*SIGMAA on RUME*

The Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (SIGMAA on RUME) was established for the advancement of quality research in undergraduate mathematics education (RUME) and its implications for teaching practices. One of the annual SIGMAA on RUME initiatives is the RUME Conference. The conference is intended to serve as an exchange of research findings from projects addressing issues related to the learning and teaching of undergraduate mathematics through plenary addresses, contributed and preliminary research paper sessions, and poster presentations. This year’s RUME Conference, jointly hosted by San Diego State University and the University of California – San Diego, was held at the Kona Kai Resort in San Diego, CA from Thursday, February 23 through Saturday, February 25 with a record-high attendance of over 350 registered conference participants.

Discussions about issues of diversity, equity, and social justice have certainly been gaining momentum in the SIGMAA on RUME community, including the 2017 RUME Conference. It has been both an honor and pleasure to participate in these important conversations over the past year. This was my second year attending the RUME Conference and serving as a co-facilitator for the *Equity in Undergraduate Mathematics Education *pre-conference working group with Aditya (Adi) Adiredja (The University of Arizona). I also had the honor to serve as a plenary speaker on equity research perspectives during the *RUME with a View *working conference funded by the National Science Foundation (Division of Undergraduate Education Grant No. 1646996) and organized by Milos Savic (The University of Oklahoma) and Gulden Karakok (University of Northern Colorado). Held on October 2016 in The University of Oklahoma, *RUME with a View *was a two-day working conference that focused on offering opportunities for faculty and graduate students to develop research agendas in undergraduate mathematics education. Topics spanned student learning, pre-calculus and calculus courses, proofs and problem solving, equity, and statistics and quantitative literacy.

*A Framework on Equity Research in Undergraduate Mathematics Education*

For the rest of this blog entry, I will use a framework from my plenary presentation as well as written notes and conversations from *RUME with a View *to synthesize insights across various equity-oriented research report presentations that I attended during the 2017 RUME Conference. This reflective analysis is intended to explore how equity in undergraduate mathematics education is currently discussed and addressed in the RUME community, and to identify possible areas and approaches for future research. The blog entry concludes with a discussion of “problems of practice” in undergraduate mathematics education identified during the *Equity in Undergraduate Mathematics Education *pre-conference working group and how research implications from my reflective analysis of equity-oriented presentations at the 2017 RUME Conference can serve as possible starting points to address them. * *

My plenary presentation during *RUME with a View* entitled “Pipelines, Pedagogy, and Participation” (Leyva, 2016c) took stock on developments in equity research in undergraduate mathematics education using a framework with three categories to organize the extant literature: outcome-based, institution-oriented, and student-oriented. Outcome-based research largely focuses on quantitative analyses of major choice and retention across the pipeline in undergraduate mathematics or STEM (science, technology, engineering, and mathematics). Institution-oriented research is comprised of studies that qualitatively and/or qualitatively examine ways in which institutional players and structures, including faculty members, course designs, and student support programs, promote inclusion and responsiveness to marginalized communities’ needs in undergraduate mathematics. Student-oriented research centers marginalized students’ experiences in undergraduate mathematics to detail how mathematics can serve as a socially exclusionary space that impacts participation and identities.

It should be noted that my reflective analysis presented here is limited to presentations that I was able to attend during the 2017 RUME Conference while capturing different theoretical and methodological approaches used in pursuing equity-oriented research. There were several other important works presented at the conference that raise the need for equity considerations in undergraduate mathematics education. This includes but not limited to:

- Gail Tang and colleagues’ theoretical paper presentation on the alignment between Rochelle Gutiérrez (2009)’s conceptualization of teaching for equity and principles of inquiry-based learning,
- Ulrike Genschel and Hien Nguyen’s (Iowa State University) statistical analysis of gendered trends in mathematical self-efficacy and academic outcomes between math intensive and non-math intensive STEM majors, and
- Janet Omitoyin’s (University of Illinois – Chicago) analysis of changes in pre-service mathematics teachers’ participation and mathematics identities in a mathematics content course for teaching.

