Background: Education researchers use quantitative methodologies to examine generalizable correlational trends or causal mechanisms in phenomena or behaviors. These methodologies stem from (post)positivist epistemologies and often rely on statistical methods that use the means of groups or categories to determine significant results. The results can often essentialize findings to all members of a group as truth knowable within some quantifiable error. Additionally, the attitudes and beliefs of the majority (i.e., in engineering, White cis men) often dominate conclusions drawn and underemphasizes responses from minoritized individuals. In recent years, engineering education research has pursued more epistemologically and methodologically diverse perspectives. However, quantitative methodologies remain relatively fixed in their fundamental epistemological framings, goals, and practices. Purpose: In this theory paper, we discuss the epistemic groundings of traditional quantitative methods and describe an opportunity for new quantitative methods that expand the possible ways of framing and conducting quantitative research-person-centered analyses. This article invites readers to re-examine quantitative research methods. Scope: This article discusses the challenges and opportunities of novel quantitative methods in engineering education, particularly in the limited epistemic framings associated with traditional statistical methods. The affordances of person-centered analyses within different epistemological paradigms and research methods are considered. Then, we provide an example of a person-centered method, topological data analysis (TDA), to illustrate the unique insights that can be gained from person-centered analyses. TDA is a statistical method that maps the underlying structure of highly dimensional data. Discussion/Conclusions: This article advances the discussion of quantitative methodologies and methods in engineering education research to offer new epistemological approaches. Considering the foundational epistemic framings of quantitative research can expand the kinds of questions that can be asked and answered. These new approaches offer ways to conduct more interpretive and inclusive quantitative research.

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IntroductionThis work-in-progress research paper seeks to understand how active learning influences student attitudes and beliefs to aid in addressing calls for one-million new STEM graduates in the next decade 1 . With 40% of students currently completing STEM majors, the aim is to increase degree completion to at least 50% by 2022 through improvements in the first two years of undergraduate STEM education. This increase in STEM graduation rates projects to meet at least 75% of the needed one-million graduates. To meet the demands for more high-quality engineers, it is necessary that engineering programs provide an education that graduates more engineers through diverse pathways and provides the engineer of the future 2 skills needed for quick and more innovative solutions to grand challenges 3 . Without doing so successfully, solutions to grand challenges will be slowed or go undeveloped. Thus, for the future of engineering, it is important that instructors embrace new evidence-based means of instruction that ensure our students graduate and with the skills they need to succeed as engineers.Design, one of these important skills, often portrayed as one of the fundamental roles for engineers, should be an important part of an engineer's education 2 . To promote skill development, research has suggested that instructors work to increase students' self-efficacy 4 , or self-belief in the ability to complete a task 5 . Shown to positively correlate with students' grade performance, persistence in college 6, and increase engineering skill development 7 , increasing engineering self-efficacy could be key to creating more engineers 8 . It is important then that we look for and use, evidence-based methods of instruction that increase self-efficacy.One evidence-based method shown to increase self-efficacy in engineering, that also meets one of PCAST's five recommendations to increase graduation rates 1 , is active learning 9 . Besides increasing engineering self-efficacy 8 , use of active methods have been shown to be more effective towards improving students' grades when compared to the norm of direct instruction 10 (i.e. lecture). Project-based learning, one active learning method used in engineering, employs the use of cooperative project completion to link learning to real application and increase motivation 7,11 . If project-based learning positively affects students' formation of self-efficacy, including development of engineering self-efficacy, or even design self-efficacy (i.e. students' feelings in their ability to conduct design) 12 , project-based learning may prove to be a more effective way to teach engineering skills such as design and help promote increased completion of an engineering degree 2 . To understand how instructors might better develop students' design self-efficacy, we pose the following research question: How does active learning affect students' development of design self-efficacy? Theoretical FoundationsSelf-efficacy examines the belief an individual has in their ability to complete a task 5...

Her research focuses what factors influence diverse students to choose engineering and stay in engineering through their careers and how different experiences within the practice and culture of engineering foster or hinder belongingness and identity development. Dr. Godwin graduated from Clemson University with a B.S. in Chemical Engineering and Ph.D. in Engineering and Science Education. Her research earned her a National Science Foundation CAREER Award focused on characterizing latent diversity, which includes diverse attitudes, mindsets, and approaches to learning, to understand engineering students' identity development. She has won several awards for her research including