PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
A case of learning how to use and order quantified variables by way of defining
Page: 623
Research literature suggests that students struggle in gaining fluency with mathematical language, and especially with statements with multiple quantifiers. I conducted a design study rooted in Realistic Mathematics Education in order to support students in developing such fluency. Drawing on the emergent model heuristic, I present a pair of students’ reinvention of relationships between variables in statements with multiple quantifiers. This work is a case study for how students might engage in defining in order to learn how and in which order to use quantified variables. Relationships between variables first emerged as a model-of a pair of students’ activity as they defined different concepts that are best defined using multiple quantified variables. Additionally, these relationships became more explicit to the students as they reflected on their definitions.