2024 ASEE Annual Conference & Exposition

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.