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Elegance Or Alchemy? An International Cross-Case Analysis Of Faculty And Graduate Student Perceptions Of Mathematical Proofs, Brooke Nicole Denney

Masters Theses

Artist Marcel Duchamp once said, ``The painter is a medium who doesn’t realize what he is doing. No translation can express the mystery of sensibility, a word, still unreliable, which is nonetheless the basis of painting or poetry, like a kind of alchemy" (Moffitt, 2012). Just as there is a puzzling aspect of creating art or writing poetry, the aesthetic quality of mathematical proofs is a mysterious and ill-defined concept. Like many other subjective terms, it can be difficult to reach a consensus on what elegance means in a mathematical context. In this thesis, I try to better understand faculty …

Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, Liet Vo

Doctoral Dissertations

This dissertation consists of three main parts with each part focusing on numerical approximations of the stochastic Stokes and Navier-Stokes equations.

Part One concerns the mixed finite element methods and Chorin projection methods for solving the stochastic Stokes equations with general multiplicative noise. We propose a modified mixed finite element method for solving the Stokes equations and show that the numerical solutions converge optimally to the PDE solutions. The convergence is under energy norms (strong convergence) for the velocity and in a time-averaged norm (weak convergence) for the pressure. In addition, after establishing the error estimates in second moment, high …

Mathematical Modeling Suggests Cooperation Of Plant-Infecting Viruses, Joshua Miller, Vitaly V. Ganusov, Tessa Burch-Smith

Chancellor’s Honors Program Projects

No abstract provided.

Recruiting Minoritized Mathematics Preservice Teachers With Retention In Mind, Nicholas Scott Kim

Doctoral Dissertations

The primary purpose of this research is to provide insight into the narratives and experiences of minoritized preservice teachers (PST) interested in teaching mathematics and how those experiences impact recruitment and retention of those minoritized teachers. “Minoritized,” as used here, is defined as one who identifies as a person from a historically underserved community based on race or ethnicity. As a result, this study is positioned to provide researchers, educators, and administrators with much needed direction into how to diversify the teaching force beyond the dominant storyline of the White majority, and why it is important to do so.

Narrative …

Assessing The Impact Of Picture Books In Primary Grades Mathematics Instruction, Jessica Stone

Doctoral Dissertations

This study documents an educational field experiment evaluating the effects of picture books on primary students’ mathematical achievement and their dispositions towards mathematics. The study involved 136 primary grade students from one elementary school in the southeastern region of the United States. The student population had an overrepresentation of students from minority backgrounds (91%), low socioeconomic status (93%) and English Language Learners (47%). During the 18-week treatment period, teacher participants from the treatment group received bi-weekly collaborative professional development regarding the use of picture books in mathematics instruction. The teachers in the control group followed their district’s mathematics curriculum.

To …

Undergraduate Motivations For Choosing A Science, Technology, Engineering, Or Mathematics (Stem) Major, Preston Taylor Mitchell

Chancellor’s Honors Program Projects

No abstract provided.

Loewner Space-Filling Curves, Hannah Marie Clark

Chancellor’s Honors Program Projects

No abstract provided.

Fully Coupled Fluid And Electrodynamic Modeling Of Plasmas: A Two-Fluid Isomorphism And A Strong Conservative Flux-Coupled Finite Volume Framework, Richard Joel Thompson

Doctoral Dissertations

Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models …

Implications For Ability Grouping In Mathematics For Fifth Grade Students, Anne M. Stinnett

Masters Theses

This study examines the effects of ability grouping on fifth grade students at 47 elementary schools in a large urban school district. Using disaggregated standardized test data that statistically measures achievement growth, this study analyzes gains among students assigned to prior achievement quintiles as compared to three grouping strategies: homogeneous, heterogeneous with special classes for advanced and special education, and heterogeneous ability groups.

The findings suggest that the grouping strategies used in these schools are effective for the students at these schools. Most significant is that, on average, low achieving schools are grouping students in ways that are exhibiting positive …

The Impact Of Analyzing Correct Versus Incorrect Student Work Samples On Students’ Learning Mathematics, Lauren Jeneva Moseley

Doctoral Dissertations

The purposes of this study are to determine if learning differs when calculus learners analyze correct or incorrect work samples and to investigate students’ perceptions of the effect of analyzing work samples on their learning of mathematics. Calculus students were randomly assigned to two groups: one group analyzing correct work samples and one group analyzing incorrect work samples. Data from enrollees in 10 sections of Basic Calculus at a large university was analyzed using ANCOVA, independent-samples t-test, and inductive analysis (Hatch, 2002). Results suggest that when students analyze incorrect work samples of moderate difficulty, they are less likely to …

Orderly Ε-Homotopies Of Discrete Chains, Alexander Thomas Happ

Chancellor’s Honors Program Projects

No abstract provided.

