Covariational reasoning and mathematical narratives: investigating students' understanding of graphs in chemical kinetics

Graphical representations are an important tool used to model abstract processes in fields such as chemistry. Successful interpretation of a graph involves a combination of mathematical expertise and discipline-specific content to reason about the relationship between the variables and to describe the phenomena represented. In this work, we studied students' graphical reasoning as they responded to a chemical kinetics prompt. Qualitative data was collected and analyzed for a sample of 70 students through the use of an assessment involving short-answer test items administered in a first-year, non-majors chemistry course at a Swedish university. The student responses were translated from Swedish to English and subsequently coded to analyze the chemical and mathematical ideas students attributed to the graph. Mathematical reasoning and ideas related to covariation were analyzed using graphical forms and the shape thinking perspective of graphical reasoning. Student responses were further analyzed by focusing on the extent to which they integrated chemistry and mathematics. This was accomplished by conceptualizing modeling as discussing mathematical narratives, characterizing how students described the story communicated by the graph. Analysis provided insight into students' understanding of mathematical models of chemical processes.