|Kathleen Melhuish ,  Jennifer A. Czocher - Vol. 40 Num. 2 (2020)|
|Division is pretty much just multiplication||38-43|
Within a study of student reasoning in abstract algebra, we encountered the claim “division and multiplication are the same operation.” What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of sameness claims to ground our inquiry resulting in a property- and context-dependent view that honors students’ sense-making and articulates an explanatory model for students’ (unexpected) responses. We illustrate the utility of this view with examples from K-12 literature and an analysis of our abstract algebra students’ claims about sameness of binary operations.