Using Symbolic and Graphical Forms To Analyze Students’ Mathematical Reasoning in Chemical Kinetics

Abstract

This work is part of a larger project that seeks to understand how students blend (integrate) chemistry and mathematics as they work through chemical kinetics problems.Here we focus on four students from our larger sample: two students that demonstrated more instances of blending chemistry and mathematics in their interviews ("high-frequency blenders") and two students that did not have any instances of blending chemistry and mathematics in their interviews ("nonblenders"). In this study, we characterized the intuitive mathematical ideas the students associated with equations (symbolic forms) and graphs (graphical forms), focusing on how the students' mathematical reasoning influenced their understanding of chemical phenomena. The findings suggest that, in order for students to integrate chemistry and mathematics in a way that supports their understanding of the chemical processes in chemical kinetics, they must be able to reason using symbolic and graphical forms.

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.…”

“…She is thinking of position and velocity algebraically, without any reference to the physical meaning of these two quantities. According to Rodriguez et al [40], this student would be described as a "nonblender": she never refers to physics ideas or to "blended" ideas, but only to mathematical concepts and procedures. It is interesting to notice that even in item 2P (which she solved correctly) the student adopted a nonblended reasoning, which was, however, productive in that case.…”

“…In recent years, "conceptual blending" has been proposed as an alternative framework to account for both context dependency and the relevance of prior knowledge in problem solving, both in physics and in other branches of science [2,[37][38][39][40]. According to this framework, a student who encounters a problem in a new context "blends" information from different "mental spaces" (e.g., mathematics, physics, everyday experience) to construct an emergent "blended space" that is unique to the problem and that is used to solve it.…”

Development of the Sci-math Sensemaking Framework: categorizing sensemaking of mathematical equations in science

“…Carlson, Jacobs, Coe, Larsen, & Hsu, 2002;Lehavi et al, 2017;Rodriguez, Santos-Diaz, Bain, & Towns, 2018;Sherin, 2001…”

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

“…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).…”