Digital Commons Network^™

Study On Algebras With Retractions And Planes Over A Dvr., Prosenjit Das Dr.

Doctoral Theses

Aim:The main aim of this thesis is to study the following problems:1. For a Noetherian ring R, to find a set of minimal sufficient fibre conditions for an R-algebra with a retraction to R to be an A1-fibration over R.2. To investigate sufficient conditions for a factorial A1-form, with a retraction to the base ring, to be A1.3. To investigate whether planes of the form b(X, Y)Zn – a(X, Y) are co- ordinate planes in the polynomial ring in three variables X, Y and Z over a discrete valuation ring.The 1st problem will be discussed in Chapter 3 entitled Codimension- …

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 …

Implementing Reading And Writing In Secondary Mathematics, Mari E. Eisenhart

Regis University Student Publications (comprehensive collection)

Literacy in secondary mathematics continues to be difficult for many. Mathematics teachers and researchers continue to develop support documents for secondary math teachers. It is important to utilize the literacy strategies already established by other content areas. It is feasible to adjust these strategies to suit the needs of mathematics students. Literacy across the content areas is a relatively new idea in education, but literacy in mathematics is even more foreign. It is necessary to use the available literacy strategies to develop materials applicable in the secondary mathematics classroom.

The Effects Of Positive School Engagement On Math And Reading Achievement In Midwestern Suburban Middle School Students, Heather C. Phipps

Student Work

Ensuring high academic achievement in schools with increasingly diverse students is a challenge. Assessing student engagement can be a powerful tool in predicting potential success and identifying students who may need additional support. Positive youth development theory supports focusing on a young person’s strengths, and an asset-based approach to education can raise student achievement. During the 2007-2008 school year, seventh grade students were assessed for school engagement using the Developmental Assets Profile. Students were identified as either not engaged or engaged in school. For two years, achievement in reading and math as well as grade point average was collected and …

Relationship Of Self-Efficacy Beliefs Of Urban Public School Students To Performance On A High-Stakes Mathematics Test, Kolajo Akinbiyi Afolabi

Open Access Dissertations

The purpose of this study was to examine the relationship of self-efficacy for Enlisting Social Resources, Self-Regulatory Efficacy, self-efficacy for Self-Regulated Learning, and self-efficacy for Academic Achievement (Bandura's Children's Self-Efficacy Scale, 2006) of urban public school students to performance on the high stakes Massachusetts Comprehensive Assessment System (MCAS) math test. A survey questionnaire was administered to eighty three participants and the data, analyzed using linear regression, conformed to the assumptions of Independence, Linearity, Normality, and Homoscedasticity. Self-Regulatory Efficacy, Academic Achievement, and Socio-economic Status were statistically significant bivariate predictors of performance on MCAS math test. Self-Regulatory Efficacy was the only consistent …

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

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 …

Learning And Serving: An Exploratory Action Research Case Study Of A Middle School Service Learning Curriculum Project, Georgina Levey

Electronic Theses and Dissertations

Service learning, a natural link between community service and standards-based education, encourages students to learn about themselves in the context of the world in which they live. In other words, service learning is a method of teaching that enriches learning by engaging students in meaningful service to their schools and communities, and integrating that service with established curricula or learning objectives (NYLC Service-Learning Glossary, 2005). Educational service activities can be done directly or indirectly and they can have a varying degree of “involvement” ranging from community service, community exploration, community action or advocacy and research. In this study, a service …

Design Of Computer-Based Assessment Secondary Education For Understanding Of Mathematics, Mark Damian Lewis

Boise State University Theses and Dissertations

The purpose of this study was to evaluate the effectiveness of a computer-based assessment to reveal mathematical understanding. Relevant literature suggested that developments in cognitive science and computer-based assessments could allow the outcomes of cognitively guided instruction to be made explicit. An assessment instrument designed to make mathematical thinking explicit was developed and administered, consisting of 15 animations showing the solutions of one and two digit multiplication problems. A consistent set of five questions followed each animation. The assessment was administered to four classes of fourth grade students in two elementary schools participating in cognitively guided instruction professional development programs. …

Mathematics In Motion: A Handbook Of Kinesthetic Teaching Strategies, Janie Brown Salazar

