Digital Commons Network^™

Survey Of Generalized Contact Structures, James Bland

College of Graduate Studies: Theses & Dissertations

A generalized complex structure, as introduced by N. Hitchin, is a common generalization of both symplectic and complex structures. Generalized complex geometry provides a natural geometric framework to understand certain recent developments in string physics, and has developed into an active area of research. Very recently, an odd dimensional analogue of a generalized complex structure, namely a generalized contact structure, has been introduced in the works of Vaizman, Poon and Wade. In this thesis, we survey the recent works on generalized contact structures. More importantly, we prove a local normal form theorem of a generalized contact structure. This result, which …

Kindergarten Assessments As A Predictor For A Student’S Need For Intervention, Victoria Ellen Weinketz Hoover

Dissertations

The purpose of this study was to determine if the kindergarten assessment results from the three windows in reading, written communication, and mathematics were a valid predictor of a student’s need for intervention up until the conclusion of second grade. Reynolds (1992) suggested that a student’s overall school success is reflective of the approach taken early in kindergarten. With the demands of the No Child Left Behind Act (2001), districts have set in place strategies to meet the standard of all students reading on grade level at the conclusion of the third grade. If districts are to rise to the …

2010 Sonia Kovalevsky Math For Girls Day Report, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Report for the Fifth Annual Lincoln University Sonia Kovalevsky Math for Girls Day that was held on April 23, 2010 from 8:00am to 2:00pm on the campus of Lincoln University in Jefferson City, MO.

Determining The Success Of Ncaa Basketball Teams Through Team Characteristics, Raymond Witkos

Honors Projects in Mathematics

Every year much of the nation becomes engulfed in the NCAA basketball postseason tournament more affectionately known as “March Madness.” The tournament has received the name because of the ability for any team to win a single game and advance to the next round. The purpose of this study is to determine whether concrete statistical measures can be used to predict the final outcome of the tournament. The data collected in the study include 13 independent variables ranging from the 2003-2004 season up until the current 2009-2010 season. Different tests were run in an attempt to achieve the most accurate …

Predictive Modeling Of Alumni Donor Behavior, Lauren Prue

Honors Projects in Mathematics

In recent years, college and universities have relied increasingly upon the charitable contributions of its previous graduates; as the costs of tuition rise substantially, development offices are facing the challenge of creating annual fund campaigns that are minimally expensive while providing the maximum potential for return. This study addresses the available constituent database at one University in particular in an effort to identify what criteria are the strongest predictors of donor response at a small, private university located within New England. The analysis utilized predictive modeling and data-mining largely within the software program Rapid Insight to build several models in …

Mathematics Discipline Assessment Report 2009/2010, Mathematics Discipline

Assessment of Student Learning Reports

No abstract provided.

The Effects Of Implementing Bloom's Taxonomy And Utilizing The Virginia Standards Of Learning Curriculum Framework To Develop Mathematics Lessons For Elementary Students, Kristel Williams Hawks

Doctoral Dissertations and Projects

The purpose of this study was to determine if teachers who developed lessons based on Bloom's Taxonomy and the Virginia Standards of Learning Curriculum Framework saw increased scores on the mathematics benchmark assessment for fourth grade. Two classes taught by different mathematics teachers participated. The mean of the posttest scores for the experimental group in which the teachers developed lessons using Bloom's Taxonomy would be significantly higher than the mean of the group which used textbook bound instruction. An analysis of covariance was conducted, and the hypothesis was rejected. The experimental group would yield significant gains as measured by the …

Sequences Of Positive Integers Containing No K-Term Arithmetic Progressions And Smooth Numbers In Short Intervals., Goutam Pal Dr.

