PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Tinker Bell’s pixie dust: Exploring the role of differentiation in emergent shape thinking
Page: 596
Researchers have described the importance of seeing a graph as an emergent trace of how two quantities’ values vary simultaneously. Researchers have also identified the many difficulties students face when constructing this conceptualization of graphs. In this paper I explore the role of two didactic objects on a student’s conceptualization of graphs. In particular, I examine how a student’s interactions with these didactic objects supported her in making key differentiations that enabled her to conceptualize a graph as emerging from simultaneously tracking two quantities’ varying values. My findings revealed that a student must differentiate a place on a function’s graph from the value of the function’s output. Also, the student must distinguish tracking a point in the plane from creating the point by simultaneously attending to the variation of two quantities.