Strengths and inconsistencies in students’ understanding of the roles of examples in proving

We report on a study investigating high-school students’ understanding of the interplay between examples and proving or disproving of statements drawn from high-school algebra and geometry curriculum. The data, collected through a series of task-based interviews with 6 pairs of students, were analyzed in terms of alignment or misalignment of students’ responses with a conventional mathematical perspective summarized in the Roles of Examples in Proving (REP) framework. The results provide insights into strengths and weaknesses in students’ understanding of the status of examples in proving. In addition, we identified three types of inconsistencies in students’ responses: inconsistency with respect to the type of example, inconsistency with respect to the type of statement, and inconsistency with respect to the type of inference.