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- Creators: Spielberg, John
Description
In this thesis, I investigate the C*-algebras and related constructions that arise from combinatorial structures such as directed graphs and their generalizations. I give a complete characterization of the C*-correspondences associated to directed graphs as well as results about obstructions to a similar characterization of these objects for generalizations of directed graphs. Viewing the higher-dimensional analogues of directed graphs through the lens of product systems, I give a rigorous proof that topological k-graphs are essentially product systems over N^k of topological graphs. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with the similarly-named conditions for topological k-graphs and for the associated product systems over N^k of C*-correspondences. Finally I consider the constructions arising from topological dynamical systems consisting of a locally compact Hausdorff space and k commuting local homeomorphisms. I show that in this case, the associated topological k-graph correspondence is isomorphic to the product system over N^k of C*-correspondences arising from a related Exel-Larsen system. Moreover, I show that the topological k-graph C*-algebra has a crossed product structure in the sense of Larsen.
ContributorsPatani, Nura (Author) / Kaliszewski, Steven (Thesis advisor) / Quigg, John (Thesis advisor) / Bremner, Andrew (Committee member) / Kawski, Matthias (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2011
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
Studies have shown that arts programs have a positive impact on students' abilities to achieve academic success, showcase creativity, and stay focused inside and outside of the classroom. However, as school funding drops, arts programs are often the first to be cut from school curricula. Rather than drop art completely, general education teachers have the opportunity to integrate arts instruction with other content areas in their classrooms. Traditional fraction lessons and Music-infused fraction lessons were administered to two classes of fourth-grade students. The two types of lessons were presented over two separate days in each classroom. Mathematics worksheets and attitudinal surveys were administered to each student in each classroom after each lesson to gauge their understanding of the mathematics content as well as their self-perceived understanding, enjoyment and learning related to the lessons. Students in both classes were found to achieve significantly higher mean scores on the traditional fraction lesson than the music-infused fraction lesson. Lower scores in the music-infused fraction lesson may have been due to the additional component of music for students unfamiliar with music principles. Students tended to express satisfaction for both lessons. In future studies, it would be recommended to spend additional lesson instruction time on the principles of music in order help students reach deeper understanding of the music-infused fraction lesson. Other recommendations include using colorful visuals and interactive activities to establish both fraction and music concepts.
ContributorsGerrish, Julie Kathryn (Author) / Zambo, Ronald (Thesis director) / Hutchins, Catherine (Committee member) / Division of Teacher Preparation (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
There are two types of understanding when it comes to learning math: procedural understanding and conceptual understanding. I grew up with a rigorous learning curriculum and learned math through endless drills and practices. I was less motivated to understand the reason behind those procedures. I think both types of understanding are equally important in learning mathematics. Procedural fluency is the "ability to apply procedures accurately, efficiently, and flexibly... to build or modify procedures from other procedures" (National Council of Teachers of Mathematics, 2015). Procedural understanding may perceive as merely about the understanding of the arithmetic and memorizing the steps with no understanding but in reality, students need to decide which procedure to use for a given situation; here is where the conceptual understanding comes in handy. Students need the skills to integrate concepts and procedures to develop their own ways to solve a problem, they need to know how to do it and why they do it that way. The purpose of this 5-day unit is teaching with conceptual understanding through hands-on activities and the use of tools to learn geometry. Through these lesson plans, students should be able to develop the conceptual understanding of the angles created by parallel lines and transversal, interior and exterior angles of triangles and polygons, and the use of similar triangles, while developing the procedural understanding. These lesson plans are created to align with the eighth grade Common Core Standards. Students are learning angles through the use of protractor and patty paper, making a conjecture based on their data and experience, and real-life problem solving. The lesson plans used the direct instruction and the 5E inquiry template from the iTeachAZ program. The direct instruction lesson plan includes instructional input, guided practice and individual practice. The 5E inquiry lesson plan has five sections: engage, explore, explain, elaborate and evaluate.
ContributorsLeung, Miranda Wing-Mei (Author) / Kurz, Terri (Thesis director) / Walters, Molina (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
This project and research intended to address how to successfully run and teach a high school level Theatre I course. The research portion of the project focused on activities to use in the classroom, how to run a drama club and put on productions, and how to create a positive classroom environment where students feel comfortable creating art. The creation portion of the project focused on the things a teacher will need in the classroom: an introduction letter, vision statement, syllabus, and unit plans. The final product includes three unit plans: Introduction to Theatre I, Introduction to Acting, and Theatre and Social Change. The use of the materials in this thesis can help first-time Theatre teachers to become better prepared to run their classroom.
