Three approaches for teaching students to solve inequalities involving absolute values, quadratic expressions, and rational expressions are illustrated. Then one technique that can be used with all of these problems is presented. (MNS)

Presents a general mathematical framework for information retrieval, in which query evaluation is seen as a mapping from the free term algebra built by query descriptors and weights to the semantic algebra of evaluation value. Competing mathematical models that try to describe how retrieval systems behave are reviewed. (Author/MBR)

Rules from an old mathematics textbook are discussed. Suggested are approaches to using the materials with students, challenging them to come up with explanations of why the rules work. (MNS)

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

Computation errors that may occur by expanded use of calculators are discussed. Potential errors with five exact arithmetic examples are described as they are translated into approximate processes. (MNS)

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

Discusses: (1) how complex roots can be made visible; (2) a proof which supplies a fresh example of mathematical induction; (3) proving Heron's formula tangentially; and (4) income tax averaging and convexity. (JN)

How to determine when there is a unique solution when two sides and an angle of a triangle are known, using simple algebra and the law of cosines, is described. (MNS)

Discusses: (1) use of matrix techniques to write secret codes (includes ready-to-duplicate worksheets); (2) a method of multiplication and division of polynomials in one variable that is not tedius, time-consuming, or dependent on guesswork; and (3) adding and subtracting rational expressions and solving rational equations. (JN)

How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

The Mathematics Attribution Scale (MAS) (Algebra) was designed to assess attributions of success and failure in algebra to ability, effort, task, and environment. This study examined the MAS (Algebra) for a separate dimension of attributes for success and a dimension of attributes for failure. The two hypothesized dimensions did not emerge.…

A college course is described in which mathematics was taught through the perspective of historical development. Readings for the course and synopses of lectures are included. (DT)

A paper staircase drawn on a grid forms the basis for a discovery lesson in algebra. (DT)

Methods for getting a computer-linked plotter to do a total plot of a relation are discussed. (DT)

This article presents, in the context of solving a specific mathematical problem, an argument to indicate how problem posing can lead to a deeper understanding of what is involved in the act of problem solving. (DT)