Digital Commons Network^™

Planar Algebras: A Category Theoretic Point Of View, Shamindra Kumar Ghosh

Doctoral Dissertations

We define Jones's planar algebra as a map of multicategories and construct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We introduce the concept of affine representations of a planar algebra and prove some finiteness results for the affine representations of finite depth planar algebras. We also show that the radius of convergence of the dimension of an affine representation of the planar algebra associated to a finite depth subfactor is at least as big as the inverse-square of the modulus.

Cupolets: Chaotic Unstable Periodic Orbits Theory And Applications, Kourosh Zarringhalam

Doctoral Dissertations

Recent theoretical work suggests that periodic orbits of chaotic systems are a rich source of qualitative information about the dynamical system. The presence of unstable periodic orbits located densely on the attractor is a typical characteristic of chaotic systems. This abundance of unstable periodic orbits can be utilized in a wide variety of theoretical and practical applications [19]. In particular, chaotic communication techniques and methods of controlling chaos depend on this property of chaotic attractors [12, 13].

In the first part of this thesis, a control scheme for stabilizing the unstable periodic orbits of chaotic systems is presented and the …

Exploring Lesson Study As A Form Of Professional Development For Enriching Teacher Knowledge And Classroom Practices, Melissa K. Mitcheltree

Doctoral Dissertations

This study tracked the development of teacher knowledge through a professional development experience called lesson study. Lesson study is a Japanese professional development process in which a group of teachers develop a series of lessons using the following stages: planning lessons, teaching/observing the lessons, reflecting on lessons taught as well as sharing and discussing the lessons with their colleagues (Lewis, 2002). The aim of this study was to explore how the lesson study process influenced teacher knowledge of mathematics content and pedagogical content.

Study participants were four secondary mathematics teachers from a rural high school in the Northeast. All participants …

Code Red (Remediation And Enrichment Days): The Complex Journey Of A School And University Partnership's Process To Increase Mathematics Achievement, Patricia S. Moyer-Packenham, K. Dockery, S. Jamieson, J. Ross

Teacher Education and Leadership Faculty Publications

This study examined a focused remediation and enrichment effort among school and university faculty to affect the mathematics achievement of a group of third-grade students in a Title 1 elementary school. A total of 87 students participated in the Code RED (Remediation and Enrichment Days) Project. During the Code RED Project, student assessment data were used to identify high-need areas for mathematics instruction. The Code RED Project sessions occurred in small groups over a 10-week period. Pre-and posttest assessments, as well as state-standardized tests, were used for data gathering during the project. Pre-and posttest data indicate that students made significant …

Listening To Student Voices: Fifth Graders' Perceptions Of Their Mathematics Learning Within The Context Of A Mathematics Reform, Elizabeth Hoffman

Electronic Theses and Dissertations

This qualitative study explored fifth graders' perceptions of their mathematics learning within the context of a reform effort. Students' voices are the focus of this study due to the paucity of literature on student learning from the students' perspective (Erickson & Shultz, 1992), particularly the elementary student (Gentilucci, 2004). The participants of this study, who in the past have been given a variety of labels including "disadvantaged" or "at-risk," clearly articulated, even in nonstandard English, their perceptions of their mathematics learning. They passionately explained what helped them learn mathematics as well as what impeded their mathematics learning and were often …

Subspaces Of Ωω That Are Paracompact In Some Forcing Extension, Akira Iwasa

Computer Science and Mathematics Faculty Publications

We discuss when a subspace of ω_ω is paracompact in some forcing extension.

Exploring The Relationship Between Teachers' Beliefs In Mathematics And Their Instructional Practice, Michelle Vander Veldt

UNLV Retrospective Theses & Dissertations

This study explored the relationship between teachers' beliefs about mathematics and their instructional practices. The personal epistemology of the case study elementary mathematics teachers was documented and analyzed to provide evidence of the connection between teachers' beliefs and practice in an elementary school setting; This study was grounded in a theoretical framework of epistemological world views, particularly the comparison of belief across three epistemological world views: (1) the realist, (2) the contextualist, and (3) the relativist. Three areas of beliefs are addressed in this study: (1) beliefs about curriculum, (2) beliefs about pedagogy, and (3) beliefs about assessment. Through analysis …

Can Blending Face-To-Face Teaching With E-Learning Support The Development Of Phase 4 Apprentices In Mathematics: A Formative Evaluation Research Study, Peter Hinch

Theses

This thesis is a formative evaluation research study_ Its purpose is to establish if

blending face--to-face and e-leaming delivery methods can support the development of

Phase 4 apprentice plumbers in mathematics in the Department of Construction Skills in

the Technologicl University Dublin. The study also included the design, development

and evaluation of a mathematics web site called Plumatics 4 U which is grounded in

established theoretical criteria for effective blended delivery within third level

education. This web site is currently in use by Phase 4 apprentice plumbers and is

delivered through WebCT. The CD accompanying this thesis contains a short …

Effects Of Student Response System Use On Student Learning And Verbal Participation For A Sixth-Grade Mathematics Unit, Gary Thomas Grissom Ii

