Reasoning Quantitatively to Develop Inverse Function Meanings

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing the literature on students' inverse function meanings, I provide my theoretical perspective, including a description of a quantitative approach in the context of inverse relations. I then present one student's activity in a teaching experiment designed to support her in reasoning about a relation and its inverse as representing the same relationship. The student's quantitative reasoning supported her in developing productive meanings for inverse function, although this required her to reorganize her understanding of various mathematical ideas. [For the complete proceedings, see ED583989.]