PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Bidirectionality and covariational reasoning
Page: 774
Students’ thinking about quantities that vary in tandem remains an important area of mathematics education research due to its implications for student success in mathematics. In this paper, we expand on a way of thinking about covarying quantities, called bidirectional reasoning, in ways not detailed in prior research. A student thinking bidirectionally understands two quantities varying so that the conceived relationship does not have an inherent dependency; the student understands and anticipates that quantities exist and covary simultaneously. After describing bidirectional reasoning and connecting to informing theories, we draw from our work with undergraduate students to illustrate a student reasoning bidirectionally. Because this paper serves as a (re)introduction to bidirectional reasoning and relationships, we close with potential implications of students’ bidirectional reasoning, and we hypothesize productive lines of future research.