ContributorsKircher, Alyssa Elaine (Author) / Sterling, Pamela (Thesis director) / Whissen, Elaine (Committee member) / Saldana, Johnny (Committee member) / Barrett, The Honors College (Contributor) / School of Film, Dance and Theatre (Contributor) / Division of Teacher Preparation (Contributor)
Created2014-05
Description
The specific focus of the curriculum guide is to encourage inquiry and exploration of sustainability with middle school students. Children need to be explicitly taught how to analyze findings, how to work together, and teachers need to begin to lay the foundation of finding ideal solutions that best serve all people. The sooner that we introduce our students to these concepts in conjunction with science concepts the better prepared they will be to face the upcoming challenges and the better developed their scientific literacy.
ContributorsSibley, Amanda Marie (Author) / Walters, Molina (Thesis director) / Oliver, Jill (Committee member) / Kurz, Terri (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2014-05
Description
The action/adventure game Grad School: HGH is the final, extended version of a BME Prototyping class project in which the goal was to produce a zombie-themed game that teaches biomedical engineering concepts. The gameplay provides fast paced, exciting, and mildly addicting rooms that the player must battle and survive through, followed by an engineering puzzle that must be solved in order to advance to the next room. The objective of this project was to introduce the core concepts of BME to prospective students, rather than attempt to teach an entire BME curriculum. Based on user testing at various phases in the project, we concluded that the gameplay was engaging enough to keep most users' interest through the educational puzzles, and the potential for expanding this project to reach an even greater audience is vast.
ContributorsNitescu, George (Co-author) / Medawar, Alexandre (Co-author) / Spano, Mark (Thesis director) / LaBelle, Jeffrey (Committee member) / Guiang, Kristoffer (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
Description
The study compares the pretest and posttest results of three groups of second-grade students studying a phonics rule to determine the effect of using music as an instructional aid. For two groups in the study, the teachers used melodies to instruct students, while the third group was held to direct instruction with no music to use for assistance. The study groups were three second-grade classes at Ishikawa Elementary School, where I was serving as a student teacher. Parental consent was received for each of the students participating in the study. The duration of the study was one week. The first test group was given a familiar melody with new lyrics to reflect the content of the phonics rule "I before E except after C." The second test group was given a melody composed specifically to accompany the phonics rule and to reflect the appropriate phonics content. On the first day of the study, students were given a pretest; these scores were recorded and then compared to the posttest scores from the end of the week. The data that were collected compared groups as a whole through composite scores from pretest to posttest to determine most effective methodology. The groups that were instructed using music demonstrated greater growth and had higher posttest scores.
ContributorsFrazee, Madison Marie (Author) / Schildkret, David (Thesis director) / Stauffer, Sandy (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2014-12
Description
Continue to Teach is a project motivated by the alarming rates of teacher attrition in Arizona and across the United States. The product is in the form of a website that gives current and future teachers resources in attempts to support them. The goal of providing these virtual resources is to positively influence teachers to stay in the profession. Each of the subsections of the website were thoughtfully selected based on extensive consideration of the research literature of the factors driving teachers' decisions to remain or leave the profession. I was personally motivated to complete this project because I am studying and practicing to become a teacher. Completing this research and project has compelled me to learn a great amount about the challenges surrounding this profession, and has assisted me in determining what I can do to stay personally motivated while helping others continue to teach as well.
ContributorsMoore, Rachael Edda (Author) / Panneton, Teresa (Thesis director) / Carman-Smith, Aaron (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This course will cover the history, ethics and impact of the fair trade movement for a variety of stakeholders in the Global South and Global North. We will be participating in various activities that will acquaint us with different topics, including globalization, the gender wage gap, environmental degradation and supply chain management. Guest speakers from the fair trade community will contribute their perspectives regarding the movement. Students will gain an understanding of the tradeoffs of the fair trade movement for the different actors throughout the length of the supply chain. Students will describe the purpose of the fair trade movement and who it seeks to serve. Students will explain what the Fair Trade certification entails for the actors who engage in the system. Students will debate the tradeoffs of the fair trade movement, incorporating the perspectives of multiple stakeholders from both the Global South and Global North. Finally, students will evaluate Fair Trade as a tool for sustainability both socially and economically.
ContributorsSimari, Daniella Jayne (Author) / Eakin, Hallie (Thesis director) / Walters, Molina (Committee member) / School of Life Sciences (Contributor) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05