Visualization and Diagrammatic Reasoning during Genuine Problem Solving in Science

Mental visualization of diagrammatic representations is presumed to be a critical strategy for learning and problem solving, particularly in the sciences. However, little is known about how students employ visualization on genuine scientific tasks. The present study describes undergraduate chemistry students’ use of visualization for problem solving using think-aloud protocols. The analysis suggests that students’ reasoning is heavily guided by the form of the molecular diagrams given in the task and self-generated inscriptions. Visualization strategies appeared critical for task that required representation translations. Exploring the Intersection of Visualization and Diagrammatic Reasoning in Chemistry The affordances of diagrams to aid in reasoning has been underscored in several arenas. Computational models of diagrammatic reasoning have indicated how diagrams facilitate the organization of knowledge, scaffold problem solving, and invoke mental images (Larkin & Simon, 1987; Narayanan, Suwa, & Motoda, 1995; Olivier, 2001). Cognitive studies have indicated how problem solvers attempt to visualize diagrams and rely on them for spatial reasoning (Hegarty, 1992; Oxman, 1997). Similar to the efforts of Qin & Simon (1992), the present study attempts to apply some of the collective findings of these communities to investigate the extent to which diagrammatic reasoning and visualization intersect with domain knowledge in science. The results provide new insights on (1) how individuals learn to reason from diagrams in specific contexts and (2) the task-specific use of visualization in scientific problem solving. Investigations of problem solving in science domains have hinted at a complex interplay between visualization and diagrammatic reasoning. By analyzing eye movement behaviors during problem solving, Hegarty (1992) inferred that students systematically and sequentially attempt to mentally animate diagrammatic representations for certain engineering tasks. Likewise, Qin and Simon (1992) identified a reciprocal relationship between visualization and inscription practices using qualitative investigations of problem solving among students of advanced physics. Such work supports computational models of diagrammatic reasoning that postulate a critical function of diagrams to preserve and coordinate spatial information during problem solving (Larkin & Simon, 1987). The field of organic chemistry provides an excellent domain in which to extend studies of the interaction of visualization and diagrammatic reasoning during problem solving. Students of organic chemistry often reason about the spatial characteristics of molecular diagrams in order to determine molecular structure, functionality, and reactivity. Additionally, organic chemistry textbooks employ several unique diagrams of molecules in which spatial information is implicitly communicated; consequently, students must learn exclusive techniques to decode three-dimensional shape and structure from two-dimensional diagrams that lack the dimension of depth (Ege, 1999). Moreover, a major component of chemistry instruction centers on the use of non-imagistic strategies for manipulating molecular diagrams with little regard to the spatial information they contain. When teaching such strategies, instructors often encourage their students to use formalisms of molecular diagrams for making judgments about the threedimensional features of a molecule. Although textbooks and instructors present these diagrammatic reasoning strategies as a more efficient and simpler strategy than the generation and manipulation of mental images of molecular structures, students often fail to correctly apprehend them (Taagepera & Noori, 2000). Unfortunately, little is known about the interaction between visualization and reasoning from diagrams during genuine problem solving in this domain. Past studies have focused on the affordances of different molecular diagrams to represent the imperceptible molecular world (Johnstone, 1993), to communicate ideas and understanding between experts and novices (Kozma, et al., 2000), or to facilitate teaching (Wu, Krajick, & Soloway, 2001). Other work has explicated the manner in which molecular diagrams attempt to represent three-dimensional space in twodimensions (Habraken, 1996; Keig & Rubba, 1993), but little has been said in these forums about how molecular diagrams and visualization strategies interact. Rather, they have focused mostly on the presumed difficulties with perceiving the embedded three-dimensionality of molecular diagrams and pursued correlations between achievement and visuo-spatial skills. Regardless, it is generally assumed that visualization is a key strategy for problem solving in chemistry (Habraken, 1996); however, the precise role of that strategy remains unclear. Design of the Present Study The present study attempted to characterize novice students’ use of visualization and diagrammatic reasoning on traditional organic chemistry tasks. Thirteen students enrolled in introductory organic chemistry completed two 45-minute think-aloud interviews. During the interviews students performed a variety of organic chemistry tasks that included representative assessments on topics such as reaction mechanisms, product generation, stereochemistry, and the translation of molecular representations. Each interview was transcribed, and the transcripts were analyzed for instances in which students explicitly made use of visualization for problem solving. Transcription and review of the 25 clinical interviews established the data corpus, which comprised 19.5 hours of video. Students completed between 16 and 24 tasks as a function of the time each took to solve each task in the interviews. The combined total of all completed tasks resulted in 246 tasks in the corpus. Seventy of these tasks were analyze tasks, which required students to analyze the structure and reactivity of a compound. Twenty-eight were translate tasks, which required students to translate one molecular representation into a different one. Finally, 148 were extended problem tasks, which required students to draw reaction schemes, design syntheses, or propose reaction mechanisms. The interviews were analyzed using accepted techniques of qualitative data analysis (Chi, 1997; Ericcson & Simon, 1980) with specific regard to utterances and gestures that indicated students were trying to visualize the threedimensional structure of the molecular compounds in each task. For the purposes of this study, individual cases of student problem solving strategies were situated either externally, when students reasoned about spatial information using the diagrams, or internally, when students engaged in the visualization of imagined molecular structures. Examples of utterances that indicated the use of visualization included explicit references to attempts to “picturing or seeing a molecule” or “visualizing models from class”. Physical behaviors that suggested the use of visualization included gestures to objects in empty space, grasping and rotating imagined objects, and physically moving diagrams with references