Beyond pipeline and pathways: Ecosystem metrics

DOI: 10.1002/jee.20250 ORIGINAL ARTICLE Beyond pipeline and pathways: Ecosystem metrics Susan M. Lord1 | Matthew W. Ohland2 | Richard A. Layton3 | Michelle M. Camacho4 1 Integrated Engineering, University of San Diego, San Diego, California Abstract 2 Background: Pipeline and pathways models influence persistence metrics used to Engineering Education, Purdue University, West Lafayette, Indiana 3 Mechanical Engineering, Rose-Hulman Institute of Technology, Terre Haute, Indiana 4 Sociology, University of San Diego, San Diego, California Correspondence Susan M. Lord, Shiley-Marcos School of Engineering, University of San Diego, 5998 Alcalá Park, San Diego, CA 92110. Email: slord@sandiego.edu Funding information National Science Foundation, Grant/Award Numbers: 1129383, 1545667 study how students navigate engineering education. Purpose: This study presents pipeline, pathways, and ecosystem models and their associated metrics, compares and contrasts these models using an intersectional approach to explore persistence, and advocates for use of an ecosystem model. Design/Method: This study presents a quantitative perspective of engineering student outcomes disaggregated by discipline, race/ethnicity, and sex. It includes 111,925 engineering students from 11 U.S. universities, including first-time-incollege and transfer students who ever majored in the most common engineering disciplines: chemical, civil, electrical, industrial, and mechanical engineering. Contemporary data visualization methods are used to display quantitative data and clarify their complexity. Results: This work captures the intersectionality of race/ethnicity, sex, and discipline with metrics that are new or little used, such as stickiness (retention by a discipline), migrator graduation rate, and migration yield (attraction of a discipline). Using these metrics, we uncover information about the success of students who migrate between and among the top five engineering disciplines. Conclusions: Stickiness, migrator graduation rates, and migration yield metrics coupled with contemporary data visualization methods provide insights into the student experience not afforded by the conventional pipeline and pathways models. Considering engineering education as an ecosystem tells stories of complexity and nuance, opening possibilities for new research. KEYWORDS ecosystem, engineering pathways, engineering pipeline, retention, underrepresentation 1 | INT RODU C T I ON : F R OM P I PE L I N E A N D PA T H WA Y S T O E C O S Y S T EM Researchers studying outcomes for students in engineering education rely upon imagery and metaphors to describe students' trajectories. The visualization of a “pipeline,” for example, through which students pass en route to graduation offers a useful metaphor for simplifying what is often a complex journey. The “pathways” metaphor offers increased accuracy in capturing the multiple entry points and typically a single exit point that students encounter. Lending insights to our theoretical paradigms for studying student retention, these two approaches align with metrics commonly used to measure success at fixed points (e.g., at 4 years, 6 years, and graduation). Both of these models have dominated the discourse for understanding student persistence in engineering education, sometimes oversimplifying students' complex journeys before they graduate or leave. Most likely because of limitations of data, even fewer 32 © 2019 ASEE wileyonlinelibrary.com/journal/jee J Eng Educ. 2019;108:32–56. LORD ET AL. 33 studies have examined students' “migratory” complexity across engineering disciplines. With increasingly more robust sources of data, the potential exists for developing more powerful tools to understand the nuances within student journeys. Another important conceptual element is student agency as students navigate through engineering education, a factor that may be hidden in both the pipeline and pathways models. In this work, we adopt and endorse a perspective that recognizes the interconnectedness of an “ecosystem” and the hidden aspects of student agency within such a complex system, focusing on the ecosystem of engineering education. Research from historians and social scientists documents structural patterns of exclusion in engineering education culture, including historical and contemporary forms of racism, sexism, and other modes of ostracism (cf. Bix, 2004; Godfrey & Parker, 2010; Hacker, 1989; Slaton, 2010; Tonso, 2007). In an ecosystem, students have agency, and while historical inequities influence access and inclusion, they do not necessarily predetermine student trajectories. Traditional retention analytics obscure student agency, while institutional variation further confounds these patterns (Ohland et al., 2011). In addition, systemic conditions predispose some groups of students to thrive in a timely fashion in the same ecosystem where success for others requires more time. These uneven flows characterize the ecosystem, and in this study, we examine the rich diversity of student experiences as they navigate them. We apply a new mindset, new metaphors, and new metrics to reveal parts of the complex system previously hidden, showing the role that the engineering discipline plays. The result is a description of a system capturing the intersectionality of race/ethnicity, sex, and discipline, using metrics that are new or little used, such as “stickiness” (retention by a discipline), graduation rate of migrators, and “migration yield” (attraction of a discipline). Using these metrics, we are able to uncover more nuanced information about students who migrate between and among the top five engineering disciplines. This work considers more than 80,000 engineering students at 11 institutions, making disciplinary comparisons while disaggregating the student population by race/ethnicity and sex. We describe pipeline, pathways, and ecosystem models, detailing the metrics associated with each model, including our methods and associated results. We advocate for the use of an ecosystem model. Our objective is to present a variety of new metrics for investigating academic trajectories using an intersectional approach to uncover new insights into the engineering education ecosystem. 2 | PIPELINE, PATHWAYS, A ND ECOSYSTEM 2.1 | Pipeline The pipeline metaphor has been historically used to address issues of recruitment and retention through academic trajectories. The pipeline visual, illustrated in Figure 1, suggests that students enter higher education at a given point and possibly “leak” out. Student success is represented with students exiting the pipeline at graduation. Indeed, many students follow this pipeline process, entering and exiting following what is characterized as a traditional route, measured by 4- or 6-year graduation. According to Fealing, Lai, and Myers Jr. (2015), A pipeline is understood to be a favored or privileged route or channel toward entering a profession. Because this is the main source of channeling members of majority groups into the profession, it is expected that others also follow these routes. The routes themselves are favored not necessarily because they are the most efficient or equitable entry points to the profession. Rather, these routes are favored because they work and have worked for the dominant group. (p. 272) Typically, the pipeline metaphor has been used to identify problems, particularly with regard to attracting and retaining students. One of the earliest uses of the pipeline metaphor for considering underrepresented minorities was a report by Astin (1982). Other researchers apply it to examine leaks in the educational system in science (Astin & Astin, 1992; Pearson, 1985), nursing (Green, 1987) and clinical research (Moskowitz & Thompson, 2001). However, a criticism of the pipeline metaphor is that it results in exclusive focus on the supply side of the underrepresentation problem (Fealing et al., 2015) because the assumption is that there is a favored route from start to graduation, based on the retaining attracting higher education “pipeline” FIGURE 1 The pipeline model focuses attention on attracting and retaining students to increase the graduating numbers in spite of the inevitable “leaks” leaking graduating LORD ET AL. 34 experience of the dominant group (White men in engineering). The pipeline is a static metaphor: if more people enter, then more will graduate, a limitation acknowledged by many early researchers (see Astin & Astin, 1992). For example, using a pipeline framework, Trent (1984) analyzed persistence by sex, race, and major, concluding that “simple summary reports of progress in higher education can generate misleading interpretations when race/ethnicity and sex differences are not considered” (p. 302). A second criticism of the typical application of the pipeline model is that many researchers do not disaggregate by student demographics because of data limitations, concerns for identifiability, and the challenges of displaying complex data. As a result, historically underrepresented students, such as women in some programs including engineering and computer science, or racial and ethnic minorities, are often invisible in the pipeline model. And conventional metrics, such as 6-year graduation rates published in the Integrated Postsecondary Education Data System (IPEDS), eliminate transfer, part-time, and spring enrollees, creating an invisible pool of students not accounted for in federal reporting structures for educational institutions. Ignoring these populations glosses over significant differences and produces an overly simplified account of students' educational journeys. 2.2 | Pathways Researchers have criticized the pipeline model and encouraged a pathways approach (Fealing et al., 2015; Watson & Froyd, 2007) to address the “one size fits all” paradigm that underlies the pipeline model (Atman et al., 2010). An example of a pathways model with multiple entry points is illustrated in Figure 2. Thus, compared to a pipeline approach, a pathways approach offers a more comprehensive understanding of the multiple entry points for traditional and nontraditional students (McNeil, Ohland, & Long, 2016) and allows for analysis of articulations between 2- and 4-year institutions. Moreover, the pathways lens allows for a more robust understanding of transfer students and students who change majors. Rather than pejoratively labeling aberrations in the pipeline as “leaks,” the pathways approach recognizes that a student's experience can involve additional entry points, including transfer from a 2-year or 4-year institution; enrollment outside the fall cohort; and re-entry after detours and stop-outs. An example of a pathways metric is the analysis of student “trajectories” (Lord, Layton, & Ohland, 2011) that offer data on student matriculation major, combined with analysis of internal and external transfer students disaggregated by race/ethnicity and sex. Other examples include multi-pathway Sankey diagrams (Sadler, Sonnert, Hazari, & Tai, 2012) and applications of graph theory to identify the shortest path through a curriculum (Aldrich, 2015). While the pathways model is powerful for its inclusivity of nontraditional students, it still lacks the capacity to capture the complexity of student agency. For example, while a pathways analysis identifies various starting points, it lacks consideration of interconnections within the ecosystem of higher education. In particular, the model overlooks the interactions of students with departments and majors of various disciplines and their structural roles in attracting students, retaining them, or repelling them. The term pathways connotes the consideration of multiple entry pathways, yet typically does not describe what happens on the paths—the extent to which some paths are smooth, some well-worn, and some rocky. Pathways models do not typically recognize a multiplicity of exit goals and outcomes. In pipeline and pathways frameworks, the use of limited metrics has been common both because they have simplified the more complex reality and because the datasets available to researchers were either incomplete or too small to study the system in greater detail. 