RUME 26
2024
Omaha, Nebraska
A Conceptual Analysis of Expressing Distances Algebraically Within the Cartesian Plane
Page: 984
This theoretical report offers a conceptual analysis of expressing distances on graphs of functions in the Cartesian plane algebraically. We frame this mental activity as a connection between the algebraic and graphical registers, and describe three key connections it comprises: (1) differences express distances between two positions, (2) points are ordered pairs of distances from the axes in the Cartesian plane, and (3) equations give the relation between x and y for every ordered pair on a graph. We detail the conceptual components of each connection, which involve a component from each of the graphical and algebraic registers and an underlying interpretation that forges the connection between the two. This conceptual analysis makes explicit the complex cognitive steps involved in algebraically expressing distances on graphs of functions, with implications for researchers and practitioners using algebraic and graphical representations together.