Digital Commons Network^™

Perceptions Of Educators On Motivational Strategies Influencing Middle School Students In Mathematics Courses, Amy Rigsby

Electronic Theses and Dissertations

This qualitative study examined educators' perceptions of motivational strategies influencing and motivating middle school students to comprehend and perform in mathematics courses. This study used interview data from 15 participants with 2 to 30 years of teaching experience. Educators may utilize this information in multiple settings within the classroom to influence and motivate students in mathematics courses.

Data collection strategies included one-on-one semi-structured middle school educator interviews. Analysis of data occurred in three phases: (a) categorization of data under the five organizational factors, (b) building the explanation in narrative form, and (c) re-examination of the data. The analysis of the …

Investigation Of Student Understanding Of Representations Of Probability Concepts In Quantum Mechanics, William D. Riihiluoma

Electronic Theses and Dissertations

The ability to relate physical concepts and phenomena to multiple mathematical representations—and to move fluidly between these representations—is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered. Thus, developing the ability to generate and translate expressions in these notations is of great importance, and the extent to which students can relate these expressions to physical quantities and phenomena is crucial to understand.

To investigate student understanding of the expressions used in these notations and the ways they relate, clinical think-aloud interviews were conducted …

Examining The Effectiveness Of Using Point-Of-View Video Modeling On Mathematics Improvement In Students With Learning Disabilities In Saudi Arabia, Tirad Alsaluli

Electronic Theses and Dissertations

Video Modeling (VM) is one of the most widely used approaches by researchers to improve many skills, such as academic skills in students with Learning Disabilities (LD; Boon et al., 2020). As the incidence rate of individuals with LD in Saudi Arabia increase (Almedlij & Rubinstein-Ávila, 2018), the need for evidence-based math interventions focused on the math development of individuals with LD also increases. Although VM is recognized as an Evidence-based Practice (EBPs), a limited number of studies have implemented VM as an intervention to improve mathematic skills. Implementing VM as a math intervention strategy would explore its effects on …

Analyzing The Influence Of Mathematics Intervention Teacher Actions On Students' Mathematics Identities: An Examination Of Bipoc Student Perceptions And Past Learning Experiences., Sydni P. Morris

Electronic Theses and Dissertations

This dissertation examines mathematics education's past and present state in the United States, emphasizing mathematics intervention instruction. This dissertation includes a complex and critical analysis of intervention practices and historical and structural inequities based on race present in these interventions and mathematics education. In combination, it examines the construct of mathematics identities, their role in student success with mathematics, and trends surrounding mathematics education and its impact on populations of students of color. Using Critical Race Theory as an underlying framework and Critical Counter-Narrative as a methodology, it argues a need for marginalized student voices to be present in the …

Mathematics And Special Education Co-Teaching In The Middle School: How Teachers Make Sense Of Their Partnership, Bethany Lavalley

Electronic Theses and Dissertations

Co-teaching is the practice of general educators and special educators sharing instruction in a general education setting to deliberately meet the needs of students with and without disabilities. Co-teacher research tends to focus on the processes of co-teaching, and little is known about how teachers go about creating a system of interconnected professional expertise that flexibly meets the diverse learning needs of students. This comparative case study examines the interpersonal and professional relationships of two co-teaching teams who were supported by their respective administration, who shared common planning time, co-instructed together in the mathematics classroom, and were engaged in a …

On Loop Commutators, Quaternionic Automorphic Loops, And Related Topics, Mariah Kathleen Barnes

Electronic Theses and Dissertations

This dissertation deals with three topics inside loop and quasigroup theory. First, as a continuation of the project started by David Stanovský and Petr Vojtĕchovský, we study the commutator of congruences defined by Freese and McKenzie in order to create a more pleasing, equivalent definition of the commutator inside of loops. Moreover, we show that the commutator can be characterized by the generators of the inner mapping group of the loop. We then translate these results to characterize the commutator of two normal subloops of any loop.