In addition to these presentations, there were various conference-wide initiatives with a commitment to equity in undergraduate mathematics education including:

- the fourth annual Mentoring & Partnerships for Women in RUME (a pre-conference meeting that provides networking and professional development opportunities for women at different career stages in the RUME community) and
- the ongoing work of the SIGMAA on RUME Committee on Equity and Mentoring for producing the RUME community’s first official position statement(s) on equity and mentoring. Members of this committee include Timothy Fukawa-Connelly (Chair, Temple University), Aditya Adiredja, Christine Andrews-Larson (Florida State University), Jessica Ellis (Colorado State University, Fort Collins), and Christopher Jett (University of West Georgia).

*Outcome-Based Research *

In relation to issues of retention and persistence in undergraduate mathematics, Martha Makowski (University of Illinois at Urbana-Champaign) presented findings in a preliminary research report from a study that documentedchanges in students’ mathematics attitudes and rates of completion in a developmental mathematics course at a community college. This analysis adopted a pre- and post-survey methodology with 150 undergraduate students enrolled in the course that centered problem solving and peer collaboration in its design. Makowski observed a 63.3% retention rate in the sample wit

h males, Black students, and younger students being less likely to complete the course. The study’s analysis also demonstrated statistically significant gains in enjoyment of mathematics and acknowledgment of multiple entry points in mathematical problem solving. Makowski’s focus on a developmental mathematics course that adopted a reform approach to instruction resonated with Philip (Uri) Treisman’s (The University of Texas-

Austin) remarks during a special RUME Conference session on the “changing landscape of undergraduate mathematics education.” In Treisman’s presentation, he alluded to the value of reform efforts toward more equitable undergraduate mathematics learning opportunities, especially in light of the gatekeeping effects of developmental courses.

Findings on student retention in Makowski’s study brought me to wonder about the impact of how outcome-based studies define starting and end points for measuring student populations’ mathematical persistence. How might findings on student attitudes and academic outcomes (e.g., course completion, mathematics degree retention) be further nuanced by considering different time points in students’ trajectories as mathematics learners? I also wonder about what insights could be gained in outcome-based research that seeks to unpack the contributing factors to students’ points of departure with undergraduate mathematics. For example, how might following up with male, Black, and younger students in Makowski’s study who did not complete the developmental mathematics course offer perspective toward more equitable course design and instructional practices?

*Institution-Oriented Research*

Like Makowski’s study in a community collee, Christopher Jett’s study captures the value in attending to variation on enhancing equitable mathematics teacher and learning opportunities across different types of institutions (e.g., predominantly white universities, two-year colleges, historically black colleges and universities [HBCU]). Jett’s preliminary research report presented findings on the roles that mathematics faculty members played in shaping the experiences of 16 African

American male mathematics majors at an all-male, private HBCU. This institution-oriented study elaborated on the importance of faculty members pr

oviding the African American males with access to challenging undergraduate coursework, mentorship outside of the classroom, and racially-affirming learning opportunities in mathematics.

Such racially-conscious forms of blending academic and social support, critical to the African American males’ development as mathematics majors, was similarly observed in my ethnographic research on undergraduate Latin@ engineering majors’ mathematics success at a large, predominantly white university (Leyva, 2016b). [I use the term, *Latin@*, to decenter the patriarchal nature of the Spanish language that traditionally groups Latin American individuals into a single descriptor, *Latino*, denoting only men (Gutiérrez, 2013). The @ symbol allows for gender inclusivity among Latin Americans compared to the either-or form *Latina/o*, implying a gender binary.] This raises considerations of how the nature of faculty support for historically marginalized student populations, including African Americans and Latin@s, comes to be shaped by the varying ways in which institutions of higher education operate as racialized contexts (Battey & Leyva, 2006; Martin, 2013). Despite such variation across institutions, much can be learned about the transferability (as opposed to the generalizability) of meaningful forms of faculty support to promote more equitable undergraduate mathematics education among students of color across different colleges and universities

Gender in relation to mathematical self-efficacy and sense of belonging was taken up in Susan Nickerson, Katie Bjorkman, Sei Jin Ko, and David Marx’s (San Diego State University) analysis on the influence of peer role model interventions in first-semester calculus courses at a large, southwestern university in the United States. These interventions consisted of two in-class peer role model presentations by a Hispanic or non-Hispanic White female majoring in STEM consisting of a self-introduction to establish common ground in mathematics, presentation of a mathematical topic related to course content, and encouraging remarks for STEM persistence. This study’s statistical analyses found increases in both constructs among high math-identified females and low math-identified females in the sampled calculus course sections. (I use the terms, “females” and “males,” here to remain consistent with the authors’ language adopted to describe findings from the sex-based analysis of mathematical self-efficacy and sense of belonging.)

