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

Abstract

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.

Submitted to the Journal of Engineering Education

References in corpus (5)

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Cited by in corpus (7)

• Language of physics, language of math: Disciplinary culture and dynamic epistemology
• Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory Physics
• Recurring questions that sustain the sensemaking frame
• A Vision of Interdisciplinary Education: Students' Reasoning about "High-Energy Bonds" and ATP
• Investigating Unprompted and Prompted Diagrams Generated by Physics MajorsDuring Problem Solving
• Case study examining graduate student sensemaking using the epistemic game framework for Laplace's equation in upper-level electrostatics
• Leveraging a Relationship with Biology to Expand a Relationship with Physics