Discussion of data repositories available in global information systems focuses on facilitating access by providing semantic views. Highlights include the mapping relation; syntax and semantics of the mapping; query formulation and processing; terminological systems for semantic views; and relational algebraic expressions. (LRW)

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

Documents what high school students showed when asked to work on tasks that involved the use of various representations. Indicates that few students made proper connections between representations and the initial situation or problem on their own and exhibited competence in procedures such as expressing an area or solving quadratic equations, but…

Introduces a computer package written for Mathematica, the purpose of which is to perform a number of difficult iterative functions with respect to the squared multiple correlation coefficient under the fixed and random models. These functions include computation of the confidence interval upper and lower bounds, power calculation, calculation of…

Most people learn to drive without knowing how the engine works. In a similar vein, the author believes that students can learn economics without knowing the algebra and calculus underlying the results. If instructors follow the philosophy of other economics courses in using graphs to illustrate the results, and draw the graphs accurately, then…

This article describes how we used the context of mailing a package with seventh-grade students to explore and connect the different representations of step and linear functions. (Contains 2 tables and 7 figures.)

Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.

We report some findings of the Longitudinal Proof Project, which investigated patterns in high-attaining students' mathematical reasoning in algebra and in geometry and development in their reasoning, by analyses of students' responses to three annual proof tests. The paper focuses on students' responses to one non-standard geometry item. It…

Packing an infinite number of cubes into a box of finite volume is the focus of this article. The results and diagrams suggest two ways of packing these cubes. Specifically suppose an infinite number of cubes; the side length of the first one is 1; the side length of the second one is 1/2 , and the side length of the nth one is 1/n. Let n approach…

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem, and used a statistical regularization method to solve it. The method is applied to three examples. It gives a good approximation to the true solution and compares well with the method given by…

Equivalence relations with a non-transparent transitive property are scarce in textbook examples. The equivalence relation given here is not only one with an interesting transitive property to prove, but also one that is instructive for students who are encountering proofs and relations for the first time.

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.

This article describes Comer's Method, a student's discovery of an alternative approach to solving the determinant of a 3x3 matrix.

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…