This volume presents recommendations from four working groups at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Working Group 1: Creating an Appropriate Algebra Experience for All Grades K-12 Students produced the following papers: (1) "Report" (A. H. Schoenfeld); (2) "Five Questions About Algebra…

This volume contains the plenary or reactor papers presented at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Papers included are: (1) "Introduction" (C. B. Lacampagne); (2) "Summary" (C. B. Lacampagne); (3) "Recommendations" (C. B. Lacampagne); (4) "The Development of Algebra…

Discusses algebra teaching by looking back into the history of algebra and the work of George Peacock, who considered algebra from two points of view: symbolic and instrumental. Claims that, to be meaningful, algebra must be linked to real-world problems. (18 references) (MKR)

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Clarifies aims and objectives of school algebra, reviews research on students' performance, and suggests curriculum modifications. This article is one of the keynote addresses of the Algebra Working Group of the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. (26 references) (Author/MKR)

Presents a summary report of a discussion subgroup of the Algebra Working Group at the Seventh International Conference on Mathematics Education held in Quebec City, Canada in August 1992. Argues that pre-algebra should be viewed as a continuation of arithmetic that asks different questions about numbers. (12 references) (Author/MKR)

This paper asserts that the key to algebra reform is to integrate algebraic reasoning across all grades and all topics, to "algebrafy" school mathematics. The distinction is made between algebra "the institution" and algebra "the web of knowledge and skill," which is also clarified. Finally, suggestions are made as to how the educational community…

This paper is a reaction to a plenary address, "A Research Base Supporting Long Term Algebra Reform?" by James Kaput (SE 057 182). The reactions fall into three categories: comments on Kaput's dimensions of algebra reform, a brief discussion of algebra and algebra reform from the viewpoint of a curriculum developer of the Connected…

Explains the importance of students learning algebra, and provides examples of how it can benefit them in typical life encounters. The article reveals how algebra quantifies relationships between quantities, basic algebraic structures, and its importance in the deductive process. Several algebra problems that illustrate these points are presented.…

This paper discusses three dimensions of algebra reform: breadth, integration, and pedagogy. Breadth of algebra includes algebra as: generalizing and formalizing patterns and constraints; syntactically-guided manipulation of formalisms; study of structures abstracted from computations and relations; study of functions, relations, and joint…

The goal of this paper is to renew interest in the structural option to algebra instruction. Concern for the usual secondary school algebra curriculum related to simplifying expressions, solving equations, and rationalizing numerators and denominators is viewed from three pedagogical approaches: (1) structural approach, (2) empirical approach, and…

This paper is a reaction to a plenary address, "A Research Base Supporting Long Term Algebra Reform?" by James Kaput (SE 057 182). Three dimensions of algebra reform identified by Kaput (breadth, integration, and pedagogy) are discussed and contrasted with the draft version of the Algebra Document from the National Council of Teachers of…

Describes a constructivist, interactive approach for teaching undergraduate mathematics, abstract algebra in particular, using computer constructions programmed in ISETL to induce students' mental constructions and collaborative learning to help students reflect on these constructions. (18 references) (MKR)

Suggests that the differences existing between the view of algebra as a mandated course at a specified grade level and the view of algebra as a way of mathematical thinking and reasoning developed gradually over time must be positively integrated to help students develop a genuine capacity for algebraic thinking and reasoning. (AIM)

Analyzes the nature and growth of students' algebraic knowledge and thinking from an epistemological perspective supported by historical observations. Focuses on two crucial transitions: from the purely operational algebra to the structural algebra of a fixed value of an unknown and then to the functional algebra of a variable. (Contains 58…