All-Inclusive List of Electronic Theses and Dissertations

The purpose of this quasi-experimental quantitative study was to examine the effects of Student Response System (SRS) use on student learning and verbal participation in an authentic K-12 classroom environment for a sixth-grade mathematics unit on probability. A self-report survey was administered to report student attitudes regarding SRS use for the unit. A sample of 84 sixth-grade students from a rural Midwestern elementary school was used for the study by established grouping. Two sections of the sixth-grade class were used as the treatment condition of SRS use and two sections of the sixth-grade class were used as the control group …

The Sonic Representation Of Mathematical Data, Charlie Cullen

Doctoral

Conveying data and information using non-speech audio is an ever growing field of research. Existing work has been performed investigating sonfication and its applications, and this research seeks to build upon these ideas while also suggesting new areas of potential. In this research, initial work focused on the sonification of DNA and RNA nucleotide base sequences for analysis. A case study was undertaken into the potential of rhythmic parsing of such data sequences, with test results indicating that a more effective method of representing data in a sonification was required. Sonification of complex data such as DNA and RNA was …

Unfolding The Labyrinth: Open Problems In Physics, Mathematics, Astrophysics, And Other Areas Of Science, Florentin Smarandache, Victor Christianto, Fu Yuhua, Radi Khrapko, John Hutchison

Branch Mathematics and Statistics Faculty and Staff Publications

The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed …

What Teachers Want To Know: A Systematic Review Of Action Research Theses Related To K-8 Mathematics And Science, Bridget Steele

Electronic Theses and Dissertations

The research conducted was a systemic review of 88 action research masters theses from a teacher enhancement program for K-8 mathematics and science at the University of Central Florida and the teachers that performed the studies. The purpose of this study is to synthesize existing research results of a collection of master's theses from a teacher enhancement program for K-8 mathematics and science teachers in order to arrive at meaningful conclusions regarding teachers' research interests and classroom practices. Also, the study will help teacher educators who deliver the teacher enhancement program to improve the effectiveness of the program. A summary …

The Paths To Becoming A Mathematics Teacher, Kimberly Lowry

Electronic Theses and Dissertations

Increasing numbers of mathematics teachers must be recruited in coming years, because of a growing student population, teacher attrition, calls for smaller class size, and the need to replace out-of-subject teachers. Recruitment can be made more effective and efficient, if better information on career paths is provided to decision makers. This study attempts to analyze the academic decisions which lead to the outcome "becoming a mathematics teacher". Four groups were compared and contrasted: mathematics teachers, science teachers, other teachers, and non-teachers. Science teachers were removed from the "other teachers" category because of their many similarities to mathematics teachers on the …

Discourse On The Interface Of Matheatics And Physics: A Panel Discussion Sponsored By Dit And The Ria., Brendan Goldsmith

Articles

No abstract available

The Effects Of Professional Development Programs On Educational Outcomes In Mathematics And Sciences, William M. Craig

MPA/MPP/MPFM Capstone Projects

Professional development programs are widely acknowledged for their success in determining outcomes in a variety of fields. These programs are particularly useful in education where new processes, methodologies, and curriculum need to be disseminated to vast numbers of administrators, educators, parents, and program analysts. Education is considered one of the top priorities for American policymakers, agencies, companies, and the general public. This fact has made educational outcomes progressively more important over time as larger expenditures are dedicated to providing positive educational effects. There has been a large body of research performed on what effects educational outcomes in the United States. …

Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao

Faculty Publications

A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi–Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, …

The Effects Of Hands-On Instructional Strategies On Fourth Grade Students' Attitudes And Performance In Mathematics, Lindsey Hosack

Electronic Theses and Dissertations

This study summarizes research conducted in a fourth grade classroom in a suburban elementary school in the fall of 2005. This study investigated the practice of using hands-on instructional strategies, enhanced with technology, to improve students' attitudes and performance in mathematics. The classroom teacher supplemented conventional mathematics instruction with hands-on activities. Attitudinal data were collected using a pre- and post anxiety survey as well as journal writing assignments and student interviews. Performance data was collected using evaluative assessments. Results of this study showed a positive change in students' attitude towards mathematics. Student performance gains were recorded and analyzed throughout the …

The Kronecker Product, Bobbi Jo Broxson

UNF Graduate Theses and Dissertations

This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be …

Middle School Mathematics Teacher Certification, Degree Level, And Experience, And The Effects On Teacher Attrition And Student Mathematics Achievement In A Large Urban District, Bonnie Swan

Electronic Theses and Dissertations

The purpose of this study was to examine the backgrounds and experiences of middle school mathematics teachers that often distinguish "quality" teachers, including certification, experience, degree type, and degree level and how those demographics and others vary for different types of schools. The emphasis was on profiling teachers in a large urban district by describing their basic features and distributions, as well as how middle school mathematics teachers, according to those differences, relate to student mathematics achievement, teacher attrition and teacher mobility. Student achievement was measured by test results from the Norm Reference Test-Normal Curve Equivalent (NRT-NCE) mathematics portion of …

Asymptotic Solutions Of Almost Diagonal Differential And Difference Systems, Fei Xue

