Faculty Publications

How Students View The General Nature Of Their Errors

Document Type

Article

Keywords

Algebraic reasoning, Generalization, Student errors

Journal/Book/Conference Title

Educational Studies in Mathematics

Volume

66

Issue

1

First Page

43

Last Page

59

Abstract

In this study we examined how two students viewed the general nature of their proportional reasoning errors as they attempted to generalize numeric situations. Using a teaching experiment methodology we studied the reasoning of two students over 18 instructional sessions. One student, Dallas, appeared to recognize that the proportional reasoning error applied to all cases of a particular problem situation and began to apply this reasoning across problems. The other student, Lloyd, exhibited difficulty seeing the generality of his mistaken use of proportional reasoning and regularly repeated this error during the study. From the data we developed a schematized description of how students view the generality of their errors and tracked the changes in these views over the course of the study. We analyze how Dallas and Lloyd's perception of errors shaped their understanding of proportional reasoning and provide suggestions for the role errors play in restructuring a student's conceptual schema. © 2007 Springer Science+Business Media, Inc.

Department

Department of Mathematics

Original Publication Date

9-1-2007

DOI of published version

10.1007/s10649-006-9067-8

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