Bringing van Hiele and Piaget Together: A Case for Topology in Early Mathematics Learning

Topological concepts arise naturally in young children\u27s spatial reasoning yet topology is not part of our current K-12 education. In this paper, we extend the van Hiele model of spatial reasoning using Piaget\u27s theory of representational space. By merging these two existing theories, we are able to place topological concepts in a context that is age appropriate

What in the World Just Happened? Students’ Self-Regulation in Asynchronous PreCalculus During the COVID-19 Pandemic

We describe students’ learning practices in an online asynchronous PreCalculus course during Fall 2020, the first complete semester of distance learning induced by the COVID-19 pandemic. Results were compiled using a thematic analysis of a questionnaire administered to 43 students enrolled in PreCalculus at a university in the Midwest (United States). Students were given opportunities for active learning and various synchronous Q&A sessions, yet they primarily learned through watching videos and reading worked examples, minimizing interactions with the instructor and available tutors. The questionnaire results show that students knew active learning was helpful, but they were unable to curtail unproductive learning practices. The questionnaire also showed that students struggled to stay motivated and keep to a schedule. We conclude that by developing their study techniques and self-regulatory habits, students will be able to take more control over their learning, particularly in asynchronous classes

The Administration and Supervision Program in the Department of Leadership, Foundations, and Policy, Curry School of Education, University of Virginia

The Department of Leadership, Foundations, and Policy at the University of Virginia is designed to meet the demand for educational leaders who can combine vision and practice. It houses three integrated academic units: leadership; foundations; and policy. The leadership programs prepare leaders who are committed to social justice and formal education as a means of personal and civic improvement. Graduates of the programs go on to careers in school administration as well as university careers. Graduate students of the educational foundations programs learn concepts and skills related to research and evaluation, human development, learning and motivation, social and cultural contexts of education, multicultural education, new information technologies and education of gifted and talented students. They go on to careers in college teaching, research, instructional technology and administration. The policy studies programs are designed to help students understand and master the processes by which social, political and economic forces influence education policy. Graduates of these programs commonly assume positions in local, state and national or international agencies and organizations

Topological structure of the space of composition operators on L∞L^\infty of an unbounded, locally finite metric space

We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we characterize the compactness of differences of two such composition operators.Comment: in submissio

Electrical Control of Linear Dichroism in Black Phosphorus from the Visible to Mid-Infrared

The incorporation of electrically tunable materials into photonic structures such as waveguides and metasurfaces enables dynamic control of light propagation by an applied potential. While many materials have been shown to exhibit electrically tunable permittivity and dispersion, including transparent conducting oxides (TCOs) and III-V semiconductors and quantum wells, these materials are all optically isotropic in the propagation plane. In this work, we report the first known example of electrically tunable linear dichroism, observed here in few-layer black phosphorus (BP), which is a promising candidate for multi-functional, broadband, tunable photonic elements. We measure active modulation of the linear dichroism from the mid-infrared to visible frequency range, which is driven by anisotropic quantum-confined Stark and Burstein-Moss effects, and field-induced forbidden-to-allowed optical transitions. Moreover, we observe high BP absorption modulation strengths, approaching unity for certain thicknesses and photon energies

For the Love of Inner Voices: Miriam Gideon, Orchestration, and Fortunato

Post-tonal American opera composer Miriam Gideon (1906-1996) completed a chamber opera, perhaps intended for television, titled Fortunato, based on a dark comic tragedy set in turn-of-the-20th-century, economically-ravaged Madrid. The expressive staged work follows the life of the unfortunate title character Fortunato in three operatic vignettes, each one becoming more desperate and moribund by the scene. A curious piece in Gideon’s oeuvre, the work remained unfinished, with a piano score for the complete work, but only a sample of her orchestration for Scene 1. This study examines the orchestration of Scene 1 as a template for creating an orchestration similar in style for the subsequent two scenes. After outlining her orchestrational tendencies in her work at large, and within the specific world of Fortunato, I conduct a close analysis of the ways in which she uses timbre and tone color of the individual instruments of the orchestra to inform my own orchestrational decisions for Scenes 2 and 3. Importantly this dissertation contains a substantial appendix with a full score to Gideon’s Fortunato and the accompanying orchestral parts to invite other performances of this work, one that deserves a permanent place in the canon of 21st century, contemporary (and post-tonal) opera