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Validations of Proofs Considered as Texts: Can Undergraduates Tell Whether an Argument Proves a Theorem?

Annie Selden, John Selden 

January 2003, Volume 34, Issue 1, Page 4

Abstract:
This article reports on an exploratory study of the way that eight mathematics and secondary education mathematics majors read and reflected on four student-generated arguments purported to be proofs of a single theorem. The results suggest that such undergraduates tend to focus on surface features of arguments and that their ability to determine whether arguments are proofs is very limited—perhaps more so than either they or their instructors recognize. The article begins by discussing arguments (purported proofs) regarded as texts and validations of those arguments, that is, reflections of individuals checking whether such arguments really are proofs of theorems. It relates the mathematics research community’s views of proofs and their validations to ideas from reading comprehension and literary theory. Then, a detailed  analysis of the four student-generated arguments is given and the eight students’ validations of them are analyzed.

Keywords:
Research Studies
Article
Algebra
Communication
Conceptual Development
Grades 9-12
Higher Education
Math Coordinator / Coach
Teacher
Problems
Variability
Reasoning and Proof
Representation
Theory