While this study speaks to the value of diversifying undergraduate classroom spaces to allow for underrepresented students’ improved attitudes towards mathematics (in this case, among students identifying with the female sex), I wonder what can be gained from situated analyses in the sampled calculus classrooms to complement Nickerson and colleagues’ findings. For example, how could observations before, during, and after peer role interventions provide a glimpse into gendered interactions between high and low math-identified students to unpack the statistical findings of self-efficacy and sense of belonging? Considering how mathematics has been documented as a masculinized domain and thus limiting opportunities for women and gender-nonconforming individuals (Leyva, in press; Mendick, 2006, Solomon, 2012), situated perspectives of underrepresented students’ experiences in Nickerson and colleagues’ as well as Jett’s study would offer insight into the social construction of masculinities in doing undergraduate mathematics. This could also explore how the masculinized landscape shapes the nature of classroom interactions and faculty support and thus further explain influences on the sample populations’ experiences in and identifications with mathematics.

Furthermore, I am curious about how a more explicit focus on intersections of race and gender (as opposed to sex) across both studies could illuminate insightful variation among participants in their findings. Jett’s research report, for example, describes the study as intended to unpack how “complexities about the constructs of race and/or gender” shape the African American male participants’ development as mathematics majors. Considering the lack of intersectional analyses in extant mathematics education research adopting critical race theory (Leyva, 2016a), I view Jett’s study as a promising call for future research to detail the construction of Black masculinities in undergraduate mathematics across different types of higher education institutions, including how mathematics faculty members may contribute to such constructions through their instruction and student support. Similarly, Nickerson and colleagues’ presentation left me interested in learning more about possible variation in documented changes for mathematical self-efficacy and sense of belonging when the peer role model was a white female or a Hispanic female. In what ways might mutual forms of racial and gender identification between the calculus students and peer role models contribute to changes (or lack thereof) in participants’ mathematical self-efficacy and sense of belonging?

*Student-Oriented Research*

More localized and intersectional analyses were adopted in actor-oriented studies shared during Fady El Chidiac’s (University of California-Berkeley) and Adi Adiredja and Michelle Zandieh’s (Arizona State University)’s contributed research report presentations. El Chidiac discussed the limitations of video records and unmediated interviews that leave in-the-moment power and socioemotional dynamics unexplored. In light of such limitations, El Chidiac introduced the Stimulated Construction of Narratives about Interactions (SCNI) data collection technique to examine such dynamics during small-group learning interactions in an undergraduate number theory course. The SCNI technique provides participants with the space to generate original narratives about social interactions during videotaped small-group learning activities re-visited during individual interviews. These narratives are conceptualized as negotiations of narrative discourses that participants use to make sense of themselves, others, and their everyday lives as well as pragmatic forces that shape their small-group learning interactions in the classroom. El Chidiac presented three cases from the SCNI interview data analysis that illuminate how the technique allows for (i) exploring variation in individual group members’ interpretations of small-group interactions, (ii) providing contextual insights about small-group interactions through interview reflections otherwise missing in the video data, and (iii) characterizing different profiles of student engagement during small-group learning.

The SNCI technique, thus, serves as a methodological tool and perspective to potentially better understand how classroom learning interactions perpetuate or disrupt discourses that privilege or oppress individuals in undergraduate mathematics education. In light of the previous studies’ focus on racialized and gendered dynamics in undergraduate mathematics, I am curious to learn more about the ways in which participants in El Chidiac’s study interpreted small-group learning behaviors as being more or less likely to be engaged by certain peers and how this shapes (in)equitable participation opportunities in the small group and mathematics classroom more broadly. Such insights can inform ways in which undergraduate mathematics instructors adopt small-group learning and other classroom structures in ways that disrupt the production of status often aligned with a racialized and gendered hierarchy of mathematical ability [e.g., Martin, (2009)], thus broadening opportunities for classroom participation that challenges status-quo conceptions of doing college mathematics.

