# Faculty Talks

**4 - 4:45 p.m.**

## Math Education Talks

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## Dr. Brittney Ellis

**Intersecting theories to study how status impacts inequities in undergraduate proof. **

Perceived status characteristics impact how people interact in social situations, particularly when they carry out tasks to achieve a common goal. Status characteristics are not fixed or innate qualities, and are relative; that is, one person may have higher status in a certain situation and lower status in another. Status hierarchies have been shown to have an effect on students’ learning because students with lower perceived status compared to their peers learn less, are less confident in their abilities, and are more likely to feel as though they do not belong. An open question for research in undergraduate mathematics education (RUME) is: How are status hierarchies in undergraduate proof classrooms legitimated or delegitimated? I will share a possible methodology blending positioning theory, status theories, and related conceptions of equity that will be used to examine how status influences inequities in immediate proof learning environments. This work is being developed for an NSF-funded project studying how to support instructors interested in making group work less inequitable in undergraduate proof.

## Dr. Cody Patterson

**Discourses for equation solving: What do secondary teachers value?**

The reasoning we use when solving equations can be viewed as a deductive process in which each step makes an equality statement that follows from the assumption that a given equation is true. However, the way we talk about solving equations often treats equations as symbolic forms that we manipulate strategically, without attending to the meanings of the symbols (e.g., “move all the x’s over to one side”). How do teachers see the tension between these two ways of talking and thinking about equations, and what benefits or challenges do they see in each? I will share some findings from an NSF-supported three-year exploratory project in which we investigated the professional knowledge and values that inform secondary teachers’ decisions about how to present conceptual content in algebra.

## Mathematics Talks

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## Dr. Christine R.S. Lee

**The quantum topology of low-dimensional knotting and linking**

In this talk I will introduce knots and links in 3-space and what it means to have a knot or a link invariant. As an example we will spend some time on a quantum link invariant called the Jones polynomial, and describe the confluence of algebraic, geometric, and topological perspectives on knot theory through the study of quantum link invariants.

## Dr. Lucas Rusnak

**Data analysis and clustering via sentiment reconstruction**

Sentiment-driven networks are modeled using signed graphs; a collection of vertices and incident edges where each edge is signed + or - to represent the sentiment between two adjacent vertices. Community detection in signed graphs is notoriously difficult as many techniques, often unknowingly, give preference to the underlying structure of the network over socially relevant outcomes. Balance theory is the study of the deviation from cognitively consistent (socially relevant) states. A signed graph is balanced if the product of the signs of the edges around each cycle is positive. For signed graphs, this is equivalent to: (1) all paths between two fixed vertices have the same sign, and (2) the deletion of the negative edges produces a bipartition of the vertices into two groups with diametrically opposed beliefs.

I will first show how my sentiment reconstruction algorithm migrates unbalanced data to a multiset of feasible balanced states to determine the likelihood of group formation. Moreover, if an outcome has occurred, we are able to detect what relationships were necessary to produce that outcome. We will then examine the efficacy of this technique across a variety of situations. These include workforce promotion and equity; pandemic quarantining and infrastructure; healthcare and patient-portal optimization; kinesiophobia and recovery in elite athletes; and student-topic amenability in the classroom.

For anyone interested in learning more regarding theoretical underpinnings, generalizations, and additional applications I encourage you to not only reach out to me but my current and former students in attendance.