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The effects of a framework for procedural understanding on college algebra students' procedural skill and understanding: Author: Hasenbank, Jon Fredrick; Date: 2006-05-15; Program: Mathematics; Abstract: This dissertation examined the effectiveness of an instructional treatment consisting of lecture content, homework tasks, and quiz assessments built around a common Framework for Procedural Understanding. The study addressed concerns about increasing numbers of students enrolling in remedial Mathematics courses because they did not develop sufficient understanding in previous courses. The Framework-oriented instruction was designed to help students develop deep and well-connected knowledge of procedures, which has been shown to facilitate recall and promote future learning. Data collection spa...; Download File | View full details

An examination of the integration of graphing calculators in formal assessments that accompany high school Mathematics textbooks: Author: Graham, Kimberly Joy; Date: 2005-05-15; Program: Mathematics; Abstract: To support teachers in their efforts to integrate graphing calculator technology in the assessment of student learning, Mathematics educators need to know the extent and the quality of graphing calculator usage in assessment materials that accompany published Mathematics textbooks. If improved student understanding through the use of graphing calculators is a goal of the curriculum and if the use of graphing calculators as recommended by the Principles and Standards (NCTM, 2000) is truly valued, but graphing calculators are not integrated into assessments, then this fact demonstrates a lack of...; Download File | View full details

Return Map Characterizations of Singular Solutions for a Model of Bursting with Two Slow Variables: Author: Griffiths, Roger Evan; Date: 2003-05-15; Program: Mathematics; Abstract: Various physiological systems display bursting electrical activity (BEA). There exist numerous three variable models to describe this behavior. However, four variables may be required to explain some qualitative features of BEA. In this dissertation a model with two slow and two fast variables is presented. For some parameter values the system has stable equilibria while for other values there exist bursting solutions. A singular construction of the latter solutions corresponds to the existence of a fixed point of a one dimensional map. The map is the composition of two maps derived from the s...; Download File | View full details

The Sinc-Galerkin Method for Problems in Oceanography: Author: Koonprasert, Sanoe; Date: 2003-12-15; Program: Mathematics; Abstract: The model for a wind-driven current with depth-dependent eddy viscosity is developed as a complex velocity formulation and a coupled system formulation. The numerical solutions, calculated by a Sinc-Galerkin method, are compared. A fully Sinc-Galerkin method in both space and time for a partial differential equation with time-dependent boundary conditions is developed. This entirely new technique is applied to the model for a wind-driven current with time-dependent viscosity. Several numerical examples are used to test the performance of the method. This fully Sinc-Galerkin method is then appl...; Download File | View full details

Using asynchronous discussions to facilitate collaborative problem solving in college algebra: Author: Kosiak, Jennifer Jean; Date: 2004-08-15; Program: Mathematics; Abstract: This research study was conducted to investigate the nature and quality of online mathematical communication that occurred during collaborative problem solving and its effect on mathematical achievement in college algebra. Two intact sections of college algebra were randomly assigned to either a treatment group (online group work) or control group (individual seatwork). Both sections of college algebra met face-to-face and were taught by the same instructor. Students in the treatment group (n = 26) were placed into six collaborative groups. Four week-long online tasks designed according to the...; Download File | View full details

Generic properties of the infinite population genetic algorithm: Author: Hayes, Christina Savannah Maria; Date: 2006-08-15; Program: Mathematics; Abstract: The infinite population model for the genetic algorithm, where the iteration of the genetic algorithm corresponds to an iteration of a map G, is a discrete dynamical system. The map G is a composition of a selection operator and a mixing operator, where the latter models the effects of both mutation and crossover. This dissertation examines the finiteness and hyperbolicity of fixed points of this model. For a typical mixing operator, the fixed point set of G is finite and all fixed points are hyperbolic....; Download File | View full details

