Students’ interpretation and use of graphical representations: insights afforded by modeling the varied population schema as a coordination class

Abstract

Explanations of phenomena in chemistry are grounded in discussions of particulate-level behavior, but there are limitations to focusing on single particles, or as an extension, viewing a group of particles as displaying uniform behavior. More sophisticated models of physical processes evoke considerations related to the dynamic nature of bulk solutions, in which an ensemble of molecules exists with a distribution of values that vary with respect to different parameters (e.g., speed, kinetic energy, etc.). Viewing phenomena as a varied population instead of a homogenous solution has been identified as a foundational idea that is critical for reasoning in chemistry, but little work has investigated how students reason about these ideas and how instructors can support students in viewing phenomena as a distribution of states. In this qualitative study, during semi-structured interivews twelve undergraduate general chemistry students were provided with frequency distribution graphs (number of molecules vs. speed, number of molecules vs. kinetic energy) and were asked to provide explanations and make predictions. The design and analysis of this study was informed by coordination class theory, a model within the knowledge-in-pieces perspective of cognition that defines a concept as a combination of approaches for obtaining information (read-out strategies) and a cluster of knowledge elements used to draw conclusions (causal net). Framing the varied population schema as a coordination class, this work focuses on the interaction between features students attended to in distribution graphs and the ideas they discussed. Analysis indicates students have productive resources for reasoning about a varied population in general terms, but these ideas are not necessarily activated when interpreting graphs, as reflected in the students’ readout strategies. Moreover, we posit that one of the barriers toward interpreting distribution graphs was the inappropriate application of covariational reasoning. As a practical consideration, we encourage interested instructors to review the Appendix, which provides a short summary of the main findings and suggestions for practitioners.

Exploring the Productive Use of Metonymy: Applying Coordination Class Theory to Investigate Student Conceptions of Rate in Relation to Reaction Coordinate Diagrams

“…As part of the construction of the resource graphs, two researchers constructed their own resource graphs and then met to combine the resource graphs and reach a consensus regarding the final structure, mirroring the process for narrative coding. For more information regarding how our use of resource graphs and how they can be used to indicate features students attended to and knowledge elements activated, see Rodriguez et al 31…”

“…30 As a note to the readers, the terminology used to describe constructs related to coordination class theory have changed over time and more recent work suggests the use of the terms inferential net and extractions to replace causal net and readout strategies, respectively. 30 In our previous work we utilized the earlier operationalizations of the related terms, 31 but in the current work we make use of the updated conceptualizations to reflect the theoretical developments of the learning sciences.…”

“…29,32 To date, coordination class theory has been applied to a variety of topics in physics 32−39 and mathematics, 40−42 and, more recently, chemistry. 31,43 As an illustration of the application of coordination class theory and its related components, Wittmann 38 investigated undergraduate physics students' reasoning related to wave pulses. He observed, as illustrated in Figure 1, that when asked to predict what would happen if two wave pulses traveled toward one another, students tended to state that the waves would recoil (as in elastic collisions) and/or that there would be a change in speed.…”

“…In our previous work related to how students reasoned about distribution graphs, we noted that students tended to focus on the same surface features of the graphs, but subsequently assigned different ideas; for example, viewing the peak as an event related to a process or viewing the peak as a measure of central tendency. 31 Thus, the coordination of extractions and an inferential net resulted in a different framing of the representation, graph as a process or graph as a distribution. In contrast, for the current work, students' extraction strategies caused them to focus on different surface features, namely, the slope or the peak of the reaction coordinate diagram, with the former suggesting an implied temporal association with the xaxis.…”

Beyond instructional practices: Characterizing learning environments that support students in explaining chemical phenomena

“…It enables a fine‐grained analysis of student reasoning and suggests manners by which students’ raw intuition might be leveraged for disciplinary work. There is evidence in physics education (Elby, 2001; Hammer, 2000; Hammer et al, 2005), and a growing evidence base in chemistry education (Cooper et al, 2013; Rodriguez et al, 2020a, 2020b), that students’ raw intuition contains all sorts of useful tools for figuring out causes for phenomena. Examining how learning environments might support the productive activation of intuitively appealing resources is a worthwhile goal for chemistry education researchers and educators.…”