2.3 | Ecosystem An ecosystem model begins with the premise that all elements related to student success operate within a complex system of higher education. Such an approach allows us to discover patterns of students whose trajectories are influenced by their context and are, therefore, nonlinear; we call these students “migrators” as they are affected by the disciplines to which they are exposed. For example, a pipeline or pathways model reveals whether a majority of students matriculating in a major will graduate; yet we know far less about students who leave their primary major, migrate to other majors, stick, switch, and ultimately succeed. We lack detail about the importance of switching, how it affects students' outcomes, and how disciplinary practices 2-year institution entry change major non-traditional student entry graduation traditional student entry FIGURE 2 re-entry stop-out The pathways model provides more entry points than the pipeline model LORD ET AL. 35 operate as gatekeepers, producing or eliminating barriers that impede or foster student success. We know even less about disciplinary cultures, their mechanisms, and the messages faculty and administrators use that attract students to their programs. Analyses of student migratory patterns provoke new questions for the study of academic persistence, namely, under what conditions do students navigate the terrain of engineering education? How do we examine these migratory flows within a broader ecosystemic framework of higher education? As Vanasupa and Schlemer (2016) astutely theorize, as engineering cultures reproduce themselves, they also reproduce systemic problems (related to a lack of diversity and problems with teaching and learning) because these are both outcomes of a system functioning as designed: “the problematized phenomena of a dynamic system result from the collective action of the system over time” (p. 6). Building on the work of anthropologist Edward Hall (1976), they draw on the imagery of an iceberg, suggesting that in engineering education, we see only the tip of the iceberg, not the underlying glacier. While the pathways model is an improvement over the pipeline model as it recognizes the many ways students enter the engineering education system and their stops along the way, an ecosystem is still more complex, considering the ways in which students interact with one another and their environment. Cheville (2017) compares biological and organizational ecosystems, helping to illustrate the challenges and benefits of using an ecosystem model by suggesting, for example, that “existence does not imply health, function, and persistence” (p. 4). Consistent with Cheville's framing, many students are permitted to enter the population of an institution or a discipline, yet some will not be able to thrive in that environment. According to Cheville, biological ecosystems are driven by bottom-up interactions, whereas organizational ecosystems can also be driven by top-down interactions. Within the engineering education ecosystem, bottom-up interactions may be considered as ways in which students engage with the system through the choices that they make and their interactions with one another and others in their networks. Top-down interactions could include what Pawley and Phillips (2014) and Pawley (2019) refer to as “ruling relations,” the written and unwritten rules that encode the structures and guide the administrative actors within the ecosystem. In describing the ecosystem, Cheville (2017) notes that stability is “dependent on keystone species or actors” (p. 4), implying power relations within the interactions. While students have some agency, this agency can be constrained by keystone elements such as historical institutional polices, long-time professors, and administrators who sustain the status quo. Within an ecosystem, populations respond to the distribution of resources and competitors (Pocheville, 2015); in the academic context, students are a limited resource distributed among the various majors upon entry and possibly later if they migrate within the ecosystem by changing majors. The environment matters. For example, certain enrollment management restrictions constrain the majors available to students based upon their grade-point averages (GPA). The environment also interacts with students in more complex ways. Earlier work has shown that industrial and chemical engineering attracts and retains a larger percentage of women than other disciplines, but for very different reasons (Brawner, Lord, Layton, Ohland, & Long, 2015). The complexity of engineering education creates challenges affecting how the ecosystem can be modeled. The results of multilevel modeling are dependent upon the ordering of the levels (Evanschitzky & Backhaus, 2015), yet the level structure of the engineering education ecosystem can be operationalized in multiple ways depending on the research design. Variability can be salient at both the departmental and the disciplinary levels. Departments are nested within institutions that control admissions process and set overarching policies, implying that students are nested within departments that are nested within institutions. It is also true that the engineering disciplines have a shared culture; engineering disciplinary societies connect instructors and students across institutions and indeed establish discipline-wide ruling relations through the design and implementation of program-specific accreditation criteria through their representation in ABET (ABET Member Societies, n.d.). In this sense, we could contend that the discipline transcends institution and is, thus, at a higher level in the model. This ambiguity creates confusion between describing students as within a department (a local unit of an institution) versus within a discipline (a high-level construct). Further complicating this issue is that a department may administrate programs in multiple disciplines, such as electrical and computer engineering departments, from which students may graduate with a degree accredited in one or both of those disciplines, resulting in a form of “disciplinary citizenship.” Our research design in this paper focuses at this disciplinary level of analysis, aggregating student data across multiple institutions. Pipeline and pathways approaches consider only what is most obvious about student outcomes, not the full system they inhabit. Like all cultural systems including science education (Carlone & Johnson, 2012), engineering education operates with agents of cultural transmission, unspoken hierarchies, and tacit knowledge of their existence (Foor & Walden, 2009; Tonso, 2006; Waller, 2004), with only murky communication about these differences. The cultural reproduction of norms in engineering education occurs at multiple levels. Faculty, of course, are not the only agents of cultural transmission. Students too, particularly juniors and seniors in engineering, enact norms and pass these on to first- and second-year students (Leonardi, Jackson, & Diwan, 2009). As students navigate this academic landscape, the terrain may lead them in multiple directions. In exploring the complexity of student migration, we can learn from frameworks used by researchers who study migration of people across nation–state borders, with three common frameworks used to examine migratory trajectories. One approach, the “push/pull” theory of 36 LORD ET AL. migration, places the onus of change on the individual actor, suggesting migrants are “pushed” by their home communities and likewise “pulled” by job prospects to host communities (Jenkins, 1977; Todaro, 1969). This model presumes that migrants make rational choices in seeking the highest income, for example, and are driven by such cost–benefit decisions. We see push/pull explanations for students in higher education, suggesting students draw upon individual rational choices to inform their outcomes (Breen & Goldthorpe, 1997; Gambetta, 1987). According to this theory, students make choices about their education based on perceptions of the utility of the degree, the risk of failure, and the motivation to avoid downward mobility relative to their parents' socioeconomic status (Gabay-Egozi, Shavit, & Yaish, 2009). A critique of push/pull models is that they fail to capture the range of factors that previously existed and impact students' successes or failures (i.e., access to higher education, economic status of region, industry employment). A second approach, attempting to address limitations of the push/pull model, suggests that a historical/structural lens is needed to understand migratory flows; that is, migration patterns emerge from a social structure and historical context that facilitates or constrains movement of people across space (Portes & Bach, 1985; Portes & Walton, 1981). This lens can also be applied to engineering education to explore how social forces produce variation. The military history of engineering, for example, continues to influence cultural notions of “rigor” (Riley, 2017; Slaton, 2010). Likewise, structurally, land grants influence curriculum, accrediting bodies influence standards and policy adoption, and funding affects programming. A third approach expands the scope of analysis to consider migrants' social networks, suggesting that social capital is the mechanism for understanding migratory flows (Chavez, 1988, 1990; Choldin, 1973; Massey, 1987; Walker & Hannan, 1989). Social capital refers to the interpersonal connections forged among migrants who share a common origin community, their friends and kin, and nonmigrants in destination areas. Applied to engineering education, we can consider how students' academic trajectories are activated when knowledge is exchanged and relationships are fostered with other students, academic advisors, campus leaders, and faculty (Camacho & Lord, 2013; Chesler & Chesler, 2002; Martin, Miller, & Simmons, 2014; Newman, 2011; Pawley & Phillips, 2014; Seymour & De Welde, 2015). Large, robust datasets allow for deeper exploration of variations in student experiences. Complemented with qualitative data, we can probe with increased specificity how students navigate contact zones within the ecosystem. For example, a multiinstitution study shows the impact of engineering students' first contact with the discipline and the different outcomes that follow from engineering programs where students matriculate directly into a discipline compared to programs in which students choose a major after a period in which they are identified as being engineering majors but have not yet developed a formal affiliation with a particular discipline (Orr et al., 2012). A deeper exploration of the same data finds that a common introduction to engineering course accounts for some of the difference in those outcomes (Orr, Brawner, Ohland, & Layton, 2013). In addition, some progress in engineering education has been made at deriving social network metrics from institutional data (Huerta-Manzanilla, Ohland, & Long, 2013). An examination of student migratory flows allows for an understanding of their experiences within an ecosystem, deepening our understanding of how race/ethnicity and sex intersect with the climate of an academic discipline, thus addressing some of the limitations of the pipeline and pathways models. The pipeline model places narrow emphasis on individual students and their choices as the locus of control with little regard for the dynamism of the pipeline itself. While the pathways model allows for more avenues for student onboarding, the possible paths appear static with minimal evidence of their influences on student directions. In addition, pathways metrics do not allow for critical analyses of how particular disciplines seem to be more welcoming to some students than others. Here we adopt a perspective that recognizes the interconnectedness identified in the ecosystem metaphor described by Cheville (2017), recognizing the hidden domain of action applied by Vanasupa and Schlemer (2016). Our analysis elucidates how students move around in the ecosystem of engineering education. By considering their intersectional identities of race/ethnicity and sex, and their engineering discipline destinations, we can identify the majors that attract or repel particular student groups, where they stick and when they leave. The ecosystem metrics we offer below reject the illusion of stasis that suggests student success is unidirectional. While a large percentage of students follow a normative academic journey, additional metrics are needed to provide a more accurate and robust analysis of the range of student experiences within the ecosystem. Previous research studies have provided evidence that engineering disciplinary cultures differ (Godfrey, 2007; Knight et al., 2012; Litzler, 2010). An ecosystem approach allows us to bring data to bear upon some of these differences. We measure what has not been measured before, embedding in an ecosystem an intersectional lens to examine variation by race/ethnicity and sex. 2.4 | Earlier research on disciplinary outcomes Due to limitations with datasets, most studies of student persistence aggregate all engineering disciplines (Hill, Corbett, & St. Rose, 2010; Ohland et al., 2008; Seymour & Hewitt, 1997). For example, Ohland et al. (2011) reviewed retention in LORD ET AL. 37 engineering, focusing on studies that disaggregate by race/ethnicity and/or gender, finding that most studies of retention are single-institution and few disaggregate by both demographics. Ohland et al. (2011) disaggregated by race/ethnicity and gender, showing that success for students in engineering varies by race/ethnicity and institution. Other examples of disaggregated data include that from Humphreys and Freeland (1992), who conducted a small single-institution study, providing data for several engineering disciplines by race/ethnicity and sex; Stine's (2010) single-institution study that showed differences in outcomes for women by engineering discipline; and a series of studies that considered the demographics and outcomes of students disaggregated by race/ethnicity and gender in engineering disciplines (see e.g., Lord, Layton, & Ohland, 2015; Ohland, Lord, & Layton, 2015; Pilotte, Ohland, Lord, Layton, & Orr, 2017). Only limited research examines migrators in engineering (Schimpf, Ricco, & Ohland, 2013; Walden & Foor, 2008) or disciplines that appear to be outliers because of their high percentage of women students (Brawner et al., 2012; Brawner, Lord, et al., 2015; Foor & Walden, 2009). However, more research with an intersectional approach considering race/ethnicity and sex is emerging in engineering education (Camacho & Lord, 2013; Martin, Simmons, & Yu, 2013; Perna et al., 2009) including research on a single mixed-race female engineering student from a socioeconomically disadvantaged background (Foor, Walden, & Trytten, 2007) and on a single marginalized female Asian American engineering student (Secules, Gupta, Elby, & Tanu, 2018). Such qualitative research has the capacity to illuminate student variation with richness and nuance, both of which large dataset analytics typically fail to do. Our work attempts to incorporate the complexity of individual student pathways in large-scale longitudinal research. 