Analysis and control of a biofilm disinfection model: Author: Szomolay, Barbara; Date: 2006-12-15; Program: Mathematics; Abstract: The goal of this dissertation is to study a complex biofilm model with a phenotypic structure presented in [34]. The model in [34] is extended - growth and detachment is added, making the new model more interesting in applications. The crucial feature of our model is that cells are able to enter an adapted resistant state when challenged with antimicrobials (adaptation). We study this model in both a qualitative and quantitative manner. Existence and uniqueness of solutions is shown as well as the existence and non-uniqueness of steady-state solutions. Another question of interest is the effec...; Download File | View full details

Environments that encourage Mathematics graduate teaching assistants: the effects of institution type and availability of training: Author: Latulippe, Christine Lynn; Date: 2007-05-15; Program: Mathematics; Abstract: This dissertation examined factors which are related to Mathematics graduate teaching assistants' (GTAs') teaching attitudes and perceptions of the support for good teaching in their respective math departments. The research questions addressed differences between math GTAs at four groups of universities, categorized using an institution's Carnegie Classification and the availability of teacher-training for GTAs, in regard to math GTA perceptions of the support for good teaching in their department and in regard to math GTA attitudes toward teaching. Additionally, correlations between math GTA...; Download File | View full details

A Non-Autonomous Bursting Model for Neurons: Author: Latulippe, Joe Jean-Marc; Date: 2007-05-15; Program: Mathematics; Abstract: Certain mammalian visual neurons exhibit On and Off responses when given a light stimulus. In addition to these responses, [51] showed that for retinal ganglion cells, the neuron will also exhibit a Mixed response when given two simultaneous stimuli in different regions of the cell's receptive field. This Mixed response is a nonlinear combination of the On and Off responses. In this dissertation, a single cell model which can reproduce On, Off, and Mixed responses is developed and examined using leading order analyses and averaging. This model is developed from a current balance equation which...; Download File | View full details

Preservice Elementary Teachers' Mathematical Content Knowledge of Prerequisite Algebra Concepts: Author: Welder, Rachael Mae; Date: 2007-05-15; Program: Mathematics; Abstract: Research illustrating that student achievement is affected by teachers' knowledge advocates for K-8 teachers to be knowledgeable regarding prerequisite algebra concepts: (1) numbers (numerical operations), (2) ratios/proportions, (3) the order of operations, (4) equality, (5) patterning, (6) algebraic symbolism (including letter usage), (7) algebraic equations, (8) functions, and (9) graphing. The theoretical framework for the knowledge for teaching Mathematics built for this study suggests that the mathematical content knowledge needed for teaching consists of specialized content knowledge in...; Download File | View full details

The use of computer algebra systems in a procedural algebra course to facilitate a framework for procedural understanding: Author: Harper, Jonathan Lee; Date: 2007-08-15; Program: Mathematics; Abstract: This dissertation study evaluated the implementation and effectiveness of an introductory algebra curriculum designed around a Framework for Procedural Understanding. A Computer Algebra System (CAS) was used as a tool to focus lessons on the Framework and help students gain a deeper, well-connected understanding of algebraic procedures. This research was conducted in response to the prevalence of remedial Mathematics and addresses the need for students in remedial Mathematics to have a successful learning experience. The curriculum was implemented in the Spring 2007 semester at a western land-...; Download File | View full details

Cognitive presence among Mathematics teachers: an analysis of tasks and discussions in an asynchronous online graduate course: Author: Colt, Diana Lynn; Date: 2008-05-15; Program: Mathematics; Abstract: Higher order learning, in terms of both process and outcome, is frequently cited as the goal of higher education (Garrison, Anderson, & Archer, 2000). However, the adoption of computer mediated communication in higher education has far outpaced our understanding of how this medium can best be used to promote higher order learning (Garrison, Anderson, & Archer, 2004). Researchers have examined quantitative components of computer mediated communication, but little work has been done to examine the cognitive aspects of online discussion. Those studies that do exist demonstrate inconsisten...; Download File | View full details