to “visualizing it from different angles”. A common example of reasoning from diagrams was an utterance in regard to spatial relationships within a particular diagram together with gestures to that diagram, such has “this line means the bond projects above the page.” More important, were instances in which students duplicated particular spatial relationships from previous diagrams into new inscriptions without regard to whether the relationships were valid or references to engaging in visualization. Two separate analyses of the data corpus illustrated a variety of interactions between diagrammatic reasoning and visualization strategies. First, a series of descriptive statistics on the coded data corpus revealed the frequency of visualization strategies across tasks for the entire participant group. Second, illustrative cases of the interviews indicated how students were able to selectively manipulate molecular diagrams to successfully complete a wide range of tasks. Task-Specific Use of Visualization and Diagrammatic Reasoning Analysis of participants’ preferred strategies revealed that the interaction between visualization and diagrammatic reasoning is a function of the task demands. By parsing the data corpus into the three types of tasks enumerated above, the selectivity of student use of visualization was immediately apparent. Figure 1 illustrates how students used the embedded features and constraints of molecular diagrams on most tasks to scaffold their reasoning about spatial information. Notably, students engaged in behaviors that suggested they were trying to inspect a visualized mental image of a molecular diagram on translate tasks. Figure 1. Student’s use of visualization was specific to translation tasks in organic chemistry. On analyze tasks, where students had to describe all relevant physical and chemical properties of a given molecular diagram, they appeared unlikely to engage in visualization of those diagrams. On the majority of these tasks, students did not make any utterances, behaviors, or inscriptions that suggested they had attended to spatial information embedded in the diagram. On 28% of these tasks, students did mention the spatial features of the molecule with specific reference to the diagram, but their utterances were of a unique sort. For the most part, utterances were in specific regard to the two tasks that included three-dimensionally rendered space-filling molecular representations. Upon viewing such representations, students mentioned that the representations helped them to “see how big it is” or “see how different groups interact”. On 8% of these tasks did students mention trying to visualize the structures to discern additional information. Analyze tasks such as those used in the interviews corresponded to approximately 25 percent of the assessment items from students’ coursework. This pattern of results persisted on extended problem tasks where students were asked to predict products, generate mechanisms, or propose syntheses in accordance with accepted concepts of organic chemistry. On 58% of these tasks, the participants referenced the diagram to note a spatial feature of a molecule. Evidence for this strategy was seen in instances of pattern matching and duplication mentioned above. On only 8.7% of these tasks did students appear to engage in the visualization of molecular diagrams. Frequently these behaviors took the form of students gesturing at an imagined molecule or mentioning that they were trying to visualize using their molecular modeling kits from class. Roughly 93 percent of the assessment items from the students’ courses contained an extended problem component. A dramatic reversal in strategy use was apparent on translation tasks. On 51.9% of the interview tasks, students referenced the diagram as a scaffold for visualization instead of merely mentioning spatial features such as size or shape. For instance, students would reference a spatial relationship in the initial representation that they then duplicated in the target molecule to which they were translating. On 81.5% of these tasks, the students engaged in clear behaviors that indicated they were attempting to manipulate an imagined three-dimensional visualized molecular structure. All students showed great difficulty in these tasks and many mentioned that they would be able to perform better if they had molecular modeling kits available. Approximately 12 percent of the assessments tasks from the students’ courses contained a translation component. Illustrative Cases of Visualization and Diagrammatic Reasoning The overall trends within the data corpus revealed that students employed visualization strategies on approximately one-fourth of the tasks in the interviews. More specifically, the students appeared to use visualization strategies selectively to perform translations of molecular representations. Although students employed visualization for successful problem solving on the translation tasks, they rarely reported using visualization on extended problem solving tasks or on analyze tasks. Each student progressed through such tasks without explicitly addressing spatial information. Instead, the participants employed several heuristics for inscribing molecular diagrams that allowed them to generate successful solutions to the tasks. These heuristics appear to describe formal principles of diagrammatic reasoning in chemistry since they were ubiquitous among all the students and all the tasks. Below are three cases that illustrate the use of both visualization and diagrammatic reasoning for problem solving in organic chemistry. Visualization for Translating Molecular Diagrams Students engaged in overt behaviors that indicated they used visualization as a major component of their overall problem solving strategy on one or more translation tasks. The following excerpt from the interview with Carrie indicates how the students used visualization to translate given molecular diagrams into target diagrams that emphasized three-dimensional spatial features of the molecule. On this task (illustrated in Figure 2), Carrie attempted to translate the given two-dimensional line-angle diagram of a substituted cyclohexane into a chair diagram. Upon seeing the task, Carrie immediately noted she knew the basic chair diagram, which she inscribed. Subsequently, she engaged in behaviors that suggest she was trying to visualize a three-dimensional image of the molecular structure in question to complete the translation. Figure 2. The bottom pathway indicates the diagrams typically used to represent the three-dimensional relationships in the top pathway. Mike: Can you re-render this molecule as a chair? Carrie: Uh...I’m so much more used to doing the chair as just the cyclohexane. I don’t know how I would go about adding this whole thing to it. Points to the cyclopentanone. How would I do that...Well, this is just the old cyclohexane chair. She draws out the cyclohexane chair. Now I don’t know if this bond-points to one of the cyclohexane bonds she has drawn-is supposed to represent this-points to bridging bond between the rings. M: You can put it wherever you like. She erases the cyclohexane and redraws it. Why are you