Graduate Theses, Dissertations, and Problem Reports (ETD)

New methods for both asymptotic integration of the linear differential systems Y'(t) = [D( t) + R(t)]Y( t) and asymptotic summation of the linear difference systems Y(t + 1) = [D(t)+ R(t)]Y(t) are derived. The fundamental solution Y(t) = phi( t)[I+P(t)] for differential and difference systems is constructed in terms of a product. The first matrix function phi(t) is decided by the diagonal matrix D(t) and the second matrix I + P(t) is a perturbation of the identity matrix I. Another fundamental solution Y( t) = [I + Q(t)]phi( t) is also constructed for difference systems. Conditions are given on …

Some New Methods For Image Compression, Muhammad Aslam

Graduate Theses, Dissertations, and Problem Reports (ETD)

The vanishing moment of wavelets and associated multi-resolution framework yield an efficient representation of smooth functions with wavelet approximation. However as pointed out in many papers, the similar result cannot be expected for the piecewise smooth functions with large jumps. In other words, wavelet approximation cannot achieve the same approximation order in the vicinity of jumps as in the smooth regions. Large wavelet coefficients associated with jumps are generated and consequently produce oscillations near discontinuities in the reconstructed signal. This is the so-called Gibbs phenomenon or a Ringing effect. In this thesis, we develop a technique which reduces the Gibbs …

Pathways To Success In Pre-College Mathematics, Bob Madsen, Ted Hodgson, Carol Ward

Faculty Publications

Like most tribal colleges, Chief Dull Knife College (CDKC, Lame Deer, MT) offers a sequence of pre-college mathematics courses - Basic Mathematics, Introductory Algebra, and Intermediate Algebra - to assist students who lack college-level skills. To enhance student support, CDKC created the Student Learning Center, which is started by instructors and student interns and offers computer work stations.

The Effects Of Professional Development To Create Standards -Based Curriculum On Student Achievement In Fourth And Fifth Grade Mathematics Classrooms, Martin Amy Mcbride

All-Inclusive List of Electronic Theses and Dissertations

The National Council of Teachers of Mathematics determined there were several concepts or standards” needed for quality teaching of math While few dispute their importance, little support and resources are provided to help teachers understand and meet these standards. Long term professional development which focuses on how to teach with these standards could play a crucial role in improving the academic achievement of students. In this study, professional development opportunities were provided for teachers to explore the various elements of mathematics and develop a better understanding of how to teach them. The main purpose of the research was to study …

Can Blending Face-To-Face Teaching With E-Learning Support The Development Of Phase 4 Apprentices In Mathematics? A Formative Evaluation Research Study., Peter Hinch

Theses

This thesis is a formative evaluation research study. Its purpose is to establish if blending face-to-face and e-learning delivery methods can support the development of Phase 4 apprentice plumbers in mathematics in the Department of Construction Skills in the Technologicl University Dublin. The study also included the design, development and evaluation of a mathematics web site called Plumatics 4 U which is grounded in established theoretical criteria for effective blended delivery within third level education. This web site is currently in use by Phase 4 apprentice plumbers and is delivered through WebCT. The CD accompanying this thesis contains a short …

Integration Of Conceptual Mathematical Relationships Into Constant Time Delay Instruction, Bethany Ann Porter

LSU Master's Theses

There is constant debate over mathematics education in the United States. One central controversy is whether or not the current methods used to teach students mathematics are effective. Some scholars believe that students are not getting enough practice and that they are not getting a good conceptual understanding of mathematics. It has been shown that mathematics equations are rich in patterns and inter-relationships and when children understand these relationships they have higher mathematic skill levels than their peers who do not. This study examined the effectiveness of using an empirically supported, fast paced mastery oriented teaching procedure that promotes automaticity …

Wallpaper Groups, Cassondra Fett

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

All-Boy Mathematics Classes In Middle School., Amanda Neel Davis

Electronic Theses and Dissertations

A comparative case study focused on six mathematics teachers of all-boy classes in three middle schools. Each school chose to experiment with gendered classes to improve specific, yet somewhat different, outcomes. A purpose of this study was not to compare single-gender schooling with coeducation, but rather, to focus on each school's implementation process and to identify school and classroom factors that seemed to contribute to success of the single-gender program. Another purpose was to examine mathematics teaching. Observational analysis used as a framework the Five Strands of Mathematics Proficiency. Related areas of inquiry were classroom time allocation, textbook selection and …

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

Maximum Size T-Cross-Intersecting And Intersecting Families With Degree Conditions, Yongbin Ou

Graduate Theses, Dissertations, and Problem Reports (ETD)

We present four main results: (1) A solution to the problem of finding two set systems A and B such that A is r1-intersecting, B is r2-intersecting, A,B are t-cross-intersecting and A+ B is a maximum; (2) A solution to the problem of finding two set systems A and B such that A,B are Sperner, t-cross-intersecting and A+ B is a maximum; (3) A solution to the problem of finding the maximum size of an intersecting set system F such that the complementary degree c( F ) = s for a specified value s; (4) An asymptotic result on the …