PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Covariational parametric reasoning
Page: 368
Researchers have argued that students can develop foundational meanings for a variety of mathematics topics via quantitative and covariational reasoning. We extend this research by examining two students’ reasoning that created an intellectual need for parametric functions. We first describe our theoretical background including different conceptions of covariation researchers have found useful when analyzing students’ activities constructing and representing relationships between covarying quantities. We then present two students’ activities during a teaching experiment in which they constructed and reasoned about covarying quantities. We highlight aspects of the students’ reasoning that we conjecture created an intellectual need for parametric functions, a need we capitalized on in a later session. We conclude with implications the students’ reasoning has for future research and curriculum design.