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Exploring Some Inattended Affective Factors In Performing Nonroutine Mathematical Tasks, John Douglas Butler

Master's Theses, Dissertations, Graduate Research and Major Papers Overview

Describes students' attempts to solve nonroutine math problems and explores possible correlates of their performance, focusing on inattended (i.e., intentionally avoided) dimensions underrepresented in the literature, including attitudes, interests, values, aesthetics, metacognition, and representation. Analyzes objective and subjective data gathered from a sample of 9th-grade students at a high school in Rhode Island. Finds strong evidence of students' math-aesthetics in problem solving.

Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr.

Doctoral Theses

Topological and geometric methods have played a major role in the study of infinite groups since the time of Poincar´e and Klein, with the work of Nielsen, Dehn, Stallings and Gromov showing particularly deep connections with the topology of surfaces and three-manifolds. This is in part because a surface or a 3-manifold is essentially determined by its fundamental group, and has a geometric structure due to the Poincar´e-K¨obe-Klein uniformisation theorem for surfaces and Thurston’s geometrisation conjecture, which is now a theorem of Perelman, for 3-manifolds.A particularly fruitful instance of such an interplay is the relation between intersection numbers of simple …

Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz

Theses and Dissertations

In recent years, multimedia identification has become important as the volume of digital media has dramatically increased. With music files, one method of identification is audio fingerprinting. The underlying method for most algorithms is the Fourier transform. However, due to a lack of temporal resolution, these algorithms rely on the short-time Fourier transform. We propose an audio fingerprinting algorithm that uses a wavelet transform, which has good temporal resolution. In this thesis, we examine the basics of certain topics that are needed in understanding audio fingerprinting techniques. We also look at a brief history of work done in this field. …

Geometric Characterization Of Digital Objects: Algorithms And Applications To Image Analysis., Arindam Biswas Dr.

Doctoral Theses

Several problems of characterizing a digital object, and particularly, those related to boundary description, have been studied in this thesis. New algorithms and their applications to various aspects of image analysis and retrieval have been reported. A combinatorial technique for constructing the outer and inner isothetic covers of a digital object has been developed. The resolution of the background 2D grid can be changed by varying the grid spacing, and this procedure can be used to extract shape and topological information about the object. Next, an algorithm has been designed for constructing the orthogonal (convex) hull of a digital object …

The Language Of Mathematics: Virginia Standards Of Learning Mathematical Pictionary For Grades K-3., Amanda Rashelle Collins-Browning

Electronic Theses and Dissertations

My experience teaching in Virginia schools, pacing and aligning instruction to the Virginia Standards of Learning, caused me to recognize the need for a mathematics tool to simplify and transition K-3 mathematics vocabulary usage and instruction. The language of mathematics uses three linguistic tools: words, symbols, and diagrams. Within this thesis I developed an instructional tool, a "Mathematics Pictionary", to accommodate primary grades K-3 and transition mathematical language and vocabulary skills between the primary grades aligned to the instruction and guidelines of the Virginia Standards of Learning. The Pictionary may be used coherently with lesson plans, available from the Virginia …

An Exploratory Study Of Mathematics Engagement Of Secondary Students, Tracy Thomas Brown

Middle-Secondary Education and Instructional Technology Dissertations

An Exploratory Study of Mathematics Engagement of Secondary Students by Tracy Thomas Brown A large proportion of American students are not psychologically connected or engaged to what is occurring in their classes; in addition, they fail to take school seriously, have lost interest in school, and do not value or seek out success (Steinberg, Brown, & Dornbusch, 1996). In addition, the relationship in a mathematics classroom between schooling and engagement from the student’s perspective is not well known (Cothran & Ennis, 2000). The purpose of this study was to investigate engagement in order to describe students’ constructs of student engagement, …

An Autoethnography:A Mathematics Teacher's Journey Of Identity Construction And Change, Anthony B. Stinson

Middle-Secondary Education and Instructional Technology Dissertations

Despite some gains, improving secondary mathematics instruction remains an area of concern of the National Council of Teachers of Mathematics (NCTM). Recitation, also known as lecturing, prevails as the practice of choice of mathematics teachers in the United States. However, the report of the NCTM Research Advisory Committee 2000 indicates that the mathematical proficiency of students increases when the practice of choice includes more than recitation. Therefore, changes in instruction in the mathematics classroom should occur to improve student learning. The purpose of this dissertation is to provide a personalized account of one mathematics teacher’s use of reflective teaching as …

African American Men And College Mathematics: Gaining Access And Attaining Success, Christopher Charlie Jett

Middle-Secondary Education and Instructional Technology Dissertations

The research literature regarding African American male college students reports that they often experience difficulties with mathematics (Stage & Kloosterman, 1995; Treisman, 1992). It is also reported that many African American students enter college seeking to complete their degrees in mathematics and science, but few of these students successfully complete the core requirements (Hrabowski, Maton, & Greif, 1998; Treisman, 1992). In spite of these reported trends, there are some African American male students who, indeed, achieve in college mathematics. The purpose of this study was to analyze how being African American and male might play out in the college mathematics …

A Case Study Of Culturally Responsive Teaching In Middle School Mathematics, Rosanne Fulton

Electronic Theses and Dissertations

This dissertation is a case study of culturally responsive teaching in middle school mathematics. The study contributes to the emerging definition of learning experiences in mathematics that support all middle school students through the use of culturally responsive teaching strategies. These experiences are organized to actualize the balance between accommodating the individual student’s culture, needs and interests and supporting the attainment of appropriate mathematics learning goals.