Second, we study automorphic loops with the desire to find more examples of …

Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …

Topics In Moufang Loops, Riley Britten

Electronic Theses and Dissertations

We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang loops which behave analogously to the generalized quaternion groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from the context of Moufang loops to discuss solvability in general loops. We then prove some results on …

Banach Spaces On Topological Ramsey Structures, Cheng-Chih Ko

Electronic Theses and Dissertations

A Banach space T₁(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T₁ defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ_∞ⁿ⁺¹ -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T₁(d, θ) is isomorphic to (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_p , where d ∈ ℕ with d ≥ 2, …

Examining Opportunities For Higher-Order Thinking In Secondary And Middle-Level Proficiency-Based Mathematics Classrooms, Quinton Donahue

Electronic Theses and Dissertations

In 2011, the state of Maine introduced a statute that required all diplomas to be awarded on the basis of proficiency by 2017. During this period of time, school districts moved to incorporate Proficiency-based Education (PBE) systems of instruction and learning. This prompted educators to bring clarity to standards, assessment, and grading practices. In many schools, they also began to focus on the idea that mastery drives movement. Districts were encouraged to integrate higher-order thinking opportunities for students when making these changes to their learning system. Despite this guidance, it is not clear as to the extent that higher-order thinking …

Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill

Electronic Theses and Dissertations

Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra V^G is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by V^G if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, V^G will also be strongly finitely generated. This is an analogue …

Understanding The Latinx Student Experience In A First-Year, Non-Remedial, Terminal College Math Course: A Convergent Mixed Methods Study, Ross Morgan

Electronic Theses and Dissertations

Working with Latinx students, a semester long study was conducted in the Spring of 2021 to better understand student’s perception of Culturally Responsive Teaching Practices (CRTP) at Mountain State University (MSU). The course sections selected are a part of a larger first year, non-remedial, terminal mathematics courses designed to provide students with smaller teacher to student ratios as well as opportunities to earn credit towards graduation. Instructors in two of the sections received special training around CRTP, while instructors in the other two sections did not receive this training. Findings demonstrate that simple adjustments to instructional practices had a statistically …

Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse

Electronic Theses and Dissertations

Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …

The Impact Of Elementary Mathematics Coaches On Elementary Teachers' Attitudes Towards Teaching Mathematics, Samuel R. Ward

Electronic Theses and Dissertations

This study compares levels of mathematics anxiety and teacher efficacy between inservice and preservice elementary teachers. Prior research has indicated that mathematics anxiety is a common trait among elementary teachers. Mathematics anxiety has also been found to have a negative impact on preservice elementary teachers’ efficacy towards teaching mathematics. To address this challenge, some states have begun hiring elementary mathematics coaches to support elementary teachers. Besides focusing on mathematics anxiety and teacher efficacy, this study also investigated the impacts of elementary mathematics coaches on inservice elementary teachers.

A total of 174 inservice teachers and 51 preservice teachers completed a survey …

Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly

Electronic Theses and Dissertations

Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy inequality, which bounds the edge distribution between two sets based on the spectral gap. More specifically, it states that a small spectral gap of a graph implies that the edge distribution is close to random. This dissertation uses this tool to study two problems in extremal graph theory, then produces similar discrepancy inequalities based …

Effective Response To Intervention In Middle School, Angela Mechelle Ellison

Electronic Theses and Dissertations

This applied mixed methods program evaluation sought to increase student proficiency in mathematics at a rural middle school in central Mississippi. The program focused on improving student achievement through effective professional development. Quantitative and qualitative data was used to gage the program’s effectiveness. Research supporting an effective Response to Intervention Model, professional learning communities, and teacher development was cited and used to construct the program’s implementation framework.

Effective Instructional Strategies In Sixth Grade Inclusion Mathematics Classrooms: The Effect Of Active And Passive Engagement On Concept Learning And Opportunity To Learn, Christy Mikolaj

Electronic Theses and Dissertations

The purpose of this mixed-method study focused on the effect of active engagement on opportunity to learn and concept learning among sixth grade special education students participating in the inclusion mathematical setting. By implementing two instructional strategies and using the theoretical frameworks of Vygotsky’s Social Constructivism and Erikson’s Stage of Psychosocial Development of Industry vs. Inferiority, findings showed there was a significant negative relationship between active engagement time during instruction and concept learning. The study showed students with identified needs within an inclusion mathematics setting increased concept learning in both instructional classrooms. Therefore, there was no difference in concept learning …

