Explains the difficulties middle school students face in algebra regarding the order of operations. Describes a more visual approach to teaching the order of operations so that students can better solve complex problems and be better prepared for the rigors of algebra. (YDS)

Identifies and addresses fundamental ideas that build the foundations of algebraic thinking and reasoning. Focuses on developing appropriate instructional approaches to these concepts. Explains what is meant by "composite unit" and how this concept framed the development of an instructional sequence to help students make sense of and find meaning…

Undergraduates often are aware of and able to apply the facts required to prove a statement but still fail to prove it. By comparing doctoral students and undergraduates constructing proofs in abstract algebra, four types of strategic knowledge are hypothesized. Found that doctoral students had knowledge of how to choose which facts and theorems…

Explains how a microcomputer-based algebra software system, muMATH, can be used to help students understand the theory of convergence of infinite series. Examples are given to illustrate nth term test, ratio test, comparison test, integral test, and Raabe's test. (10 references) (LRW)

Suggests ways parents can encourage success in algebra, including keeping a journal in which students describe in words the steps they used in solving a problem. (MKR)

Describes an approach to the initial teaching of composite functions that relies primarily on mapping representations. (MKR)

A satire of traditional algebraic word problems. (MKR)

Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)

Discards the blinders that have hampered the traditional teaching of calculus and reexamines some of the intuitive ideas that underlie this subject matter. Analyzes the various indeterminate forms that arise through the blind application of algebraic operations. (Author/ASK)

Explores the ramifications of two three-year-long experiences with different pedagogical approaches to beginning algebra. Focuses on differences in the nature of subject matter understandings and explores the impact on the teacher to support students' classroom exploration of mathematical ideas. (Contains 58 references.) (Author/ASK)

Reacts to an article published in a previous issue of this journal on the effects of graphing calculators and computer algebra systems (CAS) on students' manual calculation skills. Asks enthusiasts of CAS to learn from history and avoid pitfalls. (ASK)

Describes activities for Technical Algebra, which provides students an opportunity to solve algebraic problems through a hands-on, instructional process. (MKR)

College students (n=32) in their first abstract algebra course were asked to list elements and find the product of 2 elements in the dihedral group D4. Most students found solutions using a combination of visual approaches and analytic strategies. Proposes an alternative model, the Visualizer/Analyzer model, which assumes visualization and…

Introduces an algebra lesson plan on two people saving money over the course of a week and the problems they encounter for early elementary school students. (YDS)

Discussion of XML focuses on a description of Tequyla-TX, a typed text retrieval query language for XML documents that can search on both content and structures. Highlights include motivations; numerous examples; word-based and char-based searches; tag-dependent full-text searches; text normalization; query algebra; data models and term language;…