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Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.

Doctoral Theses

For univariate as well as finite dimensional multivariate data, there is an extensive literature on nonparametric statistical methods. One of the reasons for the popularity of nonparametric methods is that it is often difficult to justify the assumptions (e.g., Gaussian distribution of the data) made in the models used in parametric methods. Nonparametric procedures use more flexible models, which involve less assumptions. So, they are more robust against possible departures from the model assumptions, and are applicable to a wide variety of data. Nonparametric methods outperform their parametric competitors in many situations, where the assumptions required for the parametric methods …

Increasing Number Sense At The Preschool Level, Sarah Marie Koenig

School of Education and Leadership Student Capstone Theses and Dissertations

This capstone addresses the question, “What strategies can be used to increase number sense at the preschool level?”. Current research states that preschoolers need opportunities to learn about numbers and math concepts through a balance of natural play and exploration, intentional teaching, and structured learning activities embedded in their daily routines. Through the process of curriculum design using McTighe and Wiggins’ Understanding By Design framework, the author created a learning plan that includes lessons, resources, and parent/child activities using a variety of instructional strategies to teach number sense at the preschool level. The learning plan includes a sequence of activities …

Using Guided Math And Flipped Learning In A Fifth Grade Fractions Unit, Kristin Leigh Moore

School of Education and Leadership Student Capstone Theses and Dissertations

The research question addressed in this project was: How can I design a math curriculum that will increase fifth grade students’ understanding of fraction concepts? The author began her research by investigating the struggles elementary students face when learning fraction concepts, which led to a study of four instructional strategies: ability grouping, differentiation, flipped learning, and guided math. The author considered the work of Boaler, Sammons, Tomlinson, Tucker, and Vann to inform her research. After careful reflection on the benefits and limitations of each strategy, the author chose to create a hybrid unit utilizing both guided math and flipped learning. …

When And Why Do Native English Speaking Students In A Spanish Immersion Setting Switch Into English During Math Instruction?, Samantha Marie Judith Holland

School of Education and Leadership Student Capstone Theses and Dissertations

This study addressed when and why do native English speakers in a Spanish immersion switch into English during math instruction? This capstone studied 30 students in a Spanish immersion school in an affluent suburban area in the Upper Midwest. The author used literature from other types of immersion schools to highlight the lack of research on native English speakers in immersion settings. This capstone used audio- recordings, questionnaires and open-ended interviews to research the question. The researcher concludes that teaching Spanish vernacular in the immersion model would decrease the amount of English in the math classroom and that language objectives …

The Effects Of Metacognitive Writing On Student Achievement In Advanced Placement Calculus, Lindsay M. O'Neal

Education Dissertations

Grounded in metacognitive theory (Flavell, 1976) and historical foundations that reach back as far as the writings of Plato (1973), the last few decades have seen an increase in research regarding the impact of metacognitive practice on student learning, often through the use of reflective writing. Studies have focused on a range of aspects, from how to measure metacognition to the effect metacognitive practice has on the academic achievement of students in a variety of subject areas. Specifically with regard to mathematics, researchers have studied the impact of reflective strategies on primary, secondary, and university level students.

The purpose of …

Learning Support Effectiveness In Mathematics At A Tennessee University, Mark Dula

Electronic Theses and Dissertations

Every year thousands of students graduate from high school and move on to higher education, but many of them are not yet prepared for college level courses. The Tennessee Board of Regents does not currently allow 4-year institutions to teach courses that are below college level, so many institutions are using programs such as learning support courses to assist a growing population of underprepared students. The purpose of this study was to determine if the 1-term and 2-term retention rates for students with the same ACT mathematics subsection scores were different between students who took a regular section of Probability …

Influence Of Property School Wealth On Fifth Grade Student Achievement In Reading And Mathematics, Jesus R. Reyna

Theses and Dissertations

The purpose of this study was to investigate whether, or to what extent, property wealth of the upper and lower 5% districts, per pupil expenditure, limited English proficient students, economically disadvantaged students, membership, and teacher experience contribute to student achievement in 5th grade reading and mathematics. To do this, the fifth grade reading and math achievement scores, based on the TAKS Assessments, to represent student achievement were evaluated against district wealth, per pupil expenditure, economic disadvantage, limited English language proficiency, membership, and years of teaching experience of teachers for the years 2009, 2010, and 2011. A combination of descriptive statistics, …