The research site was chosen because of its diverse and changing student demographics, and because of the achievement and growth rates of these students. Data collected from classroom observations of three middle school mathematics …

Exploring Teacher Perceptions Of Influential Facilitators Of Elementary Mathematics Professional Development: A Mixed Methods Investigation, Sandra Linder

All Dissertations

This dissertation examines the role of the facilitator in elementary mathematics professional development. An exploratory sequential mixed methods design was utilized to answer the central research question: How do United States elementary school teachers perceive an influential facilitator of elementary mathematics professional development (EMPD)? Phase one of this study explored teacher perceptions through a phenomenological design, which informed the second phase of the study, the implementation of a survey instrument to elementary school mathematics teachers on a larger scale. This dissertation is divided into six chapters. Chapter One presents a rationale for examining the role of the facilitator in professional …

Graph Coloring And Flows, Xiaofeng Wang

Graduate Theses, Dissertations, and Problem Reports

Part 1. The Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is contained in exactly two of these perfect matchings. In this paper, we verify the conjecture for some families of snarks (Goldberg snarks, flower snarks) by using a technical lemma.;Part 2. A star coloring of an undirected graph G is a proper vertex coloring of G such that any path of length 3 in G is not bi-colored. The star chromatic number of a family of graphs G , denoted by chis( G ), is the minimum number …

Traditional And Nontraditional Preservice Elementary Teachers' Perceptions About Mathematics And Mathematics Teaching, Anna Marie Wheeler

Dissertations

In this qualitative dissertation, I examined six nontraditional (based on age) and six traditional preservice elementary teachers' beliefs and changes in beliefs about mathematics and mathematics teaching. These case study participants were enrolled in one of three mathematics content courses designed for preservice elementary teachers at a mid-sized doctoral granting university in the western United States. I selected the twelve participants based on the predetermined criteria of gender (female), age (less than 30 for traditional and at least 30 for nontraditional), mathematics instructor, preservice mathematics course, and group dynamics. Data collection consisted of two approximately 45-minute long interviews per preservice …

Hamiltonian Line Graphs And Claw -Free Graphs, Huiya Yan

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation was motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Matthews and Sumner that every 4-connected claw-free graph is hamiltonian. Towards the hamiltonian line graph problem, we proved that every 3-connected claw-free Z8-free graph is hamiltonian, where Z8 is obtained by identifying one end-vertex of P9 with one vertex of a triangle; let hc( G) denote the least integer m such that the iterated line graph Lm(G) is Hamilton-connected, we showed that k -- 1 ≤ hc( G) ≤ max{lcub}diam(G), k -- 1{rcub}, where k is …

Versal Deformations Of Leibniz Algebra., Ashis Mandal Dr.

Doctoral Theses

No abstract provided.

Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.

Doctoral Theses

Classical Fourier analysis derives much of its power from the fact that there are three function spaces whose images under the Fourier transform can be exactly determined. They are the Schwartz space, the L2 space and the space of all C ∞ functions of compact support. The determination of the image is obtained from the definition in the case of Schwartz space, through the Plancherel theorem for the L 2space and through the Paley-Wiener theorem for the other space.In harmonic analysis of semisimple Lie groups, function spaces on various restricted set-ups are of interest. Among the multitude of these spaces …

An Investigation Of The Support For Literacy Instruction In Elementary Mathematics Textbooks, Wendy Ann Williams

Theses and Dissertations

The purpose of this study was to investigate the kinds of support offered for integrating literacy strategies into mathematics instruction in elementary mathematics textbooks so that students are given opportunity to achieve the vision NCTM (2000) has for mathematical power for all. The research methodology for this was a qualitative content analysis using a priori codes. Two textbook series were chosen for this study. In each series examples of literacy integration ideas based on Trabasso's and Bouchard's (2002) effective comprehension strategies to teach comprehension were cited and analyzed. The results show that there is support for teachers to integrate literacy …

Effects Of After School Programs On Elementary School Students' Language Arts And Mathematics Achievement, Jennifer Lynn Presnell

