Possibilities: A framework for modeling students' deductive reasoning in physics.

摘要

Students often make errors when trying to solve qualitative or conceptual physics problems, and while many successful instructional interventions have been generated to prevent such errors, the process of deduction that students use when solving physics problems has not been thoroughly studied. In an effort to better understand that reasoning process, I have developed a new framework, which is based on the mental models framework in psychology championed by P. N. Johnson-Laird. My new framework models how students search possibility space when thinking about conceptual physics problems and suggests that errors arise from failing to flesh out all possibilities. It further suggests that instructional interventions should focus on making apparent those possibilities, as well as all physical consequences those possibilities would incur.;The possibilities framework emerged from the analysis of data from a unique research project specifically invented for the purpose of understanding how students use deductive reasoning. In the selection task, participants were given a physics problem along with three written possible solutions with the goal of identifying which one of the three possible solutions was correct. Each participant was also asked to identify the errors in the incorrect solutions. For the study presented in this dissertation, participants not only performed the selection task individually on four problems, but they were also placed into groups of two or three and asked to discuss with each other the reasoning they used in making their choices and attempt to reach a consensus about which solution was correct. Finally, those groups were asked to work together to perform the selection task on three new problems.;The possibilities framework appropriately models the reasoning that students use, and it makes useful predictions about potentially helpful instructional interventions. The study reported in this dissertation emphasizes the useful insight the possibilities framework provides. For example, this framework allows us to detect subtle differences in students' reasoning errors, even when those errors result in the same final answer. It also illuminates how simply mentioning overlooked quantities can instigate new lines of student reasoning. It allows us to better understand how well-known psychological biases, such as the belief bias, affect the reasoning process by preventing reasoners from fleshing out all of the possibilities. The possibilities framework also allows us to track student discussions about physics, revealing the need for all parties in communication to use the same set of possibilities in the conversations to facilitate successful understanding. The framework also suggests some of the influences that affect how reasoners choose between possible solutions to a given problem.;This new framework for understanding how students reason when solving conceptual physics problems opens the door to a significant field of research. The framework itself needs to be further tested and developed, but it provides substantial suggestions for instructional interventions. If we hope to improve student reasoning in physics, the possibilities framework suggests that we are perhaps best served by teaching students how to fully flesh out the possibilities in every situation. This implies that we need to ensure students have a deep understanding of all of the implied possibilities afforded by the fundamental principles that are the cornerstones of the models we teach in physics classes.