Building Depth Of Understanding Of The Concept Of Number Sense And Algebra In Students Grades 7 And 8, Catherine Janes

Dissertations, Masters Theses, Capstones, and Culminating Projects

Mathematics instruction offers both challenges and rewards to students. Teachers tend to focus on transmission of knowledge. Student creativity and problem-solving skills are not typically activated with common teaching practices. When students are engaged in mathematics they are recognizing patterns, making connections on their own, coming up with creative solutions, and discussing mathematical ideas with peers and adults. The purpose of this study was to identify, employ, and evaluate strategies that engage students in these practices and assist them in developing a deep understanding of mathematics concepts such as number sense and algebra.

The review of the literature began with …

Investigating Teachers' Content Knowledge And Pedogogical Content Knowledge In A Middle School Physical Science Curriculum On Force And Motion, Daniel Patrick Laverty

Electronic Theses and Dissertations

Teaching is a profession that requires the incorporation of many types of knowledge in order to create effective instructional experiences that promote student learning. Teachers need to blend their knowledge of the content with the methods for delivering that content and an understanding of their students' thinking. With increasing concern in the United States over student achievement in science and mathematics, there is ongoing discussion about which elements of teacher knowledge most directly correlate with effective instruction. How do specific strands of teacher knowledge blend to influence student learning outcomes? This study explores the roles of teacher content knowledge (CK) …

Montessori Mathematics Curriculum And Lower Elementary Students Understanding Of Length Measurement, Katherine L. Mcintosh

Masters of Arts in Education Action Research Papers

The intent of this action research project was to determine to what extent the Montessori Mathematics curriculum support lower elementary students’ understanding of length measurement. The research took place in a private Montessori school classroom with first and second-grade students. There were 22 students in the class, 11 first graders, and 11 second-graders. Data was collected through a pre and post-test, field notes, and observations. The students also kept a journal and performed self-assessments. Photographs were taken to record the students’ use of different measurement tools. Children’s literature about length measurement was read and discussed with the students. The data …

Designing For Immersive Technology: Integrating Art And Stem Learning, Jane Crayton

Art & Art History ETDs

Students struggle to learn STEM concepts. The arts have been proposed as a means to engage students in STEM education, resulting in the idea of STEAM. However, STEAM approaches do not always result in learning. A collaboration between a major research university and a small Native arts college in the southwestern United States provided an opportunity for studying the potential for arts to engage students in STEM learning. This study investigates how participating art students (N = 4) solved technological and design production problems when working with immersive technologies in a paid summer internship program. The internship program lasted six …

The Impact Of An Interactive Technology Application On Elementary Student Achievement In Fractions., Shannon M. Stone

Electronic Theses and Dissertations

Data reported locally and nationally show that students struggle to understand fractional concepts. The purpose of this study was to examine the effects of an interactive tablet application on student achievement in fractions. Students in grades three through five at the treatment school worked with an interactive tablet application designed to facilitate student construction of fractions knowledge. The interactive tablet application is an open-platform that allowed teachers the autonomy to work with the researcher to load their desired content activities on the topic of fractions to develop instructional sessions for students. Students worked independently during the math workshop to complete …

Understanding The Meaning Of The Equal Sign : An Investigation Of Elementary Students And Teachers., Victoria Miller Bennett

Electronic Theses and Dissertations

The purpose of this study was to investigate the impact of two different policies for implementing new mathematics standards in two schools, for grades two through five, on student understanding of the equal sign. The study also examined teachers’ knowledge of the equal sign. The research used a mixed methods design to explore differences in student understanding of the equal sign as a result of how standards were implemented in two adjoining states with two different decisions as to when the standards would be implemented. This dissertation shares research that may be of interest to teachers, administrators, teacher educators and …

Flipping In A Technological Rich Classroom, John W. Budge

EDL Sixth Year Theses

The purpose of this study was to explore eighth grade students’ perception of a flipped classroom environment. It is difficult to engage and motivate eighth grade students. This study was created in order to determine if a flipped classroom would spark more interest and therefore eventually lead to an increased ability. More specifically, this study investigated how students perceive their learning is progressing in a flipped math classroom, and how engaged are they using the technology compared to the traditional classroom setting. The classroom environment was switched to a flipped classroom at the start of a new unit in October. …

Computation In A Localization Of The Free Group Algebra, Olga Zamoruyeva

Master's Theses

The coefficients of a Taylor series expansion of any rational function in one variable satisfy a linear recurrence relation. Our main result is a generalization of this statement for rational functions of multiple non-commutative variables. We show that if such a function is represented in the form of a non-commutative formal power series via Magnus embedding, then the coefficients of this formal power series are determined by a finite set of linear homogeneous recurrence relations. This finite representation of an infinite series allows for efficient computation of operations (multiplication, addition, and in many cases inversion) on non-commutative rational functions.

