PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
A comparison of frameworks for conceptualizing graphs in the cartesian coordinate system
Page: 748
The use of the Cartesian Coordinate system (CCS) pervades secondary and tertiary mathematics curriculum, as the dominant convention for displaying graphs of functions. The CCS in two dimensions may be framed as a conceptual blend of two number lines and a Euclidean plane (Lakoff & Núñez, 2000). Within the concept of a number line is a conceptual metaphor uniting numerical values with points on a line. While such a description of the CCS may describe a shared understanding of the convention among the mathematics community, it may not account for the ways in which individual students interpret graphs presented in the CCS. Other theories, such as David et al.’s (2017) constructs of value-thinking and location-thinking, have been proposed to account for students’ graphical interpretations. In this paper, I outline these two ways of framing conceptions of graphs, the uses of each framework, and their relation to each other.