LINEAR OR NONLINEAR? STUDENTS' GRAPH REASONING AND SELECTION ON AN ONLINE ASSESSMENT.

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent relationships between attributes in dynamic situations and explained their reasoning. Each student spontaneously wondered whether to select a piecewise-linear or nonlinear graph. Our qualitative analysis revealed that students' expectations about whether a graph "should" be linear or nonlinear impacted their graph selection. These expectations also influenced how they narrowed down between two graph choices that both represented the same gross covariation in attributes. We conclude with implications for course textbooks to promote students' covariational reasoning. [ABSTRACT FROM AUTHOR]