Theses and Dissertations

This study evaluated after school program participation on student academic achievement as a way of helping schools meet Adequate Yearly Progress (AYP) standards set by the No Child Left Behind Act. After school programs were divided into academic after school programs and traditional after school programs. Student achievement was measured through Criterion Referenced Tests in Language Arts and Mathematics. This study took place in a small urban school district located in the Intermountain West. Students in after school programs were matched with students not participating in the programs on several background characteristics including socioeconomic status, English language proficiency status, school …

The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West

Theses and Dissertations

Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the …

Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo

Theses and Dissertations

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model …

Concept Booklets: Examining The Performance Effects Of Journaling Of Mathematics Course Concepts, Todd Stephen Fogdall

Boise State University Theses and Dissertations

Journaling is an effective tool for writing about mathematics, but research is mixed about the extent to its effectiveness in writing to learn mathematics. This study examined the performance effects of concept booklets on curriculum assessments. Concept booklets are a hybrid style of journal-writing that include responses to journal prompts, diagramming, and traditional note-taking. Prompts were designed to sometimes investigate new concepts and, at other times, to reflect on components of previously learned concepts.

The study, of an experimental design, was carried out at the high school level in honors-level mathematics classes with the independent variable being exposure to the …

Exploratory Study Of The Relationship Between State Fiscal Effort And Academic Achievement, Timothy A. Goodale

Teaching & Learning Theses & Dissertations

Prior empirical research has taken many varying approaches to determine if differences in funding significantly impacts student academic achievement. However, much of these studies exhibit weak generalizability due to their limited scope, timeframe and dissimilar achievement measures. To expand upon the already robust literature in education finance this study measures interstate funding disparities via state fiscal effort and determines its impact on several measures of student academic achievement. To control for threats to external validity the research investigates the variables over ten years to determine if the relationships hold over time. Statistical measures employed within the research include bivariate correlation, …

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, …

The Effects Of Different Types Of Prompts On Achievement And Attitude In Mathematics, Barbara R. Greer Edd

Dissertations

This study examined the effects of three different types of writing prompts, procedural, summary, and self-monitoring, on achievement and self-concept of ability in mathematics. Participants included 81 eighth grade students taking a course designed to prepare students for algebra in the ninth grade in a large urban school district in Southern California. Data were gathered using a quasi-experimental design, teacher-researcher created pre-and post-tests, the Minnesota Mathematics Attitude Inventory, teacher field notes, student responses to prompts, and individual and group interviews. Controlling for demographic and other variables identified in the study, simultaneous regression analysis revealed that only summary writing had a …

Certain Pattern Recognition Tasks Using Genetic Programming., Durga Muni Dr.

Doctoral Theses

No abstract provided.

Form And Numbers: Mathematical Patterns And Ordering Elements In Design, Alison Marie Thom

USF Tampa Graduate Theses and Dissertations

In America, buildings are often constructed with the intent of being utile only 30-40 years. All over the world though, there are buildings that are hundreds of years old that are still very functional. Historically, architecture was a part of mathematics, and in many periods of the past, the two were indistinguishable. Architects were often required to be also mathematicians in ancient times. The idea of this thesis is to identify the relationship between mathematics and architecture and to reintroduce them in order to create a module for successful design .

Presence of mathematical boundaries help to attain visual consistency …

Studies On Construction And List Decoding Of Codes On Some Towers Of Function Fields., M. Prem Laxman Das Dr.

Doctoral Theses

In everyday life, there arise many situations where two parties, sender and receiver, need to communicate. The channel through which they communicate is assumed to be binary symmetric, that is, it changes 0 to 1 and vice versa with equal probability. At the receiver’s end, the sent message has to be recovered from the corrupted received word using some reasonable mechanism. This real life problem has attracted a lot of research in the past few decades. A solution to this problem is obtained by adding redundancy in a systematic manner to the message to construct a codeword. The collection of …

Uncovering Transformative Experiences: A Case Study Of The Transformations Made By One Teacher In A Mathematics Professional Development Program, Rachelle Myler Orsak

Theses and Dissertations

Effective professional development is vital for improving mathematics teaching (National Council of Teachers of Mathematics [NCTM], 2007), so studying effective professional development programs is important to the field of mathematics education. This case study presents findings on one teacher, Rebecca, and her experiences in a five-semester mathematics professional development for elementary teachers. The participants in this professional development engaged in collaborative problem solving of challenging mathematical tasks over extended periods of time. I used qualitative research methods based on grounded theory methodology (Charmaz, 2006) to analyze Rebecca's entrance and exit surveys, video data of Rebecca's individual interviews, and video data …

Homogeneous Operators In The Cowen-Douglas Class., Subrata Shyam Roy Dr.

Doctoral Theses

Although, we have used techniques developed in the paper of Cowen-Douglas [18, 20], a systematic account of Hilbert space operators using a variety of tools from several different areas of mathematics is given in the book [26]. This book provides, what the authors call, a sheaf model for a large class of commuting Hilbert space operators. It is likely that these ideas will play a significant role in the future development of the topics discussed here.