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

Abstract

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.

Comparison of Students' Covariational Reasoning Based on Differences in Field-Dependent and Field-Independent Cognitive Style

“…It then becomes the potential to increase subject's reasoning. These findings concur with those of Rodriguez [36] which indicates that discussions on graph interpretation can encourage students to think productively to scaffold on mathematical reasoning. An understanding of the mathematical representation and interpretation is inseparable…”

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

“…Students' choice of distractor B could also be interpreted using the notion of "graphical forms," introduced by Rodriguez and colleagues [40,97]. Similarly to Sherin's symbolic forms [98], graphical forms involve associating intuitive mathematical ideas to a pattern, which in this case is a region of a graph.…”

Research on Students' Understanding of Michaelis-Menten Kinetics and Enzyme Inhibition: Implications for Instruction and Learning

“…Focusing more specifically on mathematical models such as graphs across the physical sciences, interpreting the information provided in a graphical representation is complex, with mathematical ability and contextual complexity serving as potential barriers for students (12)(13)(14)(15). Moreover, students tend to focus on and cue into surface features of graphs, such as an overemphasis on the shape of the graph (16) or inappropriately attributing time to the x-axis (17). There is a similar trend observed in the mathematics education research literature, in which students impose time on functions that did not have time as the independent variable (18).…”

“…Building on our recent work in chemical kinetics that emphasized students' mathematical reasoning during problem solving (7,16,60,(64)(65)(66)-tersely summarized in a recent book chapter (67)-here, we focus on students' understanding of enzyme kinetics, guided by the overarching research question: How do students reason about enzyme kinetics? Addressing this question involves a brief overview of the themes that emerged from our enzyme kinetics project, which focused on students' mathematical reasoning related to rate laws and reaction order (68), student conceptions of enzyme inhibition and the associated mechanisms (69), and student understanding of representations such as Michaelis-Menten graphs, Lineweaver-Burk plots, and reaction schemes (70).…”