PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Examining the Relationship Between Students’ Covariational Reasoning When Constructing and When Interpreting Graphs
Page: 843
Graphing tasks require students to engage in at least one of two activities: construct a graph and/or interpret a graph. Ideally, the meanings a student re-presents when constructing a graph are consistent with the meanings the student constructs from his/her sketched graph. However, this coherence is nontrivial. In this paper I present results from clinical interviews with university precalculus students to illustrate how students’ graphing actions can be governed by different images of covarying quantities. More specifically, I present two students’ mathematical activity to illustrate how these students’ imagined quantities to covary in different ways depending on whether they were reasoning about a situation, constructing a graph, or reasoning about that sketched graph. I conclude by hypothesizing that the way a student coordinates two quantities’ measures (e.g., asynchronous coordination of varying quantities or static coordination of measures) can inhibit him/her from imagining the same covariational relationship when constructing and interpreting graphs