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Browsing by Author "Ellis Hagman, Jessica, advisor"

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    Exploring women of color's expressions of mathematical identity: the role of institutional resources and mathematical values
    (Colorado State University. Libraries, 2023) Street, Ciera, author; Ellis Hagman, Jessica, advisor; Soto, Hortensia, committee member; Arnold, Elizabeth, committee member; Most, David, committee member
    There is a persistent and growing global call to examine, challenge, and transform exclusionary structures and systems within mathematics education (Laursen & Austin, 2020; Reinholz et al., 2019; Thomas & Drake, 2016; Wagner et al., 2020). An important component of this call examines students' mathematical identity. While a growing body of work considers how students' social identities interplay with their mathematical identity (e.g., Akin et al., 2022; English-Clarke et al., 2012), few studies consider mathematical identity at the intersection of gender and race (Ibourk et al., 2022; Leyva, 2016; 2021). This dissertation study explores undergraduate women of color's expressions of mathematical identity and the institutional structures and ideologies that influence these expressions. Following a three-paper model, each paper utilizes critical theories and an intersectional lens to recognize the gendered and racialized context of higher education mathematical spaces and the ways these discourses influence women of color's mathematical identity. The first paper employs large-scale quantitative and qualitative data from a national survey on students' undergraduate calculus experiences to explore women of color's expressions of mathematical identity. Informed by Data Feminism, I use a cluster analysis to group women of color survey respondents based on four subdomains of mathematical identity and contextualize each group using qualitative survey responses. The second paper draws from Nasir's (2011) material and relational identity resources to examine the institutional resources available and accessible to undergraduate women of color to support their mathematical identity. Results from participant interviews indicate various supportive identity resources, such as peer relationships and student support programs. The results also describe unavailable, inaccessible, or detrimental identity resources, such as the lack of representation within the mathematics faculty and an exclusionary mathematics community. Using a sociopolitical lens, the third paper discusses the sociohistorical background of white, patriarchal mathematical values and the ways these values create inequities in undergraduate mathematical spaces. Interviews with participants suggest a clear misalignment between these sociohistorical mathematical values and women of color's mathematical and mathematics education values. Together, these three papers emphasize within-group differences among women of color's mathematical identity and the different ways material, relational, and ideological resources can support or hinder women of color's mathematical identities. I conclude this dissertation study by illustrating connections across the three papers. I also provide implications for teaching, policy, and research to challenge exclusionary mathematical systems and support women of color's mathematical identity.
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    Graduate students' representational fluency in elliptic curves
    (Colorado State University. Libraries, 2023) Dawson, Erin, author; Cavalieri, Renzo, advisor; Ellis Hagman, Jessica, advisor; Zarestky, Jill, committee member
    Elliptic curves are an important concept in several areas of mathematics including number theory and algebraic geometry. Within these fields, three mathematical objects have each been referred to as an elliptic curve: a complex torus, a smooth projective curve of degree 3 in P2 with a chosen point, and a Riemann surface of genus 1 with a chosen point. In number theory and algebraic geometry, it can be beneficial to use different representations of an elliptic curve in different situations. This skill of being able to connect and translate between mathematical objects is called representational fluency. My work explores graduate students' representational fluency in elliptic curves and investigates the importance of representational fluency as a skill for graduate students. Through interviews with graduate students and experts in the field, I conclude 3 things. First, some of the connections between the above representations are made more easily by graduate students than other connections. Second, students studying number theory have higher representational fluency in elliptic curves. Third, there are numerous benefits of representational fluency for graduate students.