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1. Two Vignettes on Students’ Symbolizing Activity for Set Relationships

   Eckman, D.; Roh, K.H.; Dawkins, P.C.; Ruiz, S.; Tucci, A. (August 2023, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Cook, S.; Katz, B.; Moore-Russo, D. (Ed.)

   Mathematicians often use set-builder notation and set diagrams to define and show relationships between sets in proof-related courses. This paper describes various meanings that students might attribute to these representations. Our data consist of students’ initial attempts to create and interpret these representations during the first day of a paired teaching experiment. Our analysis revealed that neither student imputed or attributed our desired theoretical meanings to their diagrams or notation. We summarize our findings in two vignettes, one describing students’ attributed meanings to instructor-provided set-builder notation and the other describing students’ imputed meanings to their personally-created set diagrams to relate pairs of sets. 

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2. Student use of three registers for representing set relationships to reason about logic in undergraduate transition to proof courses

   Dawkins, PC; Roh, KH; Bruner, O; Gonzalez, M (November 2024, Psychology in Mathematics Education - North America)

   In transition to proof courses for undergraduates, we conducted teaching experiments supporting students to learn logic and proofs rooted in set-based meanings. We invited students to reason about sets using three representational systems: set notation (including symbolic expressions and set-builder notation), mathematical statements (largely in English), and Euler diagrams. In this report, we share evidence regarding how these three representations provided students with tools for reasoning and communicating about set relationships to explore the logic of statements. By analyzing student responses to tasks that asked them to translate between the representational systems, we gain insight into the accessibility and productivity of these tools for such instruction. 

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3. Characterizing Student Identities in Engineering: Attitudinal Profiles of Engineering Majors

   Benson, L.; Potvin, G.; Kirn, A.; Godwin, A.; Doyle, J.; Rohde, J.A.; Verdín, D.; Boone, H. (June 2017, ASEE annual conference & exposition)

   https://peer.asee.org/27950 This paper presents results of work completed on our project, Intersectionality of Non-normative Identities in the Cultures of Engineering (InIce). The overarching focus of this project is on how students who hold non-normative identities position themselves, grow through their education, and navigate the cultures of engineering they experience in college. Our goal is to investigate ways to engage students who hold non-normative identities to become more active and lifelong participants in engineering disciplines. Our work is proceeding in three phases: 1) Identify, through a quantitative instrument, the attitudinal profiles of normative and non-normative students in engineering; 2) Characterize students’ normative and non-normative identities through in-depth interviews and analysis of differences between students with normative and non-normative identities in engineering; and 3) Drawing from our findings, develop a workshop and set of courses to incorporate diversity topics into engineering programs to enhance the culture of engineering to be more responsive towards, and inclusive of, a diverse range of student identities. We have completed the first phase of the project in which we quantitatively measured and characterized student groups with normative and non-normative identities in engineering. Our definitions of normative and non-normative for this project are developed through Topological Data Analysis (TDA) of a set of multi-institution survey data (n = 2916). TDA allows identification of groups without imposing a priori hypotheses on how the attitudes of students may group together (nor how they may distinguish between demographic groups). This approach allows the underlying structure of the data to emerge rather than imposing pre-defined definitions of normative attitudes or identities. Our TDA results revealed one group that contains a relatively large number of students (the “normative” group) and a total of seven other distinct, but relatively populated, groups (the “non-normative” groups). We have compiled a summary of the most salient attitudinal constructs in terms of characterizing and distinguishing between all these groups including: motivation (value, goal orientation, future time perspective), engineering and physics identities (performance/competence and recognition beliefs for each), personality traits (neuroticism, extraversion, belongingness) and grit (consistency of interest). We are currently in Phase 2 of our study in which we are conducting a series of qualitative, longitudinal interviews with students selected from normative and non-normative groups to understand how they navigate their engineering experiences and define their educational trajectories over the first two years of college. This data will be deductively analyzed based on our existing attitudinal frameworks as well as inductively coded for emerging themes on how students feel belongingness within engineering culture. This project promises to move traditional measures of demographic data beyond socially constructed perceptions of others and allows for the representation of student diversity from the perspective of each participant. This more accurate reflection of diversity provides novel insight into the experiences of students who might otherwise be ignored or unjustifiably lumped in with other students with whom they share some demographic indicator and how residing at the intersection of multiple measures of diversity can influence students’ experiences in engineering culture. 

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4. Computational musicking: music + coding as a hybrid practice

   https://doi.org/10.1080/0144929X.2024.2402533  

   Roberts, Cameron L; Horn, Michael S (March 2025, Behaviour & Information Technology)

   While there is a growing body of research that explores the integration of music and coding in learning environments, much of this work has either emphasized the technical aspects of computer language design or music as a motivational context within which to learn computer science concepts. In this paper, we report on a study in which five undergraduate students with experience in both music and coding completed two creative musical tasks: one using conventional instruments and tools and one using Python code in an online music + coding environment. Inspired by the work of Christopher Small (1998. Musicking: The Meanings of Performing and Listening. University Press of New England), we describe music + coding as a set of interlocking processes which we call computational musicking and explore how practices from both domains are reimagined in this new hybrid context. We introduce semiotic theories of translation and transcription to make sense of the computational musicking process and describe strategies that participants devised in their creative process. 

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5. Intersectionality of Non-normative Identities in the Cultures of Engineering

   https://doi.org/10.18260/p.25448  

   Kirn, Adam; Godwin, Allison; Benson, Lisa; Potvin, Geoff; Doyle, Jacqueline; Boone, Hank; Verdin, Dina (June 2016, ASEE Annual Conference & Exposition)

   Traditionally, engineering culture has limited rather than fostered diversity in engineering. To address this persistent issue, we examine how diverse students identify with engineering and navigate the culture of engineering. We define diversity not by making a priori categorizations according to traditional demographic information (e.g., race, gender, sexual orientation, etc.), but instead by investigating the variation in students’ attitudinal profiles on a host of affective measures. Using these measures, we develop an identification of large, “normative” groups of engineers as well as “non-normative” students who emerge as having distinct attitudinal profiles. This mixed methods study investigates the intersectionality of engineering students' personal identities to understand: How do non-normative groups in engineering form an engineering identity and navigate a culture dominated by limited diversity? The focus of this paper is on the first phase this project, in which students' identities, motivation, psychological traits, perceived supports and barriers to engineering, and other background information is being quantitatively assessed. Pilot survey data were collected from participants enrolled in second semester first-year engineering programs across three institutions (n=374). We used topological data analysis (TDA) to create normative and non-normative attitudinal profiles of respondents. As a relatively new and powerful set of analytic methods, TDA clusters variegated data to understand an underlying structure, or topology, which emerges from the data. Our preliminary results show definite patterns which we then break down according to students' self-identified demographics. Additionally, a subset of participants who completed our quantitative instrument were interviewed about their experiences in and identification with engineering (n=7). Initial qualitative data analysis indicate that students who reside at intersectional boundaries of diversity have difficulty finding similar role models in engineering and often find themselves expending additional effort when compared to their peers to establish themselves in both engineering and non-engineering communities. Results of this quantitative and qualitative work were used to further refine the quantitative instrument that is to be used in subsequent phases of the project. 

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