When Am I (N)ever Going to Use This? How Engineers Use Algebra (NSF DRL)

Abstract Mathematics is an important tool in engineering practice, as mathematical rules govern many designed systems (e.g., Nathan et al., 2013; Nathan et al., 2017). Investigations of structural engineers suggest that mathematical modelling is ubiquitous in their work, but the nature of the tasks they confront is not well-represented in the K-12 classroom (e.g., Gainsburg, 2006). This follows a larger literature base suggesting that school mathematics is often inauthentic and does represent how mathematics is used in practice. At the same time, algebra is a persistent gatekeeper to careers in engineering (e.g., Harackiewicz et al., 2012; Olson & Riordan, 2012). In the present study, we interviewed 12 engineers, asking them a series of questions about how they use specific kinds of algebraic function (e.g., linear, exponential, quadratic) in their work. The purpose of these interviews was to use the responses to create mathematical scenarios for College Algebra activities that would be personalized to community college students' career interests. This curriculum would represent how algebra is used in practice by STEM professionals. However, our results were not what we expected. In this paper, we discuss three major themes that arose from qualitative analyses of the interviews. First, we found that engineers resoundingly endorsed the importance of College Algebra concepts for their day-to-day work, and uniformly stated that math was vital to engineering. However, the second theme was that the engineers struggled to describe how they used functions more complex than linear (i.e., y=mx+b) in their work. Students typically learn about linear functions prior to College Algebra, and in College Algebra explore more complex functions like polynomial, logarithmic, and exponential. Third, we found that engineers rarely use the explicit algebraic form of an algebraic function (e.g., y=3x+5), and instead rely on tables, graphs, informal arithmetic, and computerized computation systems where the equation is invisible. This was surprising, given that the bulk of the College Algebra course involves learning how to use and manipulate these formal expressions, learning skills like factoring, simplifying, solving, and interpreting parameters. We also found that these trends for engineers followed trends we saw in our larger sample where we interviewed professionals from across STEM fields. This study calls into question the gatekeeping role of formal algebraic courses like College Algebra for STEM careers. If engineers don't actually use 75% of the content in these courses, why are they required? One reason might be that the courses are simply outdated, or arguments might be made that learning mathematics builds more general modelling and problem-solving skills. However, research from educational psychology on the difficulty of transfer would strongly refute this point – people tend to learn things that are very specific. Another reason to consider is that formal mathematics courses like advanced algebra have emerged as a very convenient mechanism to filter people by race, gender, and socioeconomic background, and to promote the maintenance of the "status quo" inequality in STEM fields. This is a critical issue to investigate for the future of the field of engineering as a whole.