Doctoral Theses

In my thesis I have worked on two problems:1. On sequences of positive integers containing no k terms in arithmetic progressions.2. On smooth numbers in short intervals.The first two chapters of my thesis deal with the first problem and in the rest of the thesis I have focused on the 2nd problem.In the first chapter of my thesis I have considered the function rk(N) for a fixed k ≥ 3, where, by definition, rk(N) is the cardinality of a maximal subset of N consecutive natural numbers with the property that nork terms of it are in an Arithmetic Progression (A. …

Eighth Grade Mathematics Curriculum Alignment For School District 27j, Frances Bell

Regis University Student Publications (comprehensive collection)

This project aligns the curriculum taught in eighth grade mathematics courses in School District 27J to the Colorado Academic Standards (CDE, 2009b). This project includes a yearly planning matrix, for implementation in the 2010-2011 school year. The review of literature defined curriculum and the benefits of curriculum alignment. This information helped to create the yearly planning matrix that aligned the current eighth grade resources to the new standards. The main goal of this project is to ensure that all students in eighth grade receive consistent instruction in each standard, which leads to success on the state standardized tests.

Stem Talent: Moving Beyond Traditional Boundaries, Stephanie Pace Marshall

Publications & Research

The future well-being, prosperity and sustainability of our nation, the global community and our planet resides in igniting and nurturing decidedly different STEM minds that can advance both the new STEM frontier and the human future.

Attitudes Of Mathematics Teachers Towards The Inclusion Of Students With Learning Disabilities And Special Needs In Mainstream Classrooms, Dorit Patkin Ph.D., Tsafi Timor Ph.D.

Electronic Journal for Inclusive Education

The aim of this study is to examine the attitudes of 36 elementary school teachers towards the inclusion of students with learning disabilities in Mathematics in mainstream classes. The research related to three aspects: teachers’ knowledge of learning disabilities, teachers’ perceptions of the physical inclusion of these students, teachers’ perceptions of their responsibility towards the curricular inclusion of students with learning disabilities and towards curricular adaptations. Findings indicate that teachers’ knowledge of the topic is partial, whereas teachers’ attitudes towards inclusion are positive with regard to the three aspects of the research. The study yielded a need to incorporate the …

Teacher Mathematics Learning And Middle School Student Achievement, Sally Marie Mascia

ETD Archive

United States policymakers have taken measures to improve learning for all students emphasizing the use of scientifically based research in choosing educational programs to promote school improvement and student learning. However, educators, researchers and policymakers debate about which factors are most important in affecting student achievement. The No Child Left Behind Act of 2001 (NCLB) places major emphasis upon teacher quality as a factor in improving achievement for all students. This emphasis grows out of research showing that teachers' mastery of the academic content they teach is critical to engaging students and is a significant factor in raising levels of …

A Correlational Study Of The Avid Program With M.S. Math Achievement, David J. Peak

Electronic Theses and Dissertations

Improving student achievement in mathematics in secondary schools remains a priority for public education in our country. With continued federal and state mandates to improve overall student achievement in mathematics, as well as to close the achievement gap, many school districts have sought programs, such as Advancement Via Individual Determination (AVID), to assist in improving student performance. The mission of AVID is to improve the academic achievement of students who are often in the "middle" or "average" and who are typically minorities and are economically disadvantaged. AVID seeks to support these students by providing them with the strategies that successful …

Cognitive Diagnostic Assessment Of Timss-2007 Mathematics Achievement Items For 8th Graders In Turkey, Turker Toker

Electronic Theses and Dissertations

This study investigated students' responses to released TIMSS mathematics items and considered what those responses might show about participants' mastery level of cognitive areas. The least squares distance method (LSDM) was used in this cognitive diagnostic analysis. There were 4,498 8th-grade students from seven geographical regions of Turkey who took TIMSS items. In this study, using the responses of Turkish students to the released math items of TIMSS-2007, an IRT analysis was also conducted to both compare results with international item parameters A Pearson correlation between these two sets of item logit positions produced a correlation of r = .82, …

Automathic Blocks: Supporting Learning Games For Young Blind Students, Arthur Karshmer

Business Analytics and Information Systems

The AutOMathic Blocks system has been developed to help young blind students in the acquisition of elementary math skills. Through the use of Braille labeled blocks, a plastic grid, a touchpad device and any computer, the system has been defined to aid the young student in this most important domain of education. Without these basic skills, students have a much higher probability of not being able to enter math related professions.