3 | METHODS 3.1 | The engineering majors who are the focus of this study and why We limit our study to a small number of specific engineering majors so that sufficient detail can be provided within the scope of this work. The diversity of engineering programs at U.S. institutions accredited by the Engineering Accreditation Commission of ABET presents a challenge in identifying selection criteria. Because disciplinary communities have an identity that transcends individual institutions through their professional societies and accreditation requirements, it makes sense to study the majors offered at the most institutions. Alternatively, to most effectively represent the diverse experiences of U.S. engineering students, it is appropriate to focus on the majors with the largest number of students. We elected to pursue a combination of these two approaches. The five majors with the largest number of accredited programs (ABET, 2016) are mechanical engineering (321), electrical-electronics-computer-telecommunications engineering (584), civil engineering (267), chemical engineering (173), and industrial/systems engineering (118). Computer engineering (248 programs) has a considerably lower enrollment than any of these majors (Yoder, 2015) and notably different outcomes from electrical engineering (Lord, Layton, & Ohland, 2015); thus, these programs were excluded from this study. We subsequently refer to these five remaining engineering majors as mechanical (ME), electrical (EE), civil (CE), chemical (ChE), and industrial/systems (ISE). From an enrollment perspective, data from the American Society for Engineering Education (ASEE) Engineering Data Management System show that those five majors accounted for 70% of the engineering graduates in the United States in 2013 (Yoder, 2015) and 75% of the engineering graduates in the dataset used in this work. 3.2 | Dataset details: Multiple-Institution Database for Investigating Engineering Longitudinal Development We use the Multiple-Institution Database for Investigating Engineering Longitudinal Development (MIDFIELD) which comprises whole population data of degree-seeking students at 11 institutions, including students of all disciplines, transfer students, part-time students, and students who first enroll at any time of year (see Ohland & Long, 2016). When this study was initiated, MIDFIELD included longitudinal data for more than one million undergraduate students entering Fall 1987 or later. Although more recent data are available in MIDFIELD, the most recent data used in this study are from 2011. The specific dataset used in this study was frozen in 2011 to permit a series of single-discipline studies (Brawner et al., 2012; Brawner, Lord, et al., 2015; Lord et al., 2011; Lord, Layton, & Ohland, 2015; Lord, Ohland, & Layton, 2015; Ohland et al., 2015; Orr, Lord, Layton, & Ohland, 2014; Orr, Ramirez, Lord, Layton, & Ohland, 2015; Pilotte et al., 2017). Thus, using a consistent dataset makes it possible to consider those studies in relation to this multidisciplinary exploration. This dataset describes the experience of 218,900 students who ever declared engineering as a major. MIDFIELD institutions include 7 of the 50 largest U.S. engineering programs in terms of engineering bachelor's degrees awarded, resulting in a population that includes 10% of all engineering graduates of U.S. engineering programs. MIDFIELD includes 22% female engineering students, which aligns with national averages of 20–25% from 1999 to 2013 (Yoder, 2015). African American students are 38 LORD ET AL. significantly overrepresented in the MIDFIELD dataset; partner schools graduate 15% of all U.S. African American engineering B.S. degree recipients each year because the MIDFIELD participants include six of the top 20 producers of African American engineering graduates, including two Historically Black Colleges and Universities (HBCUs). The percentage of Hispanic students is not representative of other U.S. programs. Three percent of MIDFIELD engineering B.S. degrees are awarded to Hispanics in contrast to 9% in the United States. All other ethnic populations are representative of a national sample (Yoder, 2015). While the current MIDFIELD partners graduate a large number of engineering students, predicting the behavior of the engineering education system based on a 10% sampling rate suggests that it would be useful to establish the representativeness of MIDFIELD. There is no national dataset that permits a complete comparison. We studied a subset of students who self-identified their race/ethnicity using the category choices available to them at their institution and identifying those choices most similar to Asian, Black, Hispanic, or White. The specific racial/ethnic category choices provided for self-identification at MIDFIELD institutions are available in Lord et al. (2009). International students are excluded because institutions do not typically record their race/ethnicity information, and there was no option for students to select more than one racial/ethnic classification. Students who identified as “Other” or “Unknown” are excluded because these categories are hopelessly aggregated and even include “Missing” at several institutions. Selecting only Asian, Black, Hispanic, and White students who ever enrolled in one of the majors studied and who have enough data in MIDFIELD to compute a 6-year graduation rate, the number of students in this study was 81,621. 3.3 | MIDFIELD data analysis procedures While the complete MIDFIELD dataset is large and growing, frequently only a subset of it is used for a particular study. The data for this study were the same dataset used in a large number of other published studies that included only students ever enrolled in engineering and only data elements that have one value per student (Brawner et al., 2012; Brawner, Lord, et al., 2015; Lord et al., 2011; Lord, Layton, & Ohland, 2015; Lord, Ohland, & Layton, 2015; Orr et al., 2014; Orr et al., 2015; Ohland et al., 2015; Pilotte et al., 2017). That is, term-by-term data such as term GPA, courses taken, and other fields were omitted. By including dichotomous variables indicating whether a student was ever enrolled in a particular discipline, we retained information about all the disciplines a student had contact with while reducing the size and complexity of the dataset. Once a particular population has been selected for study and an analytical approach has been identified, analysis is conducted using the open-source statistical application, R (R Core Team, 2018). Data exploration continues visually with the help of the large library of display options in R. 3.4 | The definition and analysis of the “starters” population In undergraduate engineering programs, we combined two “starter” populations: those who matriculated directly into an engineering major and those who matriculated into a first-year engineering (FYE) program. While FYE students are definitively enrolled in engineering, they do not have a disciplinary identity at matriculation. Students who enter through other “undecided” pathways were similarly classified according to their first disciplinary affiliation. (See Box 1 for a detailed description of this disciplinary affiliation and definition of a student's major at “start.”) Thus, the “starters” population is more inclusive of students who enter through various pathways. This study also included transfer students who at some point enrolled in one of the majors studied. Transfer students were also classified based on their first specific disciplinary affiliation as described in Box 1. To calculate their 6-year graduation rates, transfer students were assigned to an enrolled semester using each institution's definition and assigned a corresponding enrolled time. For example, a transfer student who entered a MIDFIELD institution with enough credits to be in the fifth semester of ME in Fall 2010 was assigned an enrolled semester of “5” for Fall 2010 and a graduation time of eight semesters if graduating in Spring 2012. In regard to “migration,” the transition from a first-year engineering program is an expected part of the program and, thus, was not counted as a change of major unless the student left engineering altogether. The number of students included in this study disaggregated by starting major is available in Table A1 in the Appendix. In the next sections, we offer an overview and examples of the methods and results associated with pipeline, pathways, and ecosystem approaches. 4 | PIPE L IN E M E T HOD S AND RE S U L T S 4.1 | Pipeline metric: Graduation rate Graduation rate was calculated using a 6-year threshold. This metric is used because it is commonly understood even though it has been shown that programs can achieve the same 6-year graduation rate through widely varying student experiences LORD ET AL. 39 BOX 1 Definitions for MIDFIELD variables used in metrics for this study • FirstMajor: The specific major in which a student is enrolled at matriculation. In addition to degree-granting programs, this includes temporary majors such as first-year engineering (FYE) and undecided. • MajorAfterFYE: The first specific major in which a student enrolls after having matriculated in an FYE program. • MajorAfterUND: The first specific major in which a student enrolls after having matriculated as undecided. If a student matriculates as undecided and then switches into an FYE program, the first specific major in which a student enrolls after leaving the FYE program is used. • Start: A student's first specific disciplinary affiliation, whether entering as a first-time-in-college student or a transfer student, classified as follows.  FirstMajor, MajorAfterFYE, or MajorAfterUND, if it is one of the majors studied (chemical, civil, electrical, industrial, or mechanical)  OtherEng if FirstMajor, MajorAfterFYE, or MajorAfterUND is a specific engineering major other than the five majors studied. This category also includes a small number of students (392) who move through multiple nondisciplinary classifications (from FYE to UND, for example) before enrolling in one of the five majors studied.  STM: Science, technology, or math.  NonSTEM: Any other major. • Graduation major  Graduation major uses the same major groupings as starting major except that students cannot graduate in FYE or undecided. “Unknown” is used for students who had not graduated in any major by their sixth academic year. This would include students who have dropped out of higher education, those who have transferred to another institution, and those who have taken leave for one or more semesters and not returned during a term included in MIDFIELD. (Ohland et al., 2011). While IPEDS (2016) computes 6-year graduation rate only for first-time, full-time fall cohorts, the definition of the starter population used in this work allows a more inclusive definition as well as a more accurate classification of students entering an FYE program. Retention is then the percentage of starters in a discipline who finish in the same discipline within 6 years, where the starter population is disaggregated by race/ethnicity and sex. For a specific major, race/ethnicity, and sex, this was calculated in this study by: GradRate ðBlack, Female, CEÞ =  Black females who start in CE and graduate in CE within 6 years Black females who start in CE  ð1Þ The graduation rate of Black women in CE is, thus, the number of Black women starting in CE and graduating in CE within 6 years as a percentage of the number who originally started in CE (including FYE students imputed to have started there). However, the students who start in other majors and graduated in CE are not included in this calculation. Figure 3 shows the numbers involved in a graduation rate calculation. 