Analyzing the Effectiveness of Different Media to Enhance Mathematical Discourse

This qualitative and quantitative study compared the effect of paper-pencil work in a mathematical discourse with problems and prompts presented virtually through various technological tools. The participants of this study were ninth and tenth grade students in two separate blocks of geometry class. These classes consisted of predominantly White students split into class sizes of 26 and 21. Since students were separated into two different geometry classes, one class was given paper problems and discussion prompts while the other received problems and prompts through Desmos Classroom Activities. This way, a quantitative analysis of three data points could be compared between the two classes to analyze the effect the different media had on student to student mathematical discourse. After weeks of analysis, data showed that paper prompting was slightly more effective at stimulating mathematical discussion. In fact, most of the discussion came while students worked through discrepancies in answers. Meaning, even though technology helped students learn with immediate feedback and learning aids, it was the mistakes in students’ work, without immediate feedback, that helped students collaborate verbally and work to understand their mistakes

"The World Goes One Way and We Go Another": Movement, Migration, and Myths of Irish Cinema

The dissertation considers Irish films through the valence of movement and migration to conceptualize a cinema that can account for how films function locally and transnationally. I consider various forms of migration in films produced in Ireland to interrogate how identity and the nation are presented. Considering forms of migration opens a different approach to the films that enables questioning of the myths of the nation-state within globalized capital and culture. In Ireland, the land has given shape to the physical boundaries of imagined identity; land is understood as a material trace denoting a linear history of invasion, conquest, and ultimately independence - an evolution from colonial oppression to postcolonial identity. Movement and migration make the boundaries defining subjectivity permeable by demonstrating how place, identity, language, and consciousness are located in the intermezzo. Using a case study approach that considers diverse films, including big budget, small budget, documentary and popular genre films, I demonstrate how changes in conceptions of national cinema and identity occur on aesthetic and epistemological levels, resulting in multiple points of entry for transnational audiences. I examine the movements of people, the landscape, and storytelling as forms of mobility. Analyses of the films and their context focus on exiles, internal émigrés, nomads, disaffected young people, and Travellers to shift the consideration of migration from emigration toward a conception of epistemological mobility. A double consciousness is elicited though the use of legends derived from earlier Irish history, redefining the relationship between myth and nation. The resultant fluctuating and mobile sign systems refuse strict adherence to any one mode of narration or style, often breaking down boundaries between reality and fantasy. I discuss Irish films in terms of censorship, funding and distribution, arguing that these issues must inflect an understanding of the dispersed form this cinema exhibits. The transformations to genre conventions and meanings are an effect of the necessary movement toward international co-productions. The dissertation culminates in a discussion of how the heterogeneous body of recent films shifts, metamorphoses, and defies definition, indicating transformations in the time, space, and body of the nation