Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

Data suggests low-level college algebra students profit more from student pacing in a Personalized System of Instruction course and more advanced algebra students benefit from the extra pressure of instructor pacing. (MP)

Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

A number of traditional topics covered in school mathematics are examined, their origins discussed, and justifications sought for teaching them today. (MP)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

Presents an algebraic method for balancing complex oxidation-reduction equations. (DKM)

Discussion of the nature of the algebraic and graphical representations of functions focuses on a study integrating cognitive research and the development of an intelligent tutoring system (ITS), the Function Characteristics Tutor, to evaluate the effects of pairing representations of mathematical functions on high school students. (Author/LRW)

Introduces concepts of modern algebraic group theory in the form of a game. Peg boards and rubber bands represent nonnumerical group elements and are manipulated under the operation of reorienting a regular polygon. Symmetry groups are used to explore set properties, as well as commutative and noncommutative operations. (CMS)

Missouri high school students (n=254) in applied mathematics (AM) 1, AM2, and a control group in algebra 1 completed the Pre-ACT (American College Test) and ACT Work Keys. Students in AM2 attained skills comparable to those in algebra 1. AM students had similar math attitudes to those of algebra students despite less previous success in math. (SK)

Describes how the introduction of the TI-92 transformed a traditional first semester linear algebra course into a matrix-oriented course that emphasized conceptual understanding, relevant applications, and numerical issues. Indicates an increase in students' overall performance as they found the calculator very useful, believed it helped them…

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Demonstrates techniques for teaching quadratic equations. (KHR)

Discusses how to help students avoid some pervasive reasoning errors in solving cumulative percent problems. Discusses the meaning of ."%+b%." the additive inverse of ."%." and other useful applications. Emphasizes the operational aspect of the cumulative percent concept. (KHR)

Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…