4.2 | Pipeline results Graduation rate: Of those who start in a discipline, who graduates? Graduation rates of starters in the five majors studied here are shown in Figure 4, grouped by race/ethnicity and sex. As is conventional for multiway graphs (Cleveland, 1993), the rows are ordered from bottom to top by increasing median graduation rate of the student group; the panels are ordered from left to right and from bottom to top in order of increasing median graduation rate of the major. The panel median is indicated by a vertical dashed line. Thus, EE has the lowest median graduation rate and ISE the highest. In each panel, the rows are ordered by the data, and points that counter a trend stand out visually. For example, the graduation rate of Hispanic women and men in ISE is higher than their row order would suggest. (The rows are ordered from bottom to top by increasing median graduation rate of the student group. Note this is not the median of the discipline.) Other visual standouts are Black women in ME (higher than expected based on their position in all disciplines) and in CE, Black women and men LORD ET AL. 40 FIGURE 3 An example of how graduation rate is calculated for a student group in a given major (software courtesy of Chen, 2018) [Color figure can be viewed at wileyonlinelibrary.com] (lower), and Asian women and men (lower). Comparing the shape of the data across panels suggests that the relative rates in EE, ChE, and ME graduation rates are similar, while CE has not shown success in retaining and graduating its Black starters and ISE is adept at retaining and graduating its Hispanic starters. These examples suggest that engineering education research can continue to critically examine differentiation by race/ ethnic group. Slaton (2010) exemplifies such research, providing analysis that highlights evidence of the structural racism that emerged historically. While Slaton points out that institutions vary in their ability to serve students, our data suggest that disciplines also vary in their ability to promote student success. In Figure 4, the rows are ordered by declining graduation rate as Asian, White, Hispanic, and Black. In part, this racial/ethnic ordering is specific to this metric; as we show later, ecosystem metrics yield results that break this pattern to some extent. This pipeline metric, thus, appears to reify stereotypes. In contrast, the results in Figure 4 counter sex stereotypes in that women starters have a higher median graduation rate than men in most disciplines. This result is consistent with other research that shows that women persist at higher rates than men during undergraduate years (Consentino de Cohen & Deterding, 2009; Lord et al., 2009; Xie & Shauman, 2005). As this analysis suggests, pipeline metrics can represent some of the complexity of the engineering education system when they are applied using an intersectional lens. A more complete picture of the complexity of the system emerges as we apply more advanced metaphors and metrics. FIGURE 4 Pipeline model results: Graduation rates of starters in a discipline grouped by race/ethnicity and sex. Sex is indicated in the row labels and by marker type. Population sizes are found in the Appendix (software courtesy of Wickham, 2017) [Color figure can be viewed at wileyonlinelibrary.com] LORD ET AL. 41 5 | PATHWAYS METHODS AND RESULTS 5.1 | Pathways metric: Sankey diagrams A Sankey diagram is a graphical method of visualizing a link-node network (Sankey, 1896; Schmidt, 2008). Originally developed to illustrate mass or energy flows, the widths of the links between nodes indicate the relative magnitudes of the pathways. We used Sankey diagrams here to illustrate the relative numbers of students on pathways between their starting majors and their 6-year destinations. For example, in Figure 5 we consider all women students ever enrolled in EE. On the horizontal scale are two nodes denoting the students' starting majors and their 6-year destination majors, while the vertical scale indicates numbers of students in thousands. The width of a connecting path between nodes is proportional to the number of students on the path. Values rounded to two significant digits are shown at selected nodes. In this example, 3,222 women students ever enrolled in EE, of whom 2,549 started in EE. At Year 6, we find 1,541 graduates in EE, 1,192 of whom started in EE. One takeaway from this graph is that 53% of women EE starters leave the major: 21% (547/2,549) graduate in another major and 32% (810/2,549) leave the dataset for an unknown destination. A second takeaway is that 23% (349/1,541) of the women graduates in EE started in other majors. A strength of a Sankey diagram is that relative percentages of students on many pathways are visually inferred (if only approximately), while a weakness is that we can legibly label only selected values as enumerating every value requires a data table. We are also limited in the number of discrete crossing pathways (here, 12 are shown) that are visually distinctive, especially when limited to gray scale images. 5.2 | Pathways results Sankey diagrams: What is the relative flow of students to, from, and through a discipline? The pathways metaphor provides greater accuracy in capturing the multiple entry and exit points that students encounter as one of its important advantages is that it includes students graduating in one discipline who started in another. Those students are ignored in the graduation rate metric based on the pipeline metaphor. In addition, the Sankey diagram shows the relative proportion of populations along their pathway. To illustrate, in Figure 6 we compare the pathways between starting majors and 6-year destinations for all students ever enrolled in EE and ISE, grouped by major and sex, yielding four panels (or subplots). The height of each panel is identical and represents the total enrolled for that group. The vertical scales, therefore, are different for each panel. Values rounded to two significant digits are shown at selected nodes. The arrangement of the panels facilitates comparing the pathways of one sex, for example, comparing women in EE and ISE, or comparing pathways in one major, for example, men and women in ISE. One story that emerges visually is told by the darkest bands, indicating students graduating in the major. For men and women, the percentage of students graduating in ISE who start in some other major is much higher than in EE. Thus, the starting nodes for other engineering and nonengineering are noticeably larger percentages of the totals in ISE than in EE, indicating that ISE tends to attract students. In a complementary fashion, if we consider the lighter bands in Figure 6, the number of students who are ever in the major but leave for other destinations is much higher among students in EE than in ISE. Thus, 3 Number of students (x1000) 3 EE N = 1.5 2 Other−ENG Non−ENG 1 1 Unknown N = 1.0 Other−ENG FIGURE 5 Pathways model results: The components of a Sankey diagram for all women students ever enrolled in EE (software courtesy of Brunson, 2018) [Color figure can be viewed at wileyonlinelibrary.com] 2 EE N = 2.5 0 Non−ENG 0 Starting Major Year 6 Destination Women ever enrolled in Electrical Engineering LORD ET AL. 42 (a) 3 Number of students (x1000) 3 EE N = 1.5 2 2 EE N = 2.5 Other−ENG Non−ENG 1 1 Unknown N = 1.0 Other−ENG 0 Non−ENG 0 Starting Major Year 6 Destination Women ever enrolled in Electrical Engineering 20 Number of students (x1000) 20 15 10 EE N = 9.3 EE N = 15.7 15 10 Other−ENG Non−ENG 5 5 Unknown N = 6.4 Other−ENG 0 Non−ENG 0 Starting Major Year 6 Destination Men ever enrolled in Electrical Engineering FIGURE 6 Pathways model results: Pathways between starting majors and 6-year destinations for students ever enrolled in (a) EE (left) and (b) ISE (right), grouped by major and sex, with numbers of students in the thousands [Color figure can be viewed at wileyonlinelibrary.com] EE tends to repel students. The overall sense of the data displayed is that in EE, a high percentage of students ever enrolled leave the major to graduate in another major or leave for an unknown destination, with a small percentage being replaced by migrators who start in other majors. Overall, approximately 40% fewer graduate than start. In contrast, the overall sense of ISE is that the major attracts more students than it loses, yielding approximately 13% more graduates than starters. A weakness of the Sankey diagram for this type of research is the difficulty of grouping by race in addition to sex and major. Figure 6 shows 12 pathways in each panel, one for each combination of three starting points and four destinations per major. Including four race/ethnicity groups would create 48 pathways in each panel or, alternatively, 12 pathways as shown but with a total of 16 panels, one for each race-sex-major group. Both approaches increase the difficulty of making comparisons and extracting meaning visually. Nonetheless, compared to the pipeline metaphor, the pathways metaphor illustrated by the Sankey diagrams contributes to a more robust description of student trajectories. However, a deeper analysis merits a new metaphor, one considering engineering education as an ecosystem. 6 | ECOSYSTEM METHODS AND RESULTS 6.1 | Ecosystem metric: Stickiness The stickiness of a discipline is the percentage of students who ever enroll in a specific engineering discipline and who subsequently graduate in that same discipline (Ohland, Orr, Layton, Lord, & Long, 2012). This is referred to as the “major stickiness” of a discipline in contrast to the “engineering stickiness” and the “institutional stickiness.” Stickiness can be used to describe outcomes of interest to multiple stakeholders at multiple levels (discipline, college, and institution), speaking to different audiences who may define student success in different ways. For example, a department head might define success as graduating in the major (major LORD ET AL. 43 Number of students (x1000) (b) 3 3 Industrial N = 2.2 Industrial N = 2.5 2 2 Other−ENG 1 Other−ENG Non−ENG Non−ENG Unknown N = 0.8 0 1 0 Starting Major Year 6 Destination Women ever enrolled in Industrial Engineering 6 Number of students (x1000) 6 Industrial N = 4.0 Industrial N = 4.5 4 4 Other−ENG 2 Non−ENG Other−ENG Unknown N = 1.8 Non−ENG 0 FIGURE 6 (Continued) [Color figure can be viewed at wileyonlinelibrary.com] 2 0 Starting Major Year 6 Destination Men ever enrolled in Industrial Engineering stickiness). A dean might define success as graduating in engineering (engineering stickiness is the percentage of students who ever enroll in a specific engineering discipline that graduate in any engineering discipline). A provost might define success as graduating from the university (university stickiness is the percentage of students who ever enroll in a specific engineering discipline that graduate from the institution in any discipline). These definitions of success for students and administrators may not be in alignment. For example, while a dean might consider a student leaving engineering to be a negative outcome, the student might consider it a positive outcome. Stickiness describes the interconnectedness of the ecosystem by accounting for how each of these five disciplines affects the outcomes of students with various entry points, pathways, and destinations. An example of the calculation of each form of stickiness is given in Figure 7. The number of engineering graduates includes those graduating in other engineering disciplines as well as the engineering discipline of interest, meaning the engineering stickiness must be greater than or equal to the major stickiness. Similarly, the number of institutional graduates incorporates those graduating in all engineering disciplines including the engineering discipline of interest, so the institutional stickiness must be greater than or equal to the engineering stickiness. 