Investigating Student Reasoning When Faced with a Mathematical Statement that Contains both Confirming and Contradicting Examples

Abstract

The purpose of this study is to address the ways in which mathematically gifted students reason when faced with both confirming and contradicting examples for a mathematical statement. By addressing this issue, this study aims to investigate the types of examples, generalizations and justifications that students construct after confronting confirming and contradicting examples for the statements. Eight students who enrolled in a Science and Art Center volunteered to participate in a semi-structured individual interview. The results indicated that the types and the purposes of suggested examples varied among the students. Research investigating student reasoning suggests that students’ justification schemes reflect their current view of the collection of examples that are considered as sufficient for the validation of a mathematical generalization. This study revealed that the types of examples were informative regarding the types of generalizations and arguments that were constructed by the students.