When it’s on zero, the lines become parallel: Preservice elementary teachers’ diagrammatic encounters with division by zero
Published: 2020
Publication Name: Journal of Mathematical Behavior
Publication URL: https://doi.org/10.1016/j.jmathb.2020.100760
Abstract:
We investigated preservice elementary teachers’ diagrammatic encounters with division by zero. Pairs of preservice teachers explored a transformable diagram where the locations of points on the x and y axes could be continuously varied. Quotients were defined in the diagram as the intersection of a line with the y-axis. For zero divisors, the quotient line was parallel to the y-axis, and there was no point of intersection. We report our analysis of two episodes where the transformability of the diagram spurred encounters with division by zero. In each episode, pairs of preservice teachers used repeated movements of the points in the diagram to explore the conditions under which the quotient line would become parallel to the y-axis. Our analysis shows how these movement-based material experiments gave rise to different conceptions of division by zero. We discuss how transformable diagrams create new material contexts for exploring arithmetic concepts.
This research was supported in part by a College of Education and Human Development faculty research seed grant to both authors. Opinions expressed here are the authors’ and do not reflect the views of the University of Maine.
Dimmel, J., & Pandiscio, E. (2020). When it’s on zero, the lines become parallel: Pre-service elementary teachers’ diagrammatic encounters with division by zero. Journal of Mathematical Behavior, 58(1), 1–22. https://doi.org/10.1016/j.jmathb.2020.100760