Mathematical Biology At An Undergraduate Liberal Arts College, Stephen C. Adolph, Lisette G. De Pillis

All HMC Faculty Publications and Research

Since 2002 we have offered an undergraduate major in Mathematical Biology at Harvey Mudd College. The major was developed and is administered jointly by the mathematics and biology faculty. In this paper we describe the major, courses, and faculty and student research and discuss some of the challenges and opportunities we have experienced.

Nonmath Analogies In Teaching Mathematics, Vera Sarina, Immaculate Kizito Namukasa

Education Publications

Way too often, students find some concepts too abstract to comprehend. One of the strategies used to assist students with building conceptual knowledge is to use analogies. We investigate the place of nonmath analogies in teaching school mathematics. First, we demonstrate the widespread use of analogies by drawing examples through context analysis of tutoring websites, textbooks, and teaching experiences. Second, we argue that analogies reflect the grounded nature of mathematical concepts in common life experiences and, thus, have an essential place in instruction. To support our argument we offer a theoretical rationale based on research literature and historical sources.

Stem Education And Leadership: A Mathematics And Science Partnership Approach, Chris Merrill, Jenny Daugherty

Publications

The issue of attracting more young people to choose careers in science, technology, engineering, and mathematics (STEM) has become critical for the United States. Recent studies by businesses, associations, and education have all agreed that the United States’ performance in the STEM disciplines have placed our nation in grave risk of relinquishing its competitive edge in the marketplace (e.g., Rising above the gathering storm, 2007). A Congressional Research Service (2006) report stated that, a “large majority of secondary students fail to reach proficiency in math and science, and many are taught by teachers lacking adequate subject matter knowledge” (Congressional Research …

Teacher Goal Endorsement, Student Achievement Goals, And Student Achievement In Mathematics;A Longitudinal Study, Matthew D. Deevers

ETD Archive

This study investigated relationships among teacher practices, student motivation and student achievement on standardized mathematics assessments using an Achievement Goal Theory framework. From 2006 through 2009, 800 public school students participated in mathematics assessments and completed surveys measuring perceptions of teacher practices and student achievement goal orientations. Hierarchical linear modeling (HLM) was used to assess relationships among teacher goal endorsement practices, student goal orientations, and student mathematics achievement. Findings indicated teacher mastery goal endorsement was positively related to student mastery and performance-approach orientations, and negatively related to student performance-avoidance orientation. Performance goal endorsement was positively related to student performance-approach and …

The Relationship Between Core-Plus Mathematics Project And Student Achievement, Karen Renee Treadway-Harvel

Wayne State University Dissertations

The Third International Mathematics and Science Study (TIMSS) study revealed that test scores from high school students were below average in mathematics and science. Studies show that part of it stem from the traditional methods of teaching rather than the standards-based teaching. According to the No Child Left Behind (NCLB) act, students should receive a rigorous and relevant curriculum. The High School Content Expectations (HSCE) is a set of objectives that meet this criteria but the current curriculum still uses traditionally-based curriculum. More than 80% of textbooks located in schools today are traditionally-based. Moreover, teachers who are teaching have been …

The Fibonacci Sequence, Arik Avagyan

A with Honors Projects

A review was made of the Fibonacci sequence, its characteristics and applications.

Bimodule Categories And Monoidal 2-Structure, Justin Greenough

Doctoral Dissertations

We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C -bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky ([KV91]). We then provide a monoidal-structure preserving 2-equivalence between the 2-category of C -bimodule categories and Z( C )-module categories (module categories over the center of C ). The (braided) tensor structure of C1⊠D C2 for (braided) fusion categories over braided fusion D is introduced. For a finite group G we show that de-equivariantization is equivalent to the tensor product over Rep( G). …

Conjecturing In Dynamic Geometry: A Model For Conjecture-Generation Through Maintaining Dragging, Anna Baccaglini-Frank

