  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.
