Why research on proof-oriented mathematical behavior should attend to the role of particular mathematical content

Because proving characterizes much mathematical practice, it continues to be a prominent focus of mathematics education research. Aspects of proving, such as definition use, example use, and logic, act as subdomains for this area of research. To yield content-general claims about these subdomains, studies often downplay or try to control for the influence of particular mathematical content (analysis, algebra, number theory etc.) and students' mathematical meanings for this content. In this paper, we consider the possible negative consequences for mathematics education research of adopting such a content-general characterization of proving behavior. We do so by comparing content-general and content-specific analyses of two proving episodes taken from prior research of the two authors and by re-analyzing the data and results presented in one instance of research from the field. We intend to sensitize the research community to the role particular mathematical content can and should play in research on mathematical proving.