In the same vein of re-thinking undergraduate mathematics teaching and learning, Adiredja and Zandieh presented findings from a study on eight undergraduate women of color’s use of everyday contexts to explain the linear algebra concept of basis and how these contexts reflected characteristics and roles of basis vectors. Adiredja and Zandieh adopted the “anti-deficit achievement framework” (Harper, 2010) to approach an interview data analysis that challenges narratives of women of color as underachieving in mathematics and thus leverages women of color participants’ intuitive perspectives as productive entry points for building mathematical knowledge. The students used a broad range of everyday contexts to make meaning of a “basis,” such as cooking, fashion, and religious teachings. Adiredja and Zandieh’s adopted coding scheme detailed how the women of color’s proposed everyday examples mapped onto characteristics (e.g., representation, non-redundant) and roles of basis vectors in the larger space (e.g., generating, describing).

The intersectional sampling of women of color and analytical foregrounding of their mathematical thinking, as Adiredja and Zandieh highlighted in their presentation, allow for the centering of women of color’s voices that are largely absent in undergraduate mathematics education research. This study raises implications for curricular design in undergraduate mathematics that builds on students’ everyday lives and intuitive understandings to increase access to mathematical ideas, particularly among women of color and other student populations historically marginalized in mathematics. Such implications resonate with David Stinson’s (Georgia State University) remarks during his plenary address at last year’s RUME Conference on what culturally responsive pedagogy in undergraduate mathematics would look like and the (im)possibilities of it being used to allow for more equitable learning opportunities across undergraduate mathematics classrooms.

Considering that women of color participants in Adiredja and Zandieh’s study were enrolled in a linear algebra course, I am prompted to think about the urgency of carving more culturally-responsive and gender-affirming opportunities earlier in the undergraduate mathematics pipeline, especially in light of the racialized and gendered retention rates such as those raised in Makowski’s research. Furthermore, I wonder about the possibilities of leveraging methodological approaches of centering students’ voices about navigating systems of power in mathematics, like those in Jett’s and El Chidiac’s studies, to understand how such socially-validating pedagogy informs ways that better attend to the intersectionality of women of color and other marginalized groups’ lived experiences as undergraduate mathematics students. [Intersectionality is a concept from Black feminist thought coined and adopted by Kimberle Crenshaw (1989, 1991) to detail intersectional forms of marginalization legally and politically experienced by historically marginalized women of color in the United States. It refers to unique forms of intersecting oppression that emerge from gender, race, and other social categories that “function as parallel and interlocking systems” (Collins, 1993, p. 29) of domination and subordination.]

*Concluding Thoughts*

Before the official start of the 2017 RUME Conference, Adiredja and I co-facilitated the *Equity in Undergraduate Mathematics Education* working group as an opportunity for exchanging conceptual and methodological insights from ongoing equity-oriented research at varying stages of development. This year’s working group nearly doubled in size since last year with over 40 registered participants. Discussions and presentations centered around topics such as the role of educational equity across inquiry-based mathematics classrooms, service learning opportunities in curricular design, and multi-institutional partnerships for broadening access in STEM. This increase in the working group size was just one of the many ways that illustrates the vested interest and rising analytical attention to equity issues in the RUME community.

Through a blend of small- and whole-group discussions throughout the working group, participants raised several “problems of practice” in order to identify future next steps toward the advancement of equity through the RUME community, our respective home institutions, and the field of undergraduate mathematics education at large. This included discussions about different ways in which equity is addressed across different departments and institutions, how to increase collaborations between mathematicians and mathematics educators, and how to shape policies across mathematics and mathematics education organizations in ways that center issues of equity.