Investigating The Transfer Of Metacognition To Domains Distinct From Mathematics, Justin Teeuwen

Electronic Theses and Dissertations

The purpose of the present research was to investigate the transfer of metacognition from mathematics to other domains for a post-secondary population. A systematic literature review revealed potential transferability for metacognitive strategic knowledge, metacognitive planning, monitoring, and debugging. Mevarech and Kramarksi’s (1997) IMPROVE model was modified to incorporate the explicit instruction of transfer and then used as the metacognitive intervention for a beginner-level calculus course at the University of Windsor. This occurred over a period of five weeks with n = 90 participants for each of the experimental and control groups. A concurrent, triangulated mixed-method research design was employed to …

Barrier Graphs And Extremal Questions On Line, Ray, Segment, And Hyperplane Sensor Networks, Kirk Anthony Boyer

Electronic Theses and Dissertations

A sensor network is typically modeled as a collection of spatially distributed objects with the same shape, generally for the purpose of surveilling or protecting areas and locations. In this dissertation we address several questions relating to sensors with linear shapes: line, line segment, and rays in the plane, and hyperplanes in higher dimensions.

First we explore ray sensor networks in the plane, whose resilience is the number of sensors that must be crossed by an agent traveling between two known locations. The coverage of such a network is described by a particular tripartite graph, the barrier graph of the …

Telling Our Stories: Exploring The Path Toward Successful Mathematics Degree Attainment At An Under-Resourced Predominantly Black Institution, Lauren E. Mckittrick

Electronic Theses and Dissertations

The under-representation of Blacks in mathematics related professions stems from an American educational system of inequity. Many Black students, including a substantial proportion of those who enroll at Predominantly Black Institutions, attend elementary and secondary schools in under-resourced districts with limited access to quality teachers and rigorous, culturally-relevant instruction that would adequately prepare them for college attainment in mathematics.

The primary research question guiding this study was: What are the challenges and opportunities associated with building and sustaining a successful mathematics degree program at an under-resourced Predominantly Black Institution? Concurrently, this interpretive case study examined and documented the experiences of …

Applications Of Geometric And Spectral Methods In Graph Theory, Lauren Morey Nelsen

Electronic Theses and Dissertations

Networks, or graphs, are useful for studying many things in today’s world. Graphs can be used to represent connections on social media, transportation networks, or even the internet. Because of this, it’s helpful to study graphs and learn what we can say about the structure of a given graph or what properties it might have. This dissertation focuses on the use of the probabilistic method and spectral graph theory to understand the geometric structure of graphs and find structures in graphs. We will also discuss graph curvature and how curvature lower bounds can be used to give us information about …

Decidability For Residuated Lattices And Substructural Logics, Gavin St. John

Electronic Theses and Dissertations

We present a number of results related to the decidability and undecidability of various varieties of residuated lattices and their corresponding substructural logics. The context of this analysis is the extension of residuated lattices by various simple equations, dually, the extension of substructural logics by simple structural rules, with the aim of classifying simple equations by the decidability properties shared by their extensions. We also prove a number of relationships among simple extensions by showing the equational theory of their idempotent semiring reducts coincides with simple extensions of idempotent semirings. On the decidability front, we develop both semantical and syntactical …

Two Way Street: An Applied Research Study On The Effects Of Increased Parent And Community Involvement Activities On Student Academic Growth In Mathematics At South Lee Middle School, Jason Clifton Arledge

Electronic Theses and Dissertations

The purpose of this study was two-fold. The first overarching goal was to increase student academic growth on the Mississippi Academic Assessment Program mathematics assessment to at least 75%. This was attempted through implementation of grade-level Remind services and the Red Raider Family program. The second overarching goal was to create a cycle of continuous improvement through feedback from key stakeholders in the form of surveys, interviews, focus groups, document analysis, and descriptive statistics. South Lee Middle School evaluated each of these initiatives and utilized resources to adjust these programs for use in the 2018-2019 school year.

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

A First-Year Teacher’S Implementation Of Short-Cycle Formative Assessment Through The Use Of A Classroom Response System And Flexible Grouping, Adrienne Irving Dumas

Electronic Theses and Dissertