Learning to Model in Engineering

Abstract

Policymakers and education scholars recommend incorporating mathematical modeling into mathematics education. Limited implementation of modeling instruction in schools, however, has constrained research on how students learn to model, leaving unresolved debates about whether modeling should be reified and explicitly taught as a competence, whether it should be taught holistically or atomistically, and whether students’ limited domain knowledge is a barrier to modeling. This study used the theoretical lens of legitimate peripheral participation to explore how learning about modeling unfolds in a community of practice—civil engineering—known to develop modeling expertise among its members. Twenty participants were selected to represent various stages of engineering education, from first-year undergraduates to veteran practitioners. The data, comprising interviews, “think-aloud” problem-solving sessions, and observations of engineering courses, were analyzed to produce a description of how this professional community organizes learning about mathematical models and resolves general debates about modeling education.

Notes

¹Although perhaps not within countries. Dym (1999)claims U.S. engineering programs “look far more alike than not,” even across widely differing campus types.

²Undergraduates study engineering content for about 3600 hours, whereas 10,000 hours of “active engagement in a domain” are thought necessary to attain expertise (Litzinger et al., 2011).

³Year 1 students have been assigned pseudonyms beginning with A, Year 2 with B, etc. New engineers’ pseudonyms begin with N and veteran engineers’ with V.

⁴To protect the identity of the very few females in my sample of veteran engineers and instructors, I have assigned the male gender to all participants in these categories. Students’ and new engineers’ genders have been preserved.

⁵A graphical representation of the state of stress on a point on a body; the x-coordinates represent normal stress and the y-coordinates shear stress.

⁶A graph of stress (internal force per unit area) versus strain (deformation per unit length) for a particular material.

⁷A graph relating the axial loads and moments that produce failure in a structural column.

⁸ Spandaw (2011), however, found similar attitudes toward college-level modeling instruction among Dutch mathematics, science, and engineering professors.