Beyond Epistemological Deficits: Dynamic explanations of engineering students’ difficulties with mathematical sense-making

Abstract

Researchers have argued against deficit-based explanations of students’ difficulties with mathematical sense-making, pointing instead to factors such as epistemology. Students’ beliefs about knowledge and learning can hinder the activation and integration of productive knowledge they have. Such explanations, however, risk falling into a ‘deficit trap’—substituting a concepts/skills deficit with an epistemological one. Our interview-based case study of a freshman engineering major, ‘Jim,’ explains his difficulty solving a physics problem (on hydrostatic pressure) in terms of his epistemology, but avoids a deficit trap by modeling the dynamics of his epistemological stabilities and shifts in terms of fine-grained cognitive elements that include the seeds of epistemological expertise. Specifically, during a problem-solving episode in the interview, Jim reaches and sticks with an incorrect answer that violates common sense. We show that Jim has all the mathematical skills and physics knowledge he would need to resolve the contradiction. We argue that his difficulty doing so stems in part from his epistemological views that (i) physics equations are much more trustworthy than everyday reasoning, and (ii) physics equations do not express meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and formalism as either necessary or plausible to accomplish. But Jim’s in-the-moment shift to a more sophisticated epistemological stance highlights the seeds of epistemological expertise that were present all along: 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.

Keywords:

• Physics education
• Science education
• Qualitative research
• Mathematical sense-making

Acknowledgments

We thank ‘Jim’ for participating in our research. We thank Andrew Brantlinger, Jessica Watkins, Chandra Turpen, and members of the Physics Education Research Group, University of Maryland, for extensive discussions about the analysis and the manuscript. We also thank Jose Mestre, and three anonymous reviewers for reviewing the manuscript. This research is funded, in part, by NSF EEC 0835880. The views present in the manuscript are the authors’ own.

Notes

Pseudonym used to protect the identity of the subject.

Schoenfeld (1992b) discusses the importance of an in-depth analysis of single-subject case studies in the enterprise of building theory within learning sciences.

We intend to use the word ‘stance’ as a descriptor of students’ attitude toward something, reflected in their reasoning and behavior. At the cognitive level, a stance could be modeled as a local coherence of one or more ‘resources.’ At times, we might use the same label for a stance or a resource, but the mapping of labels should not be taken as a mapping of ontology.

Additional information

Notes on contributors

Ayush Gupta

The author contributed equally to this work.

Andrew Elby

The author contributed equally to this work.