PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Exploring experts’ covariational reasoning
Page: 664
In this paper, we discuss two experts’ reasoning abilities when tasked with drawing a graph that relates two varying quantities. We present evidence that in some cases, these experts had constructed and coordinated the amounts of change of the quantities (while interpreting and constructing graphs). By comparing each experts’ activities and corroborating previous researchers’ findings, we argue that constructing a multiplicative object is critical to conceiving a graph and situation as constituted by covarying quantities. We identify particular complexities involved in the development of covariational reasoning including the conceptualization, coordination, and referent accumulation of the amounts of change of two quantities.