Collectively engaging with others’ reasoning: Building intuition through argumentation in a paradoxical situation

One goal of inquiry-oriented instruction is student engagement with others’ mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others’ ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the apparently paradoxical zero area and infinite perimeter of the Sierpiński triangle. The instructor strategically facilitated collective argumentation centered on their reasoning, resulting in several ideas that functioned-as-if-shared in the classroom community. In this report we capitalize on this classroom discussion to contribute to theory and methods for investigating the complex intersection of engagement and argumentation.