A Validation Of The Monitoring Academic Progress Mathematics: An Experimental Multidimensional Group Administered Curriculum-Based Measure Of Mathematics Fluency And Problem Solving, Michael Brandon Hopkins

Doctoral Dissertations

The study investigated the psychometric properties of a newly developed math curriculum-based measure, the Monitoring Academic Progress: Mathematics (MAP:M), through examination of its internal consistency, alternate-form, slope, and test-retest reliability and validity. Participants included 1688 first through third-grade students from a school district in Northeast Tennessee. Application of Generalizability Theory produced reliability coefficients, score variances, and standard-error-of-measures (SEM) for both absolute and relative decisions based on a particular number of probes. MAP:M reliability coefficients for relative decisions ranged from .67 to .97 across eleven probes. The highest percentage of score variance at all three grades was attributed to the Person …

The Impact Of Secondary Mathematics Methods Courses On Preservice Secondary Teachers’ Beliefs About The Learning And Teaching Of Mathematics, Ronald Gene Smith Ii

Doctoral Dissertations

The Comprehensive Framework for Teacher Knowledge provides a model that describes an approach to the secondary mathematics methods course, as described by Robert Ronau and P. Mark Taylor. The model includes the orientation of preservice teachers toward mathematics and the teaching of mathematics, which includes the beliefs of the preservice teachers. The first questions deal with identifying the methods used in the methods course to address beliefs. The second set of questions deal with the effects of the methods course on the beliefs that preservice teachers hold on the learning and teaching of mathematics.

The study included 16 different universities …

Affective Socialization Processes In Mathematics Doctoral Study: Gaining Insight From Successful Students, Lauren L Wagener

Doctoral Dissertations

Mathematics has the highest attrition rate among all liberal arts disciplines (and among all disciplines, except for health professions) and the second highest attrition rate of all doctoral programs in the United State. In order to prevent the loss of so many students, mathematics departments must consider the root causes for attrition and determine what individual skills and knowledge and departmental systems and support will help more mathematics doctoral students to succeed. The purpose of this qualitative interview study was to explore the interactions mathematics doctoral candidates at one institution have had during graduate school and the value that the …

Creating And Validating An Instrument To Measure Middle School Mathematics Teachers’ Technological Pedagogical Content Knowledge (Tpack), Geri A. Landry

Doctoral Dissertations

Due to the pervasiveness of technology, the role and preparation of teachers as they strategically use technology for teaching mathematics needs to be examined. Technological pedagogical content knowledge (TPACK) is a framework for knowledge as teachers develop meaningful learning experiences for their students while integrating strategic use of technology (Mishra & Koehler, 2006). The purpose of this study was to develop a survey for measuring mathematics teachers’ Mathematical Technological Pedagogical Content Knowledge (M-TPACK). The survey measures the domains of mathematics content, pedagogy and technology. This mixed methods study first examined middle school mathematics teachers’ TPACK through the use of an …

Covering Maps In The Uniform Category, Brendon L. Labuz

Doctoral Dissertations

First, generalized uniform covering maps are classified in terms of subgroups of the uniform fundamental group. Hausdorff, locally uniform joinable, and chain connected covering spaces of a uniformly locally joinable chain connected space are classifieded in terms of closed subgroups of its uniform fundamental group. If the space is also semilocally simply uniform joinable, uniform covering spaces are classified in terms of all subgroups of its uniform fundamental group. Next it is shown that the inverse limit of a strong Mittag-Leer inverse system of Hausdorff uniform covering spaces is a generalized uniform covering space. The question of the converse is …

Numerical Methods For Fully Nonlinear Second Order Partial Differential Equations, Michael Joseph Neilan

Doctoral Dissertations

This dissertation concerns the numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). The numerical methods and analysis are based on a new concept of weak solutions called moment solutions, which unlike viscosity solutions, are defined by a constructive method called the vanishing moment method. The main idea of the vanishing moment method is to approximate fully nonlinear second order PDEs by a family of fourth order quasi-linear PDEs. Because the method is constructive, we can develop a wealth of convergent numerical discretization methods to approximate fully nonlinear second order PDEs. We first study the numerical …

Nonlinear Dissipative Wave Equations With Space-Time Dependent Potentials, Maisa Khader

Doctoral Dissertations

We study the long time behavior of solutions of the wave equations with absorption abs (u(t, x))[superscript p]⁻¹u(t, x) and variable damping a(t, x)u[subscript t](t, x), where p belongs to (1, n + 2/n - 2) and a(t, x) ~ a₀(1 + abs(x))⁻[superscript alpha](1 + t)⁻[superscript beta] for large abs x and t, a₀ > 0, for alpha belongs to (-infinity, 1), beta belongs to (-1, 1). We established decay estimates for the energy, L² and L[superscript p]⁺¹ norm of the solutions. 1. For alpha belongs to [0, 1), beta belongs to (-1, 1) and alpha + beta belongs to (0, …