6.2 | Stickiness results Of those students who ever enroll in a discipline, what percentage graduates? Figure 8 illustrates disciplinary stickiness disaggregated by race/ethnicity and sex. The left column of panels shows stickiness by discipline, while the right shows the associated increase in stickiness for students ever in that discipline who graduated in any other major. For example, considering all Asian female students ever enrolled in ISE, the ISE “Discipline stickiness” panel shows approximately 70% (70.1%) of these women graduate in ISE. The adjacent “In any other major” panel shows that an additional 13% leave ISE but successfully graduate in other majors in 6 years. LORD ET AL. 44 FIGURE 7 An example of how stickiness is calculated for a student group in a given major [Color figure can be viewed at wileyonlinelibrary.com] FIGURE 8 Ecosystem model results: Stickiness of a discipline (left column) and the associated increase in stickiness (right column) for students ever in that discipline who graduate in any other major [Color figure can be viewed at wileyonlinelibrary.com] LORD ET AL. 45 The panels from top to bottom are in order of decreasing median discipline stickiness, shown as a vertical dashed line. Thus, ISE has the highest stickiness and EE the lowest. For all panels, the rows from top to bottom are in order of decreasing median stickiness for that group across all disciplines; thus, Asian women and men have a higher median stickiness than other groups. In addition, stickiness shows patterns of retention by starting discipline and by graduation in any other major. As seen in Figure 8, stickiness varies by race/ethnicity and sex, and there is intracultural variation among race/ethnic groups by major with some groups displaying less stickiness variation than others. Women generally have higher stickiness than men, and stickiness varies more by race/ethnicity than sex. The general trend here is that as engineering disciplinary stickiness decreases, the “In any other major” stickiness increases. Some students leaving an engineering major continue at the institution, just not in their initial major. For each population group, approximately half of the change in stickiness from major to university can be attributed to students graduating in another engineering major and half to students graduating outside of engineering. The right panels of Figure 8 show the increase in stickiness if we consider university stickiness (graduation in any major) as the outcome of interest, highlighting disciplines and populations where outcomes follow a different pattern from the disciplinary stickiness. By definition, university stickiness must be larger than engineering discipline stickiness. Similar patterns were observed for the change in engineering stickiness compared to major stickiness as those shown in Figure 8 for university stickiness compared to major stickiness. There is little variation, approximately 5%, by race/ethnicity and sex for the change in university stickiness compared to major stickiness in CE, ISE, and ME; the patterns for graduating from the university are similar to those for graduating in the discipline. However, EE and ChE show more variation. Students in EE and ChE appear to be more successful in graduating from the university than in these fields, suggesting that there may be issues with the disciplines rather than the students' capabilities. This difference is particularly true for White female students who have the highest increases for university stickiness compared to major stickiness in EE and ChE (approximately 25%). 6.3 | Ecosystem metric: Migration yield Examining students who migrate to or among engineering disciplines is of interest to students, advisors, and others because each additional major in a student's journey can increase time to graduation by a semester (Ricco, Ngambeki, Long, Ohland, & Evangelou, 2010). In addition, disciplines losing migrators sustain an enrollment burden that does not lead to degree production. While programs acknowledged as service departments (such as FYE) expect this sort of enrollment burden, other disciplinary departments may struggle to find the resources to support transient students. Disciplines attracting migrators serve an important role for engineering colleges by providing a home for those who might otherwise leave engineering or never enter it. In designing a metric to study migration, we were inspired by Hake's (1998) introduction of normalized gain “as a rough measure of the effectiveness of a course in promoting conceptual understanding” (p. 68). The normalized gain is defined by:   Post − Pre Normalized gain = g = ð2Þ 100 − Pre In Hake's case, Pre and Post are intended to be equivalent learning measures, specifically scores on the Force Concept Inventory. The normalized gain is, thus, the amount a student's score increases (Post-Pre) as a percentage of the amount that student's score could possibly increase (100-Pre). The advantage of this approach is that it does not diminish the potential benefits of a course for students who do well on the pretest. In our work, we are interested in the “migration yield” (Lord, Ohland, Layton, & Camacho, 2018), the normalized gain of migrating students, or the ratio of the number of migrators a discipline attracts and graduates within 6 years (the gain) to the number of migrating students it could possibly attract. Thus, the numerator is the number of students graduating in a discipline who did not start there; these migrators might be drawn from the other four engineering disciplines studied in detail, from any other engineering discipline, or from nonengineering disciplines. If we measured the gain of migrators without normalization, the metric would be influenced by attrition (disciplines losing more students cannot regain them because that would not be migration). Doing so would put larger disciplines at a disadvantage even if their 6-year graduation rates were high. Figure 9 shows the populations required to compute migration yield. The starting population of a discipline is always excluded from the migrator population because a discipline cannot attract those students as migrators. In addition, students who temporarily explore other disciplines but return to their original one are not considered migrators. Those students, who are similar in some ways to “swirlers” who cycle attendance among multiple institutions (de los Santos Jr & Wright, 1990), are not specifically studied here. LORD ET AL. 46 FIGURE 9 An example of how migration yield is computed for a student group and a given major [Color figure can be viewed at wileyonlinelibrary.com] Compared to other metrics in this study, calculation of migration yield must be restricted to the nine institutions that offered all five majors studied. Two MIDFIELD partners did not offer ISE during the period of the study, so they are not included in the study of migration. At those institutions, ISE students were not available to migrate to other disciplines and migrating students did not have the option of choosing ISE, so the outcomes of migration would necessarily be different at those institutions, and, thus, their inclusion would positively bias the migration attraction and presumably the yield of the other majors examined and negatively bias that of ISE. Migration yield is another metric that applies only to the ecosystem model since it acknowledges the interconnectedness of disciplines within the larger system. 6.4 | Migration yield results How well does each discipline attract and graduate students who change disciplines within or to engineering? The data markers in Figure 10 represent the migration yield in a discipline for each race/ethnicity/sex group. Yield is read along the contour lines; markers lying on the same contour line have the same migration yield. A line of constant migration yield is curved because by definition it is the product of the quantities along the horizontal axis (proportion of migrators attracted) and the vertical axis (proportion of those attracted who graduate in the discipline). The panels are in order of increasing median migration yield (shown with a dotted curve) from left to right and from bottom to top; thus, ChE has the lowest median migration yield and ISE, the highest. There is significant variation in migration yield by discipline and by subpopulation within discipline. Each panel has a different overall distribution of the eight dots representing the eight populations studied. The lowest migration yield is 3%, the percentage of Black male migrators attracted and graduated by ChE. The largest successes in terms of attracting and graduating migrators are women in ISE and Asian and Black men in EE, all with a migration yield greater than 20%. Within a discipline, the subpopulation migration yields vary from 10% in CE to 24% in EE. Values on the same contour line accomplish the same migration yield but by different means. For example, in ISE, Hispanic, White, and Black women are all on the 25% contour. This migration yield is driven by a high rate of attracting Hispanic women, but a lower rate of graduating that population. The opposite is true for Black and White women where fewer are attracted but a higher percentage of those who are, graduate. Populations that fall on the same vertical line show the same percentage of migrators attracted but different graduation rates. For example, consider ChE, where the percentage of migrators attracted is low and fairly consistent (though different for men and women), whereas the fraction of those attracted who graduate has significant variability by race/ethnicity. Another example is White and Hispanic women in ME where about the same percentage of migrators are attracted to ME but more than twice the number of White women migrators graduate in ME compared to Hispanic women. Populations that fall on the same horizontal line show the same graduation rate of migrators but different rates of attraction. For example, the graduation rates of all groups except Hispanic women are similar in ME. However, the percentage of migrators attracted varies by sex, with men being attracted at higher rates than women to ME. A particularly interesting feature seen in Figure 10 is the sex-based grouping found in most majors. In ISE and ChE, the migration yield of women of all races/ethnicities is higher than that of all men. In ME and EE, the opposite is true with the LORD ET AL. 47 F I G U R E 1 0 Ecosystem model results: Contour plot of migration yield as the product of the fraction of migrators attracted to a discipline (horizontal scale) and the fraction of those students graduating in the discipline (vertical scale). The median yield of each discipline is represented by a dashed curve [Color figure can be viewed at wileyonlinelibrary.com] exception of Asian female students, who exhibit a slightly higher migration yield than White men in EE. In CE, migration yield does not exhibit a sex-based effect. This phenomenon seems to be related to enrollment trends: the disciplines that enroll a higher percentage of women (ChE and ISE) (ASEE, 2016) have a higher migration yield, whereas the disciplines enrolling a lower percentage of women (ME and EE) have a lower migration yield of women. In contrast, the data markers in CE cluster by race/ethnicity, not by sex, with the points representing females and males being within 1.6 percentage points within each race/ethnic group. This finding identifies a clear opportunity for future research exploring the conditions that produce segregated outcomes by race/ethnicity in CE. LORD ET AL. 48 6.5 | Ecosystem metric: Graduation rate of migrators Extending our interest in migrators, we wondered how the graduation rate of migrators might be related to the graduation rate of starters. Thus, this metric does not consider a discipline's ability to attract migrators, but only the graduation rate of those who do migrate. This rate is calculated for a particular race/ethnicity-sex group as the number of students who graduate in 6 years in a particular major who did not start in that major divided by the number of students who migrated to that major: Graduation rate of migratorsrace=ethn, sex, major  ðGraduated in 6 years this major − Started this majorÞ = ðEver enrolled this major − Started this majorÞ  ð3Þ race=ethn, sex, major 6.6 | Graduation rate of migrators results To what extent are the graduation rates of migrators similar to those of starters in specific engineering disciplines? To further explore the complexity of the engineering education ecosystem, Figure 11 compares the graduation rates of migrators and starters disaggregated by discipline, race/ethnicity, and sex. Panels represent disciplines, with the diagonal line representing equal graduation rates (parity line) for migrators and starters. The panels in Figure 11 are ordered from left to right and bottom to top by the median graduation rate for both migrators and starters of all the populations in the panel. Thus, ChE has the lowest median graduation rate, and ISE has the highest. In Figure 11, most data markers are above the parity line, revealing that the stories for migrators are not the same as those for starters. This difference underscores the importance of using a system perspective and metrics which include migrators rather than a pipeline perspective limited to starters. Migrators typically have higher graduation rates than the starting population, highlighting their resilience and success, both of which further support the importance of including them as a population of interest and emphasize the positive nature of identity exploration (San Antonio, 2016)—that “not all those who wander are lost” (Tolkien, 1954, p. 167). For Asian and White women and men, migrators have higher graduation rates in all disciplines. In a few cases, a population is below the line because the graduation rate of starters is exceptional, a situation seen in ISE for Hispanic men and women, where their starters' high graduation rates (above 65%) set a high bar for the migrators. While the Hispanic men come close, the Hispanic women have migrator graduation rates of approximately 70%, still high compared to other populations and disciplines. The situation for Black women and men in ChE seems different, where the migrator graduation rate is nearly equal to the starter graduation rate of approximately 40%. For CE and EE, the graduation rates of the migrators appear to be strongly related to those of the starters, perhaps suggesting that starters and migrators share similar experiences in these disciplines. In contrast, while ChE has a notable variation in the migrator graduation rates of the subpopulations, there is little variation in the starter graduation rate. Sex-based effects vary among the disciplines, but are particularly small in the White population, as seen in the proximity of the data markers labeled “W” in every panel. 