Preservation Of Periodicity In Variational Integrators, Jian-Long Liu

Master's Theses

Classical numerical integrators do not preserve symplecticity, a structure inherent in Hamiltonian systems. Thus, the trajectories they produce cannot be expected to possess the same qualitative behavior observed in the original system. Pooling recent results from O'Neale and West, we explore a particular class of numerical integrators, the variational integrator, that preserves one aspect of the range of behavior present in Hamiltonian systems, the periodicity of trajectories. We first establish the prerequisites and some key concepts from Hamiltonian systems, particularly symplecticity and action-angle coordinates. Through perturbation theory and its complications manifested in small divisor problems, we motivate the necessity for …

Generic Polynomials, Lucas Spencer Mattick

Master's Theses

In Galois theory one is interested in finding a polynomial over a field that has a given Galois group. A more desirable polynomial is one that parametrizes all such polynomials with that given group as its corresponding Galois group. These are called generic polynomials and we provide detailed proofs of two theorems that give methods for constructing such polynomials. Furthermore, we construct generic polynomials for Sn, C3, V , C4, C6, D3, D4, and D6.

Foliations With Geometric Structures: An Approach Through H-Principle., Sauvik Mukherjee Dr.

Doctoral Theses

A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures.The thesis consists of two parts. In the first part we classify foliations on open manifolds whose leaves are either locally conformal symplectic or contact manifolds. These foliations can be described by some higher geometric structures - namely the Poisson and the Jacobi structures. In the second part of the thesis, we consider foliations on open contact manifolds whose leaves are contact submanifolds of the ambient …

On The Analysis Of Some Recursive Equations In Probability., Arunangshu Biswas Dr.

Doctoral Theses

This thesis deals with recursive systems used in theoretical and applied probability. Recursive systems are stochastic processes {Xn}n≥1 where the Xn depends on the earlier Xn−1 and also on some increment process which is uncorrelated with the process Xn. The simplest example of a recursive system is the Random Walk, whose properties have been extensively studied. Mathematically a recursive system takes the form Xn = f(Xn−1, n), is the increment/ innovation procedure and f(·, ·) is a function on the product space of xn and n. We first consider a recursive system called Self-Normalized sums (SNS) corresponding to a sequence …

Some Issues In Unsupervised Feature Selection Using Similarity., Partha Pratim Kundu Dr.

Doctoral Theses

Pattern recognition is what humans do most of the time, without any conscious effort, and fortunately excel in. Information is received through various sensory organs, processed simultaneously in the brain, and its source is instantaneously identified without any perceptible effort. The interesting issue is that recognition occurs even under non-ideal conditions, i.e., when information is vague, imprecise or incomplete. In reality, most human activities depend on the success in performing various pattern recognition tasks. Let us consider an example. Before boarding a train or bus, we first select the appropriate one by identifying either the route number or its destination …

Achievement In Mathematics And Self-Concept Among Gifted Female High School Seniors, Leah M. Battin

School of Education and Leadership Student Capstone Theses and Dissertations

The author sought to explore the research question, What is the relationship between mathematics achievement and self-concept of gifted female high school seniors? Review of the literature included discussions of definitions and stereotypes of giftedness, gender differences in math/STEM attitudes and achievement, malleable versus fixed intelligence and ability in math, self-concept, and stereotype threat. The author worked with gifted female high school students at a summer camp for gifted students in South Dakota. Participants were recruited from the group of young women who had finished the camp in 2014. Of 20 young women contacted, five returned letters of consent. A …

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized …

Investigating Student Learning And Perceptions Through Concept Journaling: An Exploratory Case Study In Coordinate Algebra, Amber Steele

