Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

摘要

Researchers have argued against deficit-based explanations of students'troubles with mathematical sense-making, pointing instead to factors such asepistemology: students' beliefs about knowledge and learning can hinder themfrom activating and integrating productive knowledge they have. In this casestudy of an engineering major solving problems (about content from hisintroductory physics course) during a clinical interview, we show that "Jim"has all the mathematical and conceptual knowledge he would need to solve ahydrostatic pressure problem that we posed to him. But he reaches and stickswith an incorrect answer that violates common sense. We argue that his lack ofmathematical sense-making-specifically, translating and reconciling betweenmathematical and everyday/common-sense reasoning-stems in part from hisepistemological views, i.e., his views about the nature of knowledge andlearning. He regards mathematical equations as much more trustworthy thaneveryday reasoning, and he does not view mathematical equations as expressingmeaning that tractably connects to common sense. For these reasons, he does notview reconciling between common sense and mathematical formalism as eithernecessary or plausible to accomplish. We, however, avoid a potential "deficittrap"-substituting an epistemological deficit for a concepts/skills deficit-byincorporating multiple, context-dependent epistemological stances into Jim'scognitive dynamics. We argue that Jim's epistemological stance containsproductive seeds that instructors could build upon to support Jim'smathematical sense-making: He does see common-sense as connected to formalism(though not always tractably so) and in some circumstances this connection isboth salient and valued.