7 | LIMITATIONS The limitations of this work are important to bear in mind. By considering race/ethnicity and sex, we adopted an intersectional lens, yet we recognize that students have more than these two intersecting categories. Socioeconomic status, first-generation college status, native language, and veteran status are certainly important, but have not been included here due to the lack of available data in MIDFIELD. Another limitation is the underrepresentation of Hispanics and the overrepresentation of Blacks in our population compared to the national data. We consider only students who self-identified as Asian, Black, Hispanic, and White, so the experiences and outcomes of Native American students, students who identify with more than one race, and those who did not report race are not represented. While extensive student data inform this work, we have no information on other important parts of the system—faculty and administrators as actors, institutional differences, and the effects of different policies. Although others have not noted a difference in the selectivity of the starter population in these disciplines (Brawner et al., 2012), academic differences among the disciplinary populations could explain some of these effects. LORD ET AL. 49 F I G U R E 1 1 Migrator graduation rates are generally higher than starter graduation rates. The line of parity is shown as a light line [Color figure can be viewed at wileyonlinelibrary.com] 8 | DISCUSSION AND CONCLUSIONS Within this ecosystem, the more common normative pathways exist alongside more complex behaviors. In this paper, we consider three metaphors and the metrics that they each inspire. We capture pipeline insights with graduation rate, pathways insights with Sankey diagrams, and insights that give us a glimpse of deeper ecosystem features using stickiness (retention by a department), migration yield (attraction of a department), and comparisons of graduation rates of migrators and starters. 50 LORD ET AL. 8.1 | Nuances of the engineering education ecosystem Our analyses demonstrated how new metrics, such as stickiness and migration yield, afford engineering education researchers deeper insight into how students navigate higher education. Capturing a more nuanced portrait of how students behave, these metrics contribute to a more robust ecosystem model that builds on the perspectives offered by the pipeline and pathways metaphors. Increasingly, as available data and analytic methods expand, a more profound view of student behaviors between and beyond engineering majors will inform strategies for preventing student attrition and promoting student success. Although approximately half of all students who matriculate into engineering education follow a linear path, more complex student behaviors also merit analysis. When an intersectional approach guides the research, as in this paper, we shine a light on how diverse majors in engineering education structurally attract and retain students in ways that vary by sex and race/ethnicity. We posit that within the ecosystem of engineering education, students have agency in navigating the ecosystem and their behaviors vary as a consequence of their interactions with particular engineering majors. An ecosystem framework opens the possibilities for future research to critically explore the contextual factors under which students eventually find their academic homes. The conditions that produce student behaviors raise questions for engineering education researchers: For example, who are the multiple actors that shape the student experience in engineering education? How do gatekeepers influence the directions students take? Considering the relations of power and tacit knowledge about hierarchies within engineering, when and how do ruling relations (Pawley, 2019; Pawley & Phillips, 2014) emerge among students that promote knowledge transmission about succeeding and avoiding failure (Camacho & Lord, 2013) in the ecosystem? What other aspects of the “hidden domain” (Vanasupa & Schlemer, 2016) within the ecosystem remain to be explored? To what extent is migration yield subject to the forces of social reproduction, and how does migration yield interact with the demographics of the starting population? In what ways do disciplinary cultures give rise to disciplinary differences in student success? At a more granular level, what other variables might predict the graduation rate of starters? Is the stickiness of a discipline influenced by some critical mass of a population? Intrinsic to an ecosystem metaphor is a quality of messiness that is lost in the cleaner pipeline and pathways models. Nonetheless, in an ecosystem, a more realistic model emerges in which we can visualize students exploring zones that emphasize mutualism, commensalism, and predation (cf. Cheville, 2017). 8.2 | Migrating students have success stories to share Our findings suggest migrating students have graduation rates that generally exceed those of students starting in these engineering disciplines. These students have experimented with various majors and are eventually granted “disciplinary citizenship.” This disciplinary citizenship, for example, allows a student to become an electrical engineer as distinct from being a computer engineer. Like theories of border-crossing migrants cited earlier, approaches that cast student journeys as individualistically driven fail to capture how those journeys intersect with structural forces. The ruling relations (Pawley, 2019; Pawley & Phillips, 2014) of engineering education help frame the story of the migrator experience including both individual agency and the effect of structural forces. The migrators' stories are the invisible narratives of resilience and persistence. Migrating students may, for example, enter and leave disciplines with long traditions of deeply rooted segregation or by contrast find a home in disciplines that have made strong commitments to fostering greater diversity. We can find these patterns and examine student agency by race/ethnicity and sex. Less visible from a macro perspective are the disciplinary patterns that sustain students or unwittingly abandon them. It is worth considering how disciplines bear a responsibility to support these students. Such an exploration might include a framework that further considers how students resemble migrants, or even refugees, within higher education. Do students conceptualize certain majors as safe-havens, as “sanctuary disciplines”? Who are the social agents that function to support and attract students, and what other networks help students find their way? How do students find meaning, motivation, and a shared identity within the engineering education ecosystem? How can the narratives of migrators help mitigate stereotype threat? 8.3 | Consideration of more effective metrics and data displays The pipeline metaphor and aggregated statistics omit the experiences of many students. More robust sources of data allow for metrics that celebrate the experiences of students who follow non-normative pathways. As institutions increasingly use big data and predictive analytics to intervene in the student experience, researchers and academic leaders will increasingly need to consider policies that promote retention and facilitate migration. As our data show, the journeys of migratory students in search of a home discipline typically end in success, a finding made visible only with disaggregated data. Aggregated student LORD ET AL. 51 data, by contrast, depict a story that glosses over the multifaceted experiences of any single population. Commonly used pipeline measurements encode the same rigidity inherent in the metaphor. Here we expose the complexity of student behaviors, providing examples of metrics that capture this deeper level. Like pipeline and pathways metaphors, the ecosystem of engineering education is also a social construction. It remains to be seen whether researchers and administrators continue to use a static pipeline model; we generously suggest this practice persists because of limitations with institutional databases and the simplicity of the pipeline model. More critically, Vanasupa and Schlemer (2016) suggest the absence of change results from engineering education's historical context, representing manifestation of how the system is replicating itself. One might deduce that a pipeline model emerges from assumptions of rational choice theory, while the ecosystem model acknowledges that there are institutional structures that affect migration, trajectories, experiences, and stories. We call upon the engineering education community to consider these new ways of thinking to develop a richer understanding of their own ecosystem and to explore these deeper issues as part of a reflexive process. For change to occur, there has to be an element of reflexivity, and the metrics we used here inform that deeper level of reflection. Similarly, in addition to promoting improved metrics, our work promotes the use of data displays designed to make meaningful comparisons using multivariate analyses. These displays seek to improve the reader's decoding accuracy by relying on the science of human perception (Layton, Lord, & Ohland, 2009). The data graphics used here are also effective in exploring results as we seek the best way to communicate stories emerging from our data. Our work offers engineering education researchers new displays with which to visualize, explore, and imagine stories in their own data and attempts to represent the engineering education system using models of greater complexity. For researchers interested in computing these metrics and creating similar data displays on their own, an R package with a stratified sample of MIDFIELD data, helper functions, and tutorials is available via the Comprehensive R Archive Network (Layton, Long, & Ohland, 2018). 8.4 | Final recommendations: Using an ecosystem perspective offers new insights Exploring student experiences through a lens that considers the institutional structures that undergird the ecosystem allows institutions to explore the ecosystem in nonlinear ways and as a result to better serve students who come into engineering through diverse entry points. FYE programs, for example, help students make informed choices about their majors, resulting in improvements in graduation rates (Orr et al., 2012). An ecosystem perspective helps institutions demonstrate the need for and capture the effect of specialized programs for historically underserved groups such as military veteran students in engineering (Brawner, Main, Mobley, Lord, & Camacho, 2015; Ford & Ford, 2017; Mobley, Camacho, Lord, Brawner, & Main, 2017; Napoli, Sciaky, Arya, & Balos, 2017). The emergence of innovative degree programs that allow engineering students some flexibility, embed interdisciplinary perspectives, and explicitly combine the social with the technical suggest that changes are underway. Examples include general engineering for developing change making engineers (Chen & Hoople, 2017; Roberts, Huang, Olson, Camacho, & Lord, 2015), Engineering Plus (Forbes, Bielefeldt, Sullivan, & Chaker, 2017), and the Computer Science Professionals Hatchery (Anderson, Xu, Jain, Winiecki, & Salzman, 2016). If the tendency to create such innovative programs propagates, it will enrich the ecosystem, creating niches for engineering students with more diverse perspectives. Many internal and external catalysts directly and indirectly influence student success. Engineering students do not navigate higher education in isolation; rather, many support networks sustain student persistence. Engineering education research can highlight, for example, the ecosystem's “tempered radicals,” those who serve as proponents of resistance to the status quo and creatively promote change (Meyerson, 2003), as well as “radicalized seniors” who wield influence as formal and informal leaders that foster change by speaking up about the needs of students and protect junior faculty who are invested in reform (Seymour & De Welde, 2015, p. 465). Externally, the U.S. National Science Foundation's program, “Revolutionizing Engineering and Computer Science Departments,” has funded 19 U.S. campuses to disrupt patterns in engineering education and transform the professionalization of future engineers, as well as broaden the capacity to attract more diverse students (Lord et al., 2017; Lord et al., 2018; Lord, Camacho, Kellam, & Williams, 2017). An ecosystem mindset allows researchers to capture and address how these agents of social change have an impact on seemingly static engineering disciplines. The engineering education system still bears witness to staggering segregation by sex and race/ ethnicity (despite the high numbers of women and rising numbers of underrepresented minorities attending college). As Riley (2017) suggests, we need to interrogate the rigidity of the system. Researchers have recently proposed doing so by building upon asset-based frameworks (Samuelson & Litzler, 2016; Wilson-Lopez, Mejia, Hasbún, & Kasun, 2016). Academic leaders in higher education have a responsibility to adapt new metrics and strategic plans that attract and retain increasingly more diverse students. 