Middle and Secondary Education Dissertations

In order for students to comprehend mathematics, they must be able to think and apply learned knowledge to inform skill acquisition (Schoenfeld, 2013). Written communication is a skill that enables students to prepare to learn mathematics and express thoughts. Using qualitative case study methodology within symbolic interactionism framework, this study examined the effect of concept journaling on the learning of seven students in one high school Coordinate Algebra classroom. The study further explored how these students perceived concept journaling as a tool for learning mathematics. Concept journaling is defined as a type of writing activity using prompts that incorporate graphs, …

Using Graphic Organizers, Cooperative Learning, And Written Reflection To Improve Mathematics Problem Solving Skills, Kara Jean Odegaard

School of Education and Leadership Student Capstone Theses and Dissertations

The research question addressed is, how can cooperative learning, graphic organizers, and writing improve eighth grade advanced geometry students’ problem solving skills? The motivating factor for this capstone was students being unsuccessful when trying to solve an assignment which required synthesizing information and problem solving. This capstone documents the process of having students complete problem solving assignments using a graphic organizer, cooperative learning, and reflecting on the assignment through writing. The researcher found success and struggles with the use of these tools and concludes that 1) students were more successful in the problem solving process when they used the graphic …

What Concerns Are Secondary Mathematics Teachers Experiencing With The Implementation Of The Common Core State Standards For Mathematics And Is There A Relationship Between The Concerns And Professional Development Received?, Suzanne Therez Jennings

Dissertations

Using the Concerns Based Adoption Model (CBAM) as the theoretical framework, this mixed-methods study utilized three research methods, quantitative, profile interpretation, and qualitative to answer the research questions to investigate the concerns teachers were experiencing during the first year of implementing the Common Core State Standards for Mathematics (CCSSM) and to determine if professional development affected those concerns. The Stage of Concern questionnaire which included two open-ended questions was employed to survey 88 secondary Mississippi mathematics teachers. MANOVA was used to investigate any differences in the means of the relative levels of intensity present within the subgroups which are inconclusive. …

Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.

Doctoral Theses

In this chapter, we will give a brief history of wavelet analysis on R. We will also list some bask results on local felds which will be used in subvequent chapters.1.1 Wavelets on RWe fiest start with a brief history of wavelets und some basic defnitions and results conceming the orthonormal wavekts on R.1.1.1 A brief historyIn the last few decades vaveler theory has growa extensively and has drawn great atlention sot only in mathematies bu also in engineering, pitysics, computer science and many other fields. In signal and image processing, wavelets play a very important role.In 1910, A. Haar …

Euler Class Groups Of Polynomial And Sub Integral Extensions Of A Noetherian Ring., Md. Ali Zinna Dr.

Doctoral Theses

ObjectiveThe main objectives of this thesis are the following:(i) To investigate the behaviour of the Euler class groups under integral and subintegral extensions. More precisely, given a subintegral (or integral) extension R+ S of Noetherian rings, we are interested in finding out the relationship between the Euler class group of R and the Euler class group of S.(ii) To develop a theory (namely, an extension of the theory of Euler class group to the Euler class group of R[T) relative to a projective R[T|-module L of rank 1) in order to detect the precise obstruction for a projective R[T]-module P …

Teacher Beliefs And The Common Core State Standards For Mathematics, Erin M. Smith

School of Education and Leadership Student Capstone Theses and Dissertations

Widespread adoption of the Common Core State Standards for Mathematics (CCSSM) marks an unprecedented event in American education: nearly all students have an opportunity to learn the same mathematics content at the same stage of their K-12 educational experience. One goal of the CCSSM is to promote mathematics educational equity and excellence through common, rigorous standards. However, common standards may not translate to a common learning experience for all students. Teachers’ mathematical beliefs act as filters through which new information is interpreted and dispositions toward actions taken in the classroom. This study examined this beliefspractice relationship by asking two questions: …

Course Proposal For A Mathematical Modeling Course In A High School Curriculum, Thomas P. Marlowe

Masters Essays

In the winter of 2015, I will be piloting a course on mathematical modeling at Hawken School, an independent high school in Gates Mills, OH. As I develop all elements of this course, such as lesson plans, assessments, and rubrics, I will be mindful of factors such as the newly adopted Common Core mathematics standards, the variety of student backgrounds in such a course, and how various mathematical societies and organizations such as SIAM, MAA, and COMAP can help in implementing it. However, there is one basic question driving my interest in and design of this course: “when am I …

Infinity In The High School Mathematics Classroom, Alyssa Hoslar

Masters Essays

No abstract provided.