Keeping these “problems of practice” in undergraduate mathematics research and teaching in mind, I want to take stock on the intellectual contributions from the reviewed RUME Conference presentations in this blog entry to synthesize implications for future research that address these areas of concern and thus broaden equitable opportunities in undergraduate mathematics education. First, these studies highlight the need to examine the extent to which institutional factors such as teaching, curricula, and support structures perpetuate values of mathematics as a discipline that oppress some and privilege others. Second, these RUME presentations capture the promise of employing theoretical perspectives and methodologies from different fields (e.g., learning sciences, critical legal studies) to develop more nuanced understandings of equitable learning and support opportunities in undergraduate mathematics education at different intersections of students’ social identities. Finally, these reviewed presentations illustrate the multi-faceted nature of equity in undergraduate mathematics education as a complex endeavor. This captures the need for research that considers the interplay of institutional contexts and local communities operating as unique cultural spaces, different actors (including students, peers, faculty, departmental administrators), and metrics and discourses of success in mathematics from educational organizations, policy statements, and society.

If you are interested in attending the 2018 RUME conference, be sure to check out the SIGMAA on RUME website in coming months for additional information about registering and submitting proposals. You can also use this website to access information about past RUME conferences, published proceedings, and journals for research in undergraduate mathematics education.

Thank you for your time in reading my blog entry. Feel free to share your thoughts in the “Leave a Reply” section down below.

References

Battey, D., & Leyva, L. A. (2016). A framework for understanding whiteness in mathematics education. *Journal of Urban Mathematics Education, 9*(2), 49-80.

Collins, P. H. (1993). Toward a new vision: Race, class, and gender as categories of analysis and connection. *Race, Sex & Class, 1*(1), 25–45.

Crenshaw, K. (1989). Demarginalizing the intersection of race and sex: A black feminist critique of antidiscrimination doctrine, feminist theory and antiracist politics. *University of **Chicago Legal Forum, 1*(8), 139–167.

Crenshaw, K. (1991). Mapping the margins: Intersectionality, identity politics, and violence against women of color. *Stanford Law Review*, *43*(6), 1241–1299.

Gutiérrez, R. (2009). Framing equity: Helping students “play the game” and “change the game.” *Teaching for Excellence and Equity in Mathematics*, *1*(1), 5-7.

Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. *Journal for Research in **Mathematics Education, 44*(1), 37–68.

Harper, S. R. (2010). An anti-deficit achievement framework for research on students of color in STEM. In S. R. Harper & C. B. Newman (Eds.), *Students of color in STEM: Engineering **a new research agenda. New Directions for Institutional Research *(pp. 63-74). San Francisco: Jossey-Bass.

Leyva, L. A. (in press). Unpacking the male superiority myth and masculinization of mathematics at the intersections. A review of research on gender in mathematics education. To appear in the *Journal for Research in Mathematics Education.*

Leyva, L. A. (2016a). An intersectional analysis of Latin@ college women’s counter-stories in mathematics. *Journal* *of Urban Mathematics Education, 9*(2), 81-121.

Leyva, L. A. (2016b). Blending academic and social support through apoyo and consejos for undergraduate mathematics success among Latin@s. To appear in the *Proceedings of the **13 ^{th} International Congress on Mathematical Education*, Hamburg, Germany.

Leyva, L. A. (2016c). Pipelines, pedagogy, and participation: Three strands of equity research in undergraduate mathematics education. Plenary presentation at the RUME with a View: Cultivating New Researchers on the Frontier of Research on Undergraduate Mathematics Education (RUME) Conference (Supported by the National Science Foundation Division of Undergraduate Education Grant No. 1646996). Norman, OK: The University of Oklahoma.

Martin, D. B. (2009). Researching race in mathematics education. *Teachers College Record, **111*(2), 295–338.

Martin, D. B. (2013). Race, racial projects, and mathematics education. *Journal for Research in Mathematics Education*, *44*(1), 316–333.

Mendick, H. (2006). *Masculinities in mathematics*. New York, NY: Open University Press.

Solomon, Y. (2012). Finding a voice? Narrating the female self in mathematics. *Educational **Studies in Mathematics*, *80*(1-2), 171-183.

Thanks for this Luis. This is an excellent overview and you’ve left me with lots to think about.

Thanks so much for your kind words about the post, Robin. I’m looking forward to staying connected and continuing to think together.