52 LORD ET AL. In this work, we open a shutter to the examination of student patterns within and through engineering disciplines. Our data indicate that engineering programs seeking to improve student success would do well to examine the intracultural variation among engineering majors, examine attrition by race/ethnicity and sex, and create targeted interventions by major. This study also found notable positive messages about migrating students. Based on our findings, academic advisors of students failing to thrive in one engineering major should encourage them to consider other engineering majors, and other engineering majors should welcome such migrating students. We challenge the idea that academic discipline is purely a student choice by suggesting that the ecosystem embeds, constrains, and promotes practices that operate in tandem with student agency. Opportunities for future research include exploration of nuanced details within the landscape of an ecosystem, including the roles of supportive networks and leaders that foster change and nurture asset development among students. In an ecosystem, stasis is unnatural; our metrics and mindsets will continue to evolve as new engineering education practices, knowledge, and participants expand. ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the National Science Foundation (NSF) under grants 1129383 and 1545667. We also thank the MIDFIELD institutions, and all those who contributed to developing and interpreting MIDFIELD, particularly Marisa Orr and Russell Long. Finally, we thank the anonymous reviewers and editors for their careful reading and helpful suggestions. R E F E REN CE S ABET. (2016). ABET accredited program search. Retrieved from http://main.abet.org/aps/Accreditedprogramsearch.aspx ABET Member Societies. (n.d.). Retrieved from http://www.abet.org/about-abet/member-societies/ Aldrich, P. R. (2015). The curriculum prerequisite network: Modeling the curriculum as a complex system. Biochemistry and Molecular Biology Education, 43(3), 168–180. https://doi.org/10.1002/bmb.20861 American Society for Engineering Education (ASEE). (2016). Degrees awarded and enrollment reports. Washington, DC: ASEE Engineering Data Management System. Retrieved from http://www.asee.org/datamining/reports/ Anderson, T., Xu, D., Jain, A., Winiecki, D., & Salzman, N. (2016). IUSE/PFE: RED: Computer Science Professionals Hatchery (CSP Hatchery) (NSF award 1623189). Retrieved from https://www.nsf.gov/awardsearch/showAward?AWD_ID=1623189 Astin, A. W. (1982). Minorities in American higher education. Recent trends, current prospects, and recommendations. San Francisco, CA: Jossey-Bass Inc. Astin, A. W., & Astin, H. S. (1992). Undergraduate science education: The impact of different college environments on the educational pipeline in the sciences (Final Report). Los Angeles, CA: Higher Institution Research Institute. Atman, C. J., Sheppard, S. D., Turns, J., Adams, R. S., Fleming, L. N., Stevens, R., . . . Lund, D. (2010). Enabling engineering student success: The final report for the Center for the Advancement of Engineering Education. San Rafael, CA: Morgan and Claypool. Bix, A. S. (2004). From “engineeresses” to “girl engineers” to “good engineers”: A history of women's U.S. engineering education. NWSA Journal, 16(1), 27–49. https://doi.org/10.1353/nwsa.2004.0028 Brawner, C. E., Camacho, M. M., Lord, S. M., Long, R. A., & Ohland, M. W. (2012). Women in Industrial Engineering: Stereotypes, persistence, and perspectives. Journal of Engineering Education, 101(2), 288–318. https://doi.org/10.1002/j.2168-9830.2012.tb00051.x Brawner, C. E., Lord, S. M., Layton, R. A., Ohland, M. W., & Long, R. A. (2015). Factors affecting women's persistence in chemical engineering. International Journal of Engineering Education, 31(6A), 1431–1447. Brawner, C. E., Main, J. B., Mobley, C., Lord, S. M., & Camacho, M. M. (2015). The institutional environment for student veterans in engineering. Proceedings of the 2015 Frontiers in Education Conference, El Paso, Texas. Retrieved from https://doi.org/ 10.1109/FIE.2015.7344318 Breen, R., & Goldthorpe, J. H. (1997). Explaining educational differentials: Towards a formal rational action theory. Rationality and Society, 9(3), 275–305. Brunson, J. C. (2018). ggalluvial: Alluvial diagrams in ggplot2 (R package version 0.6.0) [Computer software]. Retrieved from https://CRAN. R-project.org/package=ggalluvial Camacho, M. M., & Lord, S. M. (2013). The borderlands of education: Latinas in engineering. Lanham, MD: Lexington Books. Carlone, H., & Johnson, A. (2012). Unpacking ‘culture’ in cultural studies of science education: Cultural difference versus cultural production. Ethnography and Education, 7(2), 151–173. Chavez, L. R. (1988). Settlers and sojourners: The case of Mexicans in the United States. Human Organization, 47, 95–108. Chavez, L. R. (1990). Coresidence and resistance: Strategies of survival among undocumented Mexicans and Central Americans in the United States. Urban Anthropology, 19, 31–61. Chen, D. A., & Hoople, G. D. (2017). Contextualizing a new General Engineering curriculum in the Liberal Arts. Proceedings of the ASEE Annual Conference, Columbus, OH. Retrieved from https://peer.asee.org/28073 Chen, H. (2018). VennDiagram: Generate high-resolution Venn and Euler plot (R package version 1.6.20) [Computer software]. Retrieved from https://CRAN.R-project.org/package=VennDiagram LORD ET AL. 53 Chesler, N. C., & Chesler, M. A. (2002). Gender-informed mentoring strategies for women engineering scholars: On establishing a caring community. Journal of Engineering Education, 91(1), 49–55. https://doi.org/10.1002/j.2168-9830.2002.tb00672.x Cheville, A. (2017). Ecosystems as analogies for engineering education. Proceedings of the ASEE Annual Conference & Exposition, Columbus, OH. Retrieved from https://peer.asee.org/27808 Choldin, H. M. (1973). Kinship networks in the migration process. International Migration Review, 7, 163–176. Cleveland, W. (1993). Visualizing data. Summit, NJ: Hobart Press. Consentino de Cohen, C., & Deterding, N. (2009). Widening the net: National estimates of gender disparities in engineering. Journal of Engineering Education, 98(3), 211–226. https://doi.org/10.1002/j.2168-9830.2009.tb01020.x de los Santos, A., Jr., & Wright, I. (1990). Maricopa's swirling students: Earning one-third of Arizona State's bachelor's degrees. Community, Technical, and Junior College Journal, 60(6), 32–34. Evanschitzky, H., & Backhaus, C. (2015). Multi-Level Modeling. In C. L. Cooper, N. Lee and A. M. Farrell (Eds.), Wiley encyclopedia of management. https://doi.org/10.1002/9781118785317.weom090175 Fealing, K. H., Lai, Y., & Myers, S. L., Jr. (2015). Pathways vs. pipelines to broadening participation in the STEM workforce. Journal of Women and Minorities in Science and Engineering, 21(4), 271–293. https://doi.org/10.1615/JWomenMinorScienEng.2015004760 Foor, C. E., & Walden, S. E. (2009). “Imaginary engineering” or “re-imagined engineering”: Negotiating gendered identities in the borderland of a college of engineering. NWSA Journal, 21(2), 41–64. Foor, C. E., Walden, S. E., & Trytten, D. A. (2007). “I wish that I belonged more in this whole engineering group”: Achieving individual diversity. Journal of Engineering Education, 96(2), 103–115. https://doi.org/10.1002/j.2168-9830.2007.tb00921.x Forbes, M. H., Bielefeldt, A. R., Sullivan, J. F., & Chaker, D. (2017). Exploring impacts of flexible, balanced engineering program curricula. Proceedings of the ASEE Annual Conference & Exposition, Columbus, OH. Retrieved from https://peer.asee.org/28330 Ford, J. C., & Ford, G. D. (2017). Articulation of military earned college credit into the University of North Carolina University system, Proceedings of the ASEE Annual Conference & Exposition, Columbus, OH. Retrieved from https://peer.asee.org/27613 Gabay-Egozi, L., Shavit, Y., & Yaish, M. (2009). Curricular choice: A test of a rational choice model of education. European Sociological Review, 26(4), 447–463. Gambetta, D. (1987). Were they pushed or did they jump?: Individual decision mechanisms in education. Cambridge, England: Cambridge University Press. Godfrey, E. (2007). Cultures within cultures: Welcoming or unwelcoming for women? Proceedings of the ASEE Annual Conference & Exposition, Honolulu, HI. Retrieved from https://peer.asee.org/2302 Godfrey, E. G., & Parker, L. (2010). Mapping the cultural landscape in engineering education. Journal of Engineering Education, 99(1), 5–22 https://doi.org/10.1002/j.2168-9830.2010.tb01038.x Green, K. C. (1987). The educational “pipeline” in nursing. Journal of Professional Nursing, 3(4), 247–257. Hacker, S. (1989). Pleasure, power, and technology: Some tales of gender, engineering, and the cooperative workplace. Boston, MA: Unwin Hyman, Inc. Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64–74. Hall, E. T. (1976). Beyond culture. Garden City, NY: Anchor Books. Hill, C., Corbett, C., & St. Rose, A. (2010). Why so few? Women in science, technology engineering, and mathematics. Washington, DC: AAUW Retrieved from https://www.aauw.org/research/why-so-few/ Huerta-Manzanilla, E. L., Ohland, M. W., & Long, R. A. (2013). The impact of social integration on engineering students' persistence, longitudinal, interinstitutional database analysis. Proceedings of the ASEE Annual Conference & Exposition, Atlanta, GA. Retrieved from https://peer.asee. org/22596 Humphreys, S., & Freeland, R. (1992). Retention in engineering: A study of freshman cohorts. Berkeley, CA: University of California Press. Integrated Postsecondary Education Data System (IPEDS). (2016). Retrieved from https://nces.ed.gov/ipeds/ Jenkins, J. C. (1977). Push/pull in recent Mexican migration to the US. International Migration Review, 11(2), 178–189. Knight, D. B., Lattuca, L. R., Yin, A., Kremer, G., York, T., & Ro, H. K. (2012). An exploration of gender diversity in engineering programs: A curriculum and instruction-based perspective. Journal of Women and Minorities in Science and Engineering, 18(1), 55–78. https://doi.org/10.1615/ JWomenMinorScienEng.2012003702 Layton, R. A, Long, R. A., & Ohland, M. W. (2018). midfieldr: Tools for student records research (R package version 0.1.0.9002) [Computer software]. Retrieved from https://github.com/MIDFIELDR/midfieldr Layton, R. A., Lord, S. M., & Ohland, M. W. (2009). Reasoning about categorical data: Multiway plots as useful research tools. Proceedings of the ASEE Annual Conference, Austin, TX. Retrieved from https://peer.asee.org/4683 Leonardi, P. M., Jackson, M. H., & Diwan, A. (2009). The enactment-externalization dialectic: Rationalization and the persistence of counterproductive technology design practices in student engineering. Academy of Management Journal, 52(2), 400–420. Litzler, E. (2010). Sex segregation in undergraduate engineering majors (Doctoral dissertation). University of Washington, Seattle, WA. Retrieved from https://search.proquest.com/openview/e9c24c4a5420d5e143200a36b0d6d00f/1?pq-origsite=gscholar&cbl=18750&diss=y Lord, S. M., Berger, E. J. Kellam, N. N., Ingram, E. L. Riley, D. M., Rover, D. T., Salzman, N., & Sweeney, J. D. (2017). Talking about a revolution: Overview of NSF RED projects. Proceedings of the ASEE Annual Conference, Columbus, OH. Retrieved from https://peer.asee.org/28903 Lord, S. M., Camacho, M. M, Kellam, N. N., & Williams, J. M. (2017). Institutional mentoring to incite a revolution through NSF's RED program. Proceedings of the ASEE Annual Conference, Columbus, OH. Retrieved from https://peer.asee.org/28538 54 LORD ET AL. Lord, S. M., Camacho, M. M., Layton, R. A., Long, R. A., Ohland, M. W., & Wasburn, M. (2009). Who's persisting in engineering? A comparative analysis of female and male Asian, Black, Hispanic, Native American and White students. Journal of Women and Minorities in Science and Engineering, 15(2), 167–190. https://doi.org/:10.1615/JWomenMinorScienEng.v15.i2.40 Lord, S. M., Layton, R. A., & Ohland, M. W. (2011). Trajectories of Electrical Engineering and Computer Engineering students by race and gender. IEEE Transactions on Education, 54(4), 610–618. https://doi.org/10.1109/TE.2010.2100398 Lord, S. M., Layton, R. A., & Ohland, M. W. (2015). A multi-institution study of student demographics and outcomes for Electrical and Computer Engineering students in the U.S.A. IEEE Transactions on Education, 58(3), 141–150. https://doi.org/10.1109/TE.2014.2344622 Lord, S. M., Ohland, M. W., & Layton, R. A. (2015). Disciplinary comparison of student outcomes in the USA. Proceedings of the Research in Engineering Education Symposium, Dublin, Ireland. Lord, S. M., Ohland, M. W., Layton, R. L., and Camacho, M. M. (2018). “Not all those who wander are lost.” Examining outcomes for migrating engineering students using ecosystem metrics. Proceedings of the Frontiers in Education Conference, San Jose, CA. Lord, S. M., Sukumaran, B., Maciejewski, A. A., Ingram, E., Sweeney, J., Martin, T., LeDoux, J., London, J., & Salzman, N. (2018). WIP: Progress of the revolution. Proceedings of the ASEE Annual Conference, Salt Lake City, UT. Retrieved from https://peer.asee.org/31299 Martin, J. P., Miller, M. K., & Simmons, D. R. (2014). Exploring the theoretical social capital “deficit” of first generation college students: Implications for engineering education. International Journal of Engineering Education, 30(4), 822–836. Martin, J. P., Simmons, D. R., & Yu, S. L. (2013). The role of social capital in the experiences of Hispanic women engineering majors. Journal of Engineering Education, 102(2), 227–243. https://doi.org/10.1002/jee.20010 Massey, D. S. (1987). Understanding Mexican migration to the United States. American Journal of Sociology, 92(6), 1372–1403. McNeil, J. B., Ohland, M. W., & Long, R. A. (2016). Entry pathways, academic performance, and persistence of nontraditional students in engineering by transfer status. Proceedings of the Frontiers in Education Conference, Erie, PA. Retrieved from https://doi.org/ 10.1109/FIE.2016. 