Date of Completion

12-1993

Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Patricia S. Davidson

Second Advisor

Arthur Millman

Third Advisor

Judy A. Clark

Abstract

Students enter the classroom with individual schemas, based on their experiences and ideas, which influence the reception, interpretation, and recollection of new information. Effective teachers must understand the implications of these existing schemas. As an experienced classroom teacher, the author finds students often manipulate and apply new information well in class, only to forget or alter the material a few weeks later;. When misconceptions are woven into schemas, they interfere with reception of information. This thesis examines specific student-held misconceptions about the area and perimeter of rectangles and the process of their identification and eradication. Identification of the misconception is the first step in bringing about change. The process of identification begins through the analysis of a pre-test which is designed to highlight specific erroneous ideas that the students hold. Through this pre-test, the author identifies five misconceptions. For ease of discussion they have been named; Fallacy of Multiples, Increase/Decrease assumption, Conversion Conclusion, Spatial Bias, and Equality Assumptions. Each misconception is defined and explained and the specific pre-test questions used for its identification are included. There are several learning theories which can aid the teacher n establishing a process of misconception eradication and educational change. The author works within a framework including theoretical components of cognitive psychology, Anderson's theory of memory, and Ennis' definition of critical thinking and taxonomy of critical thinking dispositions and abilities. The mathematical components of this framework are developed utilizing metacognition, transfer, and recent curriculum and professional development standards of the National Council of Teachers of Mathematics. This multi-faceted framework provides the foundation on which to build lessons targeting the eradication of specific misconceptions. Three lesson plans are presented to illustrate the practical implementation of the theories in the classroom. Each lesson contains four components: Motivation, Activity, Metacognition, and Transfer;. The author concludes the thesis with more general classroom teaching suggestions and a review of current innovative educational approaches.

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