PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
The Sierpinski smoothie: Blending area and perimeter
Page: 169
In this report, we present an analysis of 10 individual interviews with graduate mathematics education students about the area and perimeter of the Sierpinski triangle (ST) and the resulting paradoxical situation. We use conceptual blending as a theoretical and methodological tool for analyzing students’ reasoning to investigate how students encounter and cope with the ST having zero area and infinite perimeter. Our analysis documents the diverse ways in which the students reasoned about the situation. Results suggest that an infinite perimeter is more accessible to these students than zero area, that encountering the paradox is dependent on how blends are composed, and that resolution of the paradox comes through completion and elaboration. The analysis contributes to what we know about how students think about infinite limit processes and furthers the theoretical/methodological framing of conceptual blending as a useful tool for revealing the structure and process of student reasoning.