When Is It Relevant? A Collaborative Autoethnographic Study by Engineering Students on Statistical Variability

Context, background, gap In this research paper, we examine engineering students' thinking about statistical variability. Mathematical models are ubiquitous in engineering practice and are used to make design decisions. However, such models often ignore statistical variability and engineering curricula have been shown to underemphasize variability. This is concerning because prior engineering failures have been attributed to a neglect of variability; for instance, military aircraft designed in the 1950's were sized for "the average man," which contributed not only to the exclusion of female pilots, but also made aircraft dangerously uncontrollable for virtually all pilots. Purpose of the paper The purpose of this paper is to analyze three first-year engineering students' experiences learning about statistical variability in engineering training. In particular we investigate their perceptions of relevance, as it is a necessary precondition to working with variability in practice. Theoretical framework We draw on recent education research on mathematical modeling and statistical thinking, and examine student experiences through the lens of Wenger's communities of practice. Namely, this theory predicts that a community's reifications will be tailored to its practice, suggesting differences across engineering disciplines that may manifest in perceived relevance. Research questions We address two research questions: To what extent do engineering students perceive statistical variability as being relevant to engineering practice? What experiences affect their views? Research methodology / methods Our study investigated first-year engineering student culture with a focus on mathematics and variability. Three first-year engineering students guided by a faculty member engaged in collective autoethnography (CAE) as researcher/participants for ~200 hours over a 10 week period. The students had recently taken a first-year course on mathematical modeling that emphasized statistical variability. The students engaged in six cycles of reflection and debrief guided by the faculty member. We used the Q3 framework to promote quality in making and handling our data along six quality facets. For instance, to promote Communicative Validation while making the data, the faculty member defined an initial set of reflection prompts that treated the mathematical modeling course as a focal point. The entire team then collaborated on updated prompts that expanded the study's view while resonating with the students and maintaining the study's focus. To promote Ethical Validation, the entire research team co-wrote and followed a set of dissemination rules that created a safe space for all researcher/participants. We present an episode that illustrates this "veto rule" as evidence of achieving this safe space. Findings The students all described an increasing sense of relevance based on personal experiences with variability. However, these experiences occurred at different times and with different valences. For instance, one student found relevance early in childhood navigating an inequitable world, while another did not find relevance until encountering it in a major-related college course. Discussion / Implications Faculty interested in teaching mathematical modeling or statistical thinking can use our findings to help their own students develop a sense of relevance for statistical variability. Our methods also illustrate ways to implement Ethical Validation to promote research quality.