Teachers' beliefs regarding effective teaching strategies for American Indian students in Mathematics: Author: Vallines Mira, Raquel; Date: 2008-08-15; Program: Mathematics; Abstract: Extensive research has been conducted on teaching strategies that are effective for American Indians in Mathematics. Despite the variety of cultural, linguistic, socioeconomic, and geographic factors influencing student learning within and among American Indian communities, common characteristics of learning styles and effective teaching practices have been identified. Though the wording in each definition varies, research based on a variety of theoretical frameworks and using a variety of methodologies and instruments suggests that among American Indian students, there is a tendency to learn ...; Download File | View full details

An alternating-direction Sinc-Galerkin method for elliptic problems on finite and infinite domains: Author: Alonso, Nicomedes III; Date: 2009-05-15; Program: Mathematics; Abstract: Alternating-Direction Implicit (ADI) schemes are a class of very efficient algorithms for the numerical solution of differential equations. Sinc-Galerkin schemes employ a sinc basis to produce exponentially accurate approximate solutions to differential equations even in the presence of singularities. In this dissertation we begin with a broad overview of sinc methods for problems posed on both finite and infinite, one- and two-dimensional domains. We then present a variety of finite difference methods that lead to the introduction of a new Alternating-Direction Sinc-Galerkin scheme based on t...; Download File | View full details

Action research in Mathematics education: a study of a master's program for teachers: Author: Segal, Sarah Ultan; Date: 2009-05-15; Program: Mathematics; Abstract: Action research is a methodology that has been found to be valuable as a problem-solving tool. It can provide opportunities for reflection, improvement, and transformation of teaching. The purpose of this study is to better understand these claims about the benefits of action research. Several research questions stand out: How is action research experienced by teachers? Is it beneficial and practical for teachers who use it? How are action research findings typically validated? What factors influence whether teachers are able to continue to practice action research? What kind of change has it ...; Download File | View full details

Classical mechanics with dissipative constraints: Author: Harker, Shaun Russell; Date: 2009-08-15; Program: Mathematics; Abstract: The aim of this thesis is to consider the mathematical treatment of mechanical systems in the presence of constraints which are energetically dissipative. Constraints may be energetically dissipative due to impacts and friction. In the frictionless setting, we generalize Hamilton's principle of stationary action, central to the Lagrangian formulation of classical mechanics, to reflect optimality conditions in constrained spaces. We show that this generalization leads to the standard measure-theoretic equations for shocks in the presence of unilateral constraints. Previously, these equations we...; Download File | View full details

Gene regulation in the lac operon: Author: Patterson, Kathryn Grace; Date: 2009-08-15; Program: Mathematics; Abstract: The lac operon, a jointly controlled series of genes in the bacteria E. coli, has been studied extensively since the 1940's. The lac operon genes are transcribed and then translated into proteins necessary for transport and digestion of lactose. The operon is activated in the presence of lactose after glucose, the preferred carbon source, has been expended. In this thesis, we introduce a biophysical model using the Shea-Ackers framework for modeling promoter dynamics. The model spans two scales: the inputs are biophysical parameters of molecular interactions and the result is a level of gene e...; Download File | View full details

Multicellular mathematical models of somitogenesis: Author: Campanelli, Mark Benjamin; Date: 2009-12-15; Program: Mathematics; Abstract: Somitogenesis is an important pattern formation process in the developmental biology of vertebrates. The phenomenon has received wide attention from experimental, theoretical, and computational biologists. Numerous mathematical models of the process have been proposed, with the clock and wavefront mechanism rising to prominence over the last ten years. This work presents two multicellular mathematical models of somitogenesis. The first is a phenomenological phase oscillator model that reproduces both the clock and wavefront aspects of somitogenesis, but lacks a biological basis. The second is ...; Download File | View full details

Determining the biomechanical response of a filiform hair array: a low Reynolds number fluid-structure model: Author: Cummins, Breschine; Date: 2009-12-15; Program: Mathematics; Abstract: A model system that has been the subject of many anatomical, developmental, functional, and theoretical studies over the last 30 years is the cercal sensory system of the cricket. This system is composed of two antenna-like appendages covered with hundreds of filiform mechanosensory hairs, and encodes information about the direction and dynamics of low-velocity air currents. The encoding is determined by the biomechanical properties of the mechanosensory hairs. These properties are poorly understood, primarily because accurate experimental measurements of the air-current-driven movements of th...; Download File | View full details

