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How Mathematicians Determine if an Argument Is a Valid Proof

Keith Weber 

July 2008, Volume 39, Issue 4, Page 431

Abstract:
The purpose of this article is to investigate the mathematical practice of proof validation—that is, the act of determining whether an argument constitutes a valid proof. The results of a study with 8 mathematicians are reported. The mathematicians were observed as they read purported mathematical proofs and made judgments   about their validity; they were then asked reflective interview questions about their validation processes and their views on proving. The results suggest that mathematicians use several different modes of reasoning in proof validation, including formal reasoning and the construction of rigorous proofs, informal deductive reasoning, and example-based reasoning.  

Keywords:
Research Studies
Article
Calculus and Higher Level Mathematics
Conceptual Development
Higher Education
Higher Education
Teacher
Problems
Professional Development / Teacher Education
Reasoning and Proof
Representation
Theory