**ERIC Number:**ED364409

**Record Type:**RIE

**Publication Date:**1993-Apr

**Pages:**19

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

The Structural Algebra Option: A Discussion Paper.

Kirshner, David

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 (3) drill approach. The arguments for the structuralist approach are presented in four sections. The first section presents an analysis of algebraic symbol manipulation into six components of knowledge: (1) morphological, (2) graphological, (3) parsing, (4) transformational, (5) pragmatic, and (6) semantic components. The second section discusses the deductive structure of algebraic symbol manipulation. The third section discusses the visual structure of algebra and summarizes two empirical studies involving visual parsing and visual transformations that implicate the visual structure of algebra in students' unconscious assimilation of algebraic knowledge. The fourth section presents a structural algebra curriculum. The paper concludes by warning against abandoning entirely the formalist aspect of algebra in implementing a strictly empirical approach to algebra. Contains 72 references. (LDR)

Descriptors: Algebra, Cognitive Processes, Course Evaluation, Curriculum Evaluation, Elementary School Mathematics, Elementary Secondary Education, Error Correction, Instructional Effectiveness, Instructional Material Evaluation, Mathematics Instruction, Mathematics Skills, Secondary School Mathematics, Structural Equation Models, Symbols (Mathematics), Visual Learning, Visual Stimuli

**Publication Type:**Opinion Papers; Speeches/Meeting Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Note:**Paper presented at the Annual Meeting of the American Educational Research Association (Atlanta, GA, April 1993).