A study of the relationship between introductory calculus students' understanding of function and their understanding of limit: Author: Jensen, Taylor Austin; Date: 2009-12-15; Program: Mathematics; Abstract: Introductory calculus students are often successful in doing procedural tasks in calculus even when their understanding of the underlying concepts is lacking, and these conceptual difficulties extend to the limit concept. Since the concept of limit in introductory calculus usually concerns a process applied to a single function, it seems reasonable to believe that a robust understanding of function is beneficial to and perhaps necessary for a meaningful understanding of limit. Therefore, the main goal of this dissertation is to quantitatively correlate students' understanding of function and t...; Download File | View full details

The design, implementation, and evaluation of a teacher training workshop for Mathematics graduate teaching assistants: Author: Trouba, Jerome Charles; Date: 2009-12-15; Program: Mathematics; Abstract: To help train new graduate Mathematics teaching assistants (GMTAs), a teacher training workshop was designed based on K-12 literature on the components of effective professional development (Garet, et al., 2001). The workshop consisted of six two-hour seminars over a six week period followed by a classroom feedback component of either peer coaching or observation, for a total time commitment of 18 hours. The content of the workshop addressed teaching techniques specifically targeted to GMTAs. These ideas included elements of reflection, techniques for engaging students through active learning,...; Download File | View full details

The branch locus for two dimensional tiling spaces: Author: Olimb, Carl Andrew; Date: 2010-08-15; Program: Mathematics; Abstract: We explore the asymptotic arc components made by the continuous R²-action of translation on two-dimensional nonperiodic substitution tiling spaces. As there is a strong connection between the topology of a tiling space and the tiling dynamics that it supports, the results in this dissertation represent a qualitative approach to the study of tiling dynamics. Our results are the establishment of techniques to isolate and visualize the asymptotic behavior. In a recent paper, Barge, et al, showed the cohomology formed from the asymptotic structure in one-dimensional Pisot substitution ...; Download File | View full details

Implementing professional development: a case study of Mathematics teachers using inquiry in the classroom context: Author: Mathison, Heather Renee; Date: 2011-05-15; Program: Mathematics; Abstract: A body of research supports the use of inquiry-based instruction in science and its use has been advocated in Mathematics, but mathematical inquiry remains ill defined and difficult to enact in the Mathematics classroom. While helpful, simply valuing inquiry as a learning tool is not sufficient to enable teachers to implement it successfully with their students. In part, the trouble with using inquiry may arise from the fact that teachers received insufficient exposure to inquiry when they were students themselves. The purpose of this case study was to examine how a sample of four teachers who...; Download File | View full details

Computing multifractal spectra via simplicial measures: Author: Berwald, Jesse James; Date: 2011-12-15; Program: Mathematics; Abstract: Complex dynamical systems occur on many scales in the natural world, and serve as rich subjects of study. Examples include ecosystems, physiological systems, and financial markets. Simplified versions of these system can be described by dynamical systems. As such, understanding the qualitative behavior of dynamical systems provides an important window into real-world phenomena. In this manuscript we focus on the qualitative behavior described by the measure concentrated on the attractor of a dynamical system. A common way to study such complicated measures is through their multifractal spectra...; Download File | View full details

Rotation and dynamics for simple solenoidal maps of Tori: Author: Mathison, Mark Tyler; Date: 2012-05-15; Program: Mathematics; Abstract: The rotation number for a circle map has provided a complete and useful classification for that class of maps. In higher dimensions there is still progress to be made towards obtaining a more complete understanding of the relationship between the map and its average rotation. In this dissertation, we explore a class of homeomorphisms on the d dimensional torus T d that preserve each leaf of a foliation of the torus into parallel lines densely winding on T d. First the rotation sets of such maps are explored, with particular emphasis on those maps that have a single fixed point; zero is necessa...; Download File | View full details

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