem. (MDH)

Presents activities utilized with primary teachers to alleviate instructional concerns about using calculators and provide reasons for using calculators in their mathematics instruction. Activities address the topics of estimation, number sense, numeration, whole number and fraction operations, probability, and problem solving. (MDH)

Presents the problem of finding the maximum area of a quadrilateral when three of the four sides are given. Incorporates several parts of the secondary school precalculus curriculum into the solution. Develops the formula to solve the problem. (MDH)

Presented is the idea that art can be used to present early concepts of geometry, including the notion of the infinite. Discussed is the symbiosis that exists between the artistic and mathematical views of points, lines, and planes. Geometric models in art and using art in the classroom are discussed. (KR)

Presented is a way to provide students with a review and an appreciation of the versatility of pointers in data structures by improvising with binary trees. Examples are described using the Pascal programing language. (KR)

Included are probability models for various strategies that contestants on the television game show, "Let's-Make-a-Deal," might use when given the option to stick with their original choice of three unopened doors or switch to the unopened door after one of the other two doors has been opened. (JJK)

Investigates the question concerning the maximum number of lines of symmetry possessed by irregular polygons. Gives examples to illustrate and justify the generalization that the number of lines of symmetry equals the largest proper divisor of the number of sides. Suggests related classroom activities. (MDH)

Proposes lessons for algebra students using the context of tax calculations to learn about the concepts of slope, split functions, averages, rates, marginal rates, and percents. Students explore ramifications of possible tax revisions. (MDH)

Presents an activity for representing a given number in as many ways as possible using short periods of time to develop students' number sense and provide the teacher the opportunity to make informal student assessment and diagnosis. Provides specific dialogue of the activity being used in a third grade class. (MDH)