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Previous research on physics identity by Hazari et al. has shown that interest, recognition, and performance are three key factors in students’ development of a physics identity. Learning Assistants have potential to improve students’ experiences in STEM classrooms by increasing performance and recognition. In this poster, we will present preliminary results from the STEM Identity (STEM-PIO-4) and STEM Career Interest surveys for courses supported by Learning Assistants in order to evaluate the impact of Learning Assistants on STEM identity. 

Learning computer science (CS) is important for careers of tomorrow. Informal CS opportunities, however, are often limited by a student's socioeconomic disposition, location, ethnicity, gender, and ability. In Montana, these limitations are exemplified in rural communities where a dedicated CS teacher is not available. In order to make informal CS opportunities more equitable, we developed culturally responsive outreach modules for students across Montana by using storytelling as a basis of inquiry. In this paper, we present an outreach module based on the Skokomish story of `How Daylight Came to Be.' In this story, the two main characters---Ant and Bear---each dance for Dokweebah (the Changer). Students animate these dances using event-driven programming in the drag-and-drop programming environment Alice. While creating their dances, students construct knowledge of targeted CS concepts and make design decisions based on the context of the story. This outreach module reframes the context and activity of computing in an effort to transform the way in which students see themselves as potential future computer scientists, and democratize computing as a means of telling stories. By using Brayboy's Tribal Critical Race Theory as a theoretical framework for the development of the outreach program, we introduce computing from a lens of American Indian ways of knowing, culture, and power. To demonstrate the effectiveness of this unit in this exploratory study, we describe students' responses to the outreach programs in terms of perceptions of CS and perceptions of Alice as a culturally relevant programming tool. 

We aim to bring computer science (CS) to rural and American Indian students by blending American Indian storytelling practices with the educational computer programming environment called Alice. The lessons we develop cover CS concepts within the framework of the Content Standards of our state, and the Essential Understandings of American Indians. In this paper, we describe the Plateau Indian Beaded Bags lesson plan, its implementation, and the results of a lesson pilot. In the Plateau Indian Beaded Bags lesson, students learn about the beadwork of Columbia River Plateau-centered tribes. After viewing a picture of a beaded bag with a scene depicting a man on a horse in front of a woman with a tipi in the background, students are asked to construct a story based on this image. They then translate their story into code to create an animation of the story in Alice. Through this hands-on experience, students engage in algorithmic problem solving while using their imagination and creativity, increasing their exposure to, and interest in, CS. 

Let γ be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if γ is self-overlapping by geometrically constructing a combinatorial word from γ. More recently, Zipei Nie, in an unpublished manuscript, computed the minimum homotopy area of γ by constructing a combinatorial word algebraically. We provide a unified framework for working with both words and determine the settings under which Blank’s word and Nie’s word are equivalent. Using this equivalence, we give a new geometric proof for the correctness of Nie’s algorithm. Unlike previous work, our proof is constructive which allows us to naturally compute the actual homotopy that realizes the minimum area. Furthermore, we contribute to the theory of self-overlapping curves by providing the first polynomial-time algorithm to compute a self-overlapping decomposition of any closed curve γ with minimum area. 

Blank, in his Ph.D. thesis on determining whether a planar closed curve $$\gamma$$ is self-overlapping, constructed a combinatorial word geometrically over the faces of $$\gamma$$ by drawing cuts from each face to a point at infinity and tracing their intersection points with $$\gamma$$. Independently, Nie, in an unpublished manuscript, gave an algorithm to determine the minimum area swept out by any homotopy from a closed curve $$\gamma$$ to a point. Nie constructed a combinatorial word algebraically over the faces of $$\gamma$$ inspired by ideas from geometric group theory, followed by dynamic programming over the subwords. In this paper, we examine the definitions of the two words and prove the equivalence between Blank's word and Nie's word under the right assumptions. 

Given a simplicial complex K and an injective function f from the vertices of K to R, we consider algorithms that extend f to a discrete Morse function on K. We show that an algorithm of King, Knudson and Mramor can be described on the directed Hasse diagram of K. Our description has a faster runtime for high dimensional data with no increase in space.