Regis University Student Publications (comprehensive collection)

Howard Gardner first proposed his theory of Multiple Intelligences and the bodily-kinesthetic intelligence in 1983. Unfortunately, almost three decades later, teacher programs still do not train teachers about Bodily-Kinesthetic intelligence in depth; nor do they train teachers how to integrate Bodily-Kinesthetic intelligence into daily learning procedures and classroom environment. Schools focus very little on other factors that contribute to how successful a person might be in life, throughout life. Incorporating bodily-kinesthetic strategies in teaching can positively influence children's learning experience. The following research project investigates the research on the bodily-kinesthetic intelligence, bodily-kinesthetic teaching strategies, teaching strategies linked to student achievement, …

Mathematics Vocabulary And English Learners: A Study Of Students' Mathematical Thinking, Hilary Hart

Theses and Dissertations

This study examined the mathematical thinking of English learners as they were taught mathematics vocabulary through research-based methods. Four English learners served as focus students. After administering a pre-performance assessment, I taught a 10-lesson unit on fractions. I taught mathematics vocabulary through the use of a mathematics word wall, think-pair-shares, graphic organizers, journal entries, and picture dictionaries. The four focus students were audio recorded to capture their spoken discourse. Student work was collected to capture written discourse. Over the course of the unit, the four focus students used the mathematics vocabulary words that were taught explicitly. The focus students gained …

Physical Models In Community Detection With Applications To Identifying Structure In Complex Amorphous Systems, Peter Ronhovde

All Theses and Dissertations (ETDs)

We present an exceptionally accurate spin-glass-type Potts model for the graph theoretic problem of community detection. With a simple algorithm, we find that our approach is exceptionally accurate, robust to the effects of noise, and competitive with the best currently available algorithms in terms of speed and the size of solvable systems. Being a "local" measure of community structure, our Potts model is free from a "resolution limit" that hinders community solutions for some popular community detection models. It further remains a local measure on weighted and directed graphs. We apply our community detection method to accurately and quantitatively evaluate …

Preservice Elementary Teachers‟ Pedagogical Content Knowledge Related To Area And Perimeter: A Teacher Development Experiment Investigating Anchored Instruction With Web-Based Microworlds, Matthew S. Kellogg

USF Tampa Graduate Theses and Dissertations

Practical concepts, such as area and perimeter, have an important part in today's school mathematics curricula. Research indicates that students and preservice teachers (PSTs) struggle with and harbor misconceptions regarding these topics. Researchers suggest that alternative instructional methods be investigated that enhance PSTs' conceptual understanding and encourage deeper student thinking. To address this need, this study examined and described what and how PSTs learn as they engage in anchored instruction involving web-based microworlds designed for exploring area and perimeter. Its focus was to examine the influences of a modified teacher development experiment (TDE) upon 12 elementary PSTs' content knowledge (CK) …

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 …

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 …

The Impact Of Experience On Elementary School Teacher Affective Relationship With Mathematics, John Salzer

Ed.D. Dissertations

This study was designed as an exploratory examination of the impact of teaching experience on elementary school teachers’ affective relationships with mathematics. A self-reporting survey was used to examine a wide variety of experience factors, including factors related to quantity of experience, type of experience, and post-certification training opportunities (n = 275). Participants were also asked to identify services that might impact their affective relationships with mathematics. This study resulted in recommendations for seven follow-up studies to gain insight into factors that significantly correlated to teacher attitudes toward math or to their perceived changes in attitudes over time. Recommended practices …

Survey Of Generalized Contact Structures, James Bland

Electronic Theses and 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 …

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.

Developing Fourth Graders' Proficiency In Basic Multiplication Facts Through Strategy Instruction, Stacey Braddock

Electronic Theses and Dissertations

The purpose of this action research study was to evaluate my own practice of teaching basic multiplication facts to fourth graders. I wanted to see how focusing my instruction on strategies would help my students develop proficiency in basic multiplication facts. I chose this topic because Florida was in the process of shifting to new standards that encourage teaching for deeper meaning. I hoped this research would give my students the opportunity to make sense of multiplication on a deeper level, while giving me insight into how students learn multiplication. Through this study, I learned that students initially find multiplication …

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 …

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 …

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 …

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 …

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 …

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 …

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 …