7757548 Meyerson, D. E. (2003). Tempered radicals: How everyday leaders inspire change at work. Boston, MA: Harvard Business School. Mobley, C., Camacho, M. M., Lord, S. M., Brawner, C., & Main, J. B. (2017). Entering the engineering pathway: Student veterans' decision to major in engineering. Proceedings of the ASEE Annual Conference, Columbus, OH. Retrieved from https://peer.asee.org/28285 Moskowitz, J., & Thompson, J. N. (2001). Enhancing the clinical research pipeline: Training approaches for a new century. Academic Medicine, 76(4), 307–315. Napoli, M. T., Sciaky, E., Arya, D. J., & Balos, N. (2017). PIPELINES: Fostering University-Community College partnerships and STEM professional success for underrepresented populations. Proceedings of the ASEE Annual Conference, Columbus, OH. Retrieved from https://peer.asee. org/28745 Newman, C. B. (2011). Engineering success: The role of faculty relationships with African American undergraduates. Journal of Women and Minorities in Science and Engineering, 17(3), 193–209. https://doi.org/10.1615/JWomenMinorScienEng.2011001737 Ohland, M. W., Brawner, C. E., Camacho, M. M., Layton, R. A., Long, R. A., Lord, S. M., & Wasburn, M. H. (2011). Race, gender, and measures of success in engineering education. Journal of Engineering Education, 100(2), 225–252. https://doi.org/10.1002/j.2168-9830.2011.tb00012.x Ohland, M. W., & Long, R. A. (2016). The Multiple-Institution Database for Investigating Longitudinal Development: An experiential case study of data sharing and reuse. Advances in Engineering Education, 5(2), 1–28. Ohland, M. W., Lord, S. M., & Layton, R. A. (2015). Student demographics and outcomes in Civil Engineering in the U.S. Journal of Professional Issues in Engineering Education and Practice, 141(4), 1–7. https://doi.org/10.1061/(ASCE)EI.1943-5541.0000244 Ohland, M. W., Orr, M. K., Layton, R. A., Lord, S. M., & Long, R. A. (2012, October). Introducing “stickiness” as a versatile metric of engineering persistence. Proceedings of the Frontiers in Education Conference, Seattle, WA. Retrieved from https://doi.org/10.1109/FIE.2012.6462214 Ohland, M. W., Sheppard, S. D., Lichtenstein, G., Eris, O., Chachra, D., & Layton, R. (2008). Persistence, engagement, and migration in engineering. Journal of Engineering Education, 97(3), 259–278. https://doi.org/10.1002/j.2168-9830.2008.tb00978.x Orr, M. K. Brawner, C. E., Lord, S. M., Ohland, M. W., Layton, R. A., & Long, R. A. (2012). Engineering matriculation paths: Outcomes of direct matriculation, first-year engineering, and post-general education models. Proceedings of the Frontiers in Education Conference, Seattle, WA. Retrieved from https://doi.org/10.1109/FIE.2012.6462357 Orr, M. K., Brawner, C.E., Ohland, M.W., & Layton, R.A. (2013). The effect of required introduction to engineering courses on major selection. Proceedings of the ASEE Annual Conference, Atlanta, GA. Retrieved from https://peer.asee.org/22577 Orr, M. K., Lord, S. M., Layton, R. A., & Ohland, M. W. (2014). Student demographics and outcomes in Mechanical Engineering in the U.S. International Journal of Mechanical Engineering Education, 42(1), 48–60. https://doi.org/10.7227/IJMEE.42.1.5 Orr, M. K., Ramirez, N. M., Lord, S. M., Layton, R. A., & Ohland, M. W. (2015). Student choice and persistence in Aerospace Engineering. Journal of Aerospace Information Systems (JAIS), 12(4), 365–373. https://doi.org/10.2514/1.I010343 Pawley, A. (2019). Learning from small numbers: Studying ruling relations that gender and race the structure of U.S. engineering education. Journal of Engineering Education, 108(1), 13–31. Pawley, A. & Phillips, C. M. L. (2014). From the mouths of students: Two illustrations of narrative analysis to understand engineering education's ruling relations as gendered and raced. Proceedings of the ASEE Annual Conference, Indianapolis, IN. Retrieved from https://peer.asee. org/20524 Pearson, W. (1985). Black scientists, white society, and colorless science: A study of universalism in American science. New York, NY: Associated Faculty Press, Inc. Perna, L., Lundy-Wagner, V., Drezner, N. D., Gasman, M., Yoon, S., Bose, E., & Gary, S. (2009). The contribution of HBCUs to the preparation of African American women for STEM careers: A case study. Research in Higher Education, 50(1), 1–23. https://doi.org/10.1007/s11162-008-9110-y LORD ET AL. 55 Pilotte, M., Ohland, M. W., Lord, S. M., Layton, R. A., & Orr, M. K. (2017). Student demographics and outcomes in Industrial Engineering. International Journal of Engineering Education, 33(2A), 506–518. Pocheville, A. (2015). The ecological niche: History and recent controversies. In T. Heams, P. Huneman, G. Lecointre, & M. Silberstein (Eds.), Handbook of evolutionary thinking in the sciences (pp. 547–586). Dordrecht, The Netherlands: Springer. Portes, A., & Bach, R. L. (1985). Latin journey: Cuban and Mexican immigrants in the United States. Los Angeles, CA: University of California Press. Portes, A., & Walton, J. (1981). Labor, Class, and the International System. New York, NY: Academic Press. R Core Team. (2018). R: A Language and Environment for Statistical Computing (Version 3.5.0) [Computer software]. Vienna, Austria: R Foundation for Statistical Computing Retrieved from https://www.R-project.org/ Ricco, G.D., Ngambeki, I., Long, R.A., Ohland, M.W., & Evangelou, D. (2010). Describing the pathways of students continuing in and leaving engineering. Proceedings of the ASEE Annual Conference, Louisville, KY. Retrieved from https://peer.asee.org/16749 Riley, D. (2017). Rigor/Us: Building boundaries and disciplining diversity with standards of merit. Engineering Studies, 9(3), 249–265. https://doi. org/10.1080/19378629.2017.1408631 Roberts, C., Huang, M., Olson, R., Camacho, M., & Lord, S. (2015). IUSE/PFE: RED: Developing Changemaking Engineers (NSF Award 1519453). Retrieved from https://www.nsf.gov/awardsearch/showAward?AWD_ID=1519453 Sadler, P. M., Sonnert, G., Hazari, Z., & Tai, R. (2012). Stability and volatility of STEM career interest in high school: A gender study. Science Education, 96(3), 411–427. https://doi.org/10.1002/sce.21007 Samuelson, C. C., & Litzler, E. (2016). Community cultural wealth: An assets-based approach to persistence of engineering students of color. Journal of Engineering Education, 105(1), 93–117. https://doi.org/10.1002/jee.20110 San Antonio, D. M. (2016). The complex decision-making processes of rural emerging adults: Counseling beyond dualism. Peabody Journal of Education, 91(2), 246–269. https://doi.org/10.1080/0161956X.2016.1151749 Sankey, H. R. (1896). The thermal efficiency of steam-engines. Minutes of the Proceedings of the Institution of Civil Engineers, 125(1896), 182–212. Schimpf, C. T., Ricco, G. D., & Ohland, M. W. (2013). The dynamics of attracting switchers: A cross-disciplinary comparison. Proceedings of the ASEE Annual Conference, Atlanta, GA. Retrieved from https://peer.asee.org/22572 Schmidt, M. (2008). The Sankey diagram in energy and material flow management. Journal of Industrial Ecology, 12, 82–94. https://doi.org/10. 1111/j.1530-9290.2008.00004.x Secules, S., Gupta, A., Elby, A., & Tanu, E. (2018). Supporting the narrative agency of a marginalized engineering student. Journal of Engineering Education, 107(2), 186–218. https://doi.org/10.1002/jee.20201 Seymour, E., & De Welde, K. (2015). Why doesn't knowing change anything? Constraints and resistance, leverage and sustainability. In G. C. Weaver, W. D. Burgess, A. L. Childress, & L. Slakey (Eds.), Transforming institutions: 21st century undergraduate STEM education (pp. 462–484). West Lafayette, IN: Purdue University Press. Seymour, E., & Hewitt, N. M. (1997). Talking about leaving: Why undergraduates leave the sciences. Boulder, CO: Westview. Slaton, A. E. (2010). Race, rigor, and selectivity in U.S. engineering: The history of an occupational color line. Cambridge, MA: Harvard University Press. Stine, M. (2010). The power of numbers: Grades and female density in influencing the persistence of women in engineering majors (Doctoral dissertation). State College, PA: The Pennsylvania State University Retrieved from https://etda.libraries.psu.edu/files/final_submissions/4224 Todaro, M. P. (1969). A model of labor migration and urban unemployment in less-developed countries. The American Economic Review, 59(1), 38–148. Tolkien, J. R. R. (1954). The Fellowship of the Ring: The Lord of the Rings. Boston, MA: Houghton Mifflin. Tonso, K. L. (2006). Student engineers and engineer identity: Campus engineer identities as figured world. Cultural Studies of Science Education, 1(2), 1871–1502. https://doi.org/10.1007/s11422-005-9009-2 Tonso, K. L. (2007). On the outskirts of engineering: Learning identity, gender, and power via engineering practice. Rotterdam, The Netherlands: Sense Publishers. Trent, W. T. (1984). Equity considerations in higher education: Race and sex differences in degree attainment and major field from 1976 through 1981. American Journal of Education, 92(3), 280–305. Vanasupa, L., & Schlemer, L. T. (2016). Transcending industrial era paradigms: Exploring together the meaning of academic leadership for diversity. Proceedings of the ASEE Annual Conference, New Orleans, LA. Retrieved from https://doi.org/10.18260/p.27073 Walden, S. E., & Foor, C. (2008). “What's to keep you from dropping out?” Student immigration into and within engineering. Journal of Engineering Education, 97(2), 191–205. https://doi.org/10.1002/j.2168-9830.2008.tb00967.x Walker, R., & Hannan, M. (1989). Dynamic settlement processes: The case of U.S. immigration. The Professional Geographer, 41, 172–183. Waller, A. A. (2004). T-shirts and ponytails: Engineering women talk about self-presentation. Proceedings of the ASEE Annual Conference, Salt Lake City, UT. Retrieved from https://peer.asee.org/12779 Watson, K., & Froyd, J. (2007). Diversifying the U.S. engineering workforce: A new model. Journal of Engineering Education, 96(1), 19–32. https://doi.org/10.1002/j.2168-9830.2007.tb00912.x Wickham, W. H. (2017). tidyverse: Easily Install and Load the tidyverse (R package version 1.2.1) [Computer software]. Retrieved from https:// CRAN.R-project.org/package=tidyverse Wilson-Lopez, A., Mejia, J. A., Hasbún, I. M., & Kasun, G. S. (2016). Latina/o adolescents' funds of knowledge related to engineering. Journal of Engineering Education, 105(2), 278–311. https://doi.org/10.1002/jee.20117 Xie, Y., & Shauman, K. A. (2005). Women in science: Career processes and outcomes. Cambridge, MA: Harvard University Press. Yoder, B. L. (2015). Engineering Data Management System, American Society for Engineering Education. Retrieved from http://edms.asee.org/ LORD ET AL. 56 A U T H O R B IO G R A P H I E S S. M. LORD is a Professor and the Chair of Integrated Engineering and a Professor of Electrical Engineering at the University of San Diego, San Diego, CA; slord@sandiego.edu. M. W. OHLAND is a Professor and the Associate Head of Engineering Education at Purdue University, W. Lafayette, IN; ohland@purdue.edu. R. A. LAYTON is a Professor of Mechanical Engineering at the Rose-Hulman Institute of Technology, Terre Haute, IN; layton@rose-hulman.edu. M. M. CAMACHO is a Professor of Sociology and the Faculty Administrator at the University of San Diego, San Diego, CA; mcamacho@sandiego.edu. How to cite this article: Lord SM, Ohland MW, Layton RA, Camacho MM. Beyond pipeline and pathways: Ecosystem metrics. J Eng Educ. 2019;108:32–56. https://doi.org/10.1002/jee.20250 A P P E N D IX TABLE A1 Groups Starting disciplines of MIDFIELD students ever enrolled in ChE, CE, EE, ISE, and ME ChE CE EE ISE ME Other Eng. STM Non-STM Total Asian female 422 185 342 252 179 277 200 79 1,936 Black female 1,211 515 1,291 754 634 357 152 117 5,031 199 174 130 148 116 111 46 32 956 White female 3,533 2,836 1,520 2,027 2,439 1,983 798 527 15,663 Subtotals female 5,365 3,710 3,283 3,181 3,368 2,728 1,196 755 23,586 Asian male 721 464 2,256 524 1,313 901 326 141 6,646 Black male 831 1,056 3,355 834 2,001 653 226 227 9,183 Hispanic female Hispanic male 327 538 805 356 832 497 131 82 3,568 White male 7,239 11,891 14,024 3,987 19,482 8,571 2,142 1,606 68,942 Subtotals male 9,118 13,949 20,440 5,701 23,628 10,622 2,825 2,056 88,339 14,483 17,659 23,723 8,882 26,996 13,350 4,021 2,811 111,925 Total