Title:

Prospective Secondary Mathematics Teachers’ Understanding of the Role of Examples in Proving

Secondary teachers’ knowledge of reasoning and proving is fundamental to supporting students’ opportunities to meaningfully participate in proof-related practices. Prior research has identified several gaps in teacher knowledge of proof, such as misunderstanding the role of examples and counterexamples in proving. This study analyzes Prospective Secondary Teachers’ (PST) responses to an online, scenario-based task, called What Can You Infer from This Example, which they took during a capstone course designed to foster expertise in teaching secondary proof. PST’s justification on the survey were analyzed using both Buchbinder and Zaslavsky’s (2019) Role of Examples in Proving framework and open coding. The results suggest that the PSTs have strong declarative knowledge, yet tend to have difficulty distinguishing between supportive, irrelevant, and counter examples. Our findings provide a novel contribution to the existing literature as we provide a nuanced analysis of how PSTs deal with examples that constitute presumably conflicting evidence for truth-falsehood of a given statement, and report on aspects of PSTs’ understanding of roles of examples in proving, which has not been previously detailed. These results also carry implication for teacher education as we illustrate an example of a rich task, embedded in pedagogical practice that elicits and enhances PSTs’ knowledge of proof.

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