Doctoral Dissertations

The purpose of this research is to study aspects of the impact of Dynamic Geometry Systems (DGS) in the process of producing conjectures in Euclidean geometry. Previous research has identified and classified a set of dragging schemes spontaneously used by students. Building on these findings, the study focuses on cognitive processes that arise in correspondence to particular dragging modalities in Cabri. Specifically, we have conceived a model describing what seems to occur during a process of conjecture-generation that involves the use of a particular dragging modality, described in the literature as dummy locus dragging. In order to accomplish this goal, …

The Impact Of A Mathematics Research Experience On Teachers' Conceptions Of Student Learning, Todd Abel

Doctoral Dissertations

Many mathematics teacher professional development programs have either incorporated or been organized around a goal of providing "research-like" (Cuoco, 2001) experiences. That is, teachers participate in a project that somehow simulates the mathematics research process. Though some research studies have shown positive outcomes from such programs, researchers have cautioned against assuming universally positive benefits without sufficient evidence (Proulx and Bednarz, 2001). Teacher conceptions of student learning play an important role in lesson development and preparation for classroom work (Penso & Shoham, 2003). Similarities between the processes of mathematics research and student learning (Dreyfus, 1991) beg the question of whether experience …

Von Neumann Algebras, Affiliated Operators And Representations Of The Heisenberg Relation, Zhe Liu

Doctoral Dissertations

Von Neumann algebras are self-adjoint, strong-operator closed subalgebras (containing the identity operator) of the algebra of all bounded operators on a Hilbert space. Factors are von Neumann algebras whose centers consist of scalar multiples of the identity operator. In this thesis, we study unbounded operators affiliated with finite von Neumann algebras, in particular, factors of Type II1. Such unbounded operators permit all the formal algebraic manipulations used by the founders of quantum mechanics in their mathematical formulation, and surprisingly, they form an algebra. The operators affiliated with an infinite von Neumann algebra never form such an algebra. The Heisenberg commutation …

Admissible Orders On Quotients Of The Free Associative Algebra, Jeremiah William Johnson

Doctoral Dissertations

An admissible order on a multiplicative basis of a noncommutative algebra A is a term order satisfying additional conditions that allow for the construction of Grobner bases for A -modules. When A is commutative, a finite reduced Grobner basis for an A -module can always be obtained, but when A is not commutative this is not the case; in fact in many cases a Grobner basis theory for A may not even exist.

E. Hinson has used position-dependent weights, encoded in so-called admissible arrays, to partially order words in the free associative algebra in a way which produces a length-dominant …

Mf Algebras And A Bishop -Stone -Weierstrass Theorem Result, Qihui Li

Doctoral Dissertations

This dissertation consists of two parts. In the first part, we obtain many new results about MF algebras. First, we continue the work on D. Voiculescu's topological free entropy dimension deltatop (x1, ..., xn) for an n-tuple x&ar; = (x1, ..., xn) of elements in a unital C*-algebra. We also introduce a new invariant that is a C*-algebra analog of the invariant K3 introduced for von Neumann algebras. Second, we discuss a full amalgamated free product of unital MF (and residually finite-dimensional) algebras with amalgamation over a finite-dimensional C*-subalgebra. Necessary and sufficient conditions are given in this situation. In the …

An Amazing Mathematical Card Trick, Arthur T. Benjamin

All HMC Faculty Publications and Research

A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether …

Mathematical Notation: Help Or Hindrance?, Geoff D. Tennant Dr

Institute for Educational Development, East Africa

This article puts forward a range of reasons for using mathematical notation, emphasizing the need to allow children learning it time and space to come to terms with it. Examples are given in furthering the argument that the time to introduce notation is after the concept is already fully understood.

Towards Evidence-Based Practices In Mathematics Instruction: Investigating The Impact Of Writing On Student Ability To Solve Mathematics Problems, Shaalein Carroll Lopez

Dissertations

Achievement in mathematics education for students in elementary school through college has lagged behind that of other students internationally. As a result, enhancing mathematics achievement for students in the United States of America has long been a priority. Best practices in teaching across all grades emphasize using instructional methods that have been validated through research, though a review of the literature demonstrates a lack of such substantiated practices in mathematics education. This dissertation attempts to contribute to the field of research-based practices in mathematics education by measuring the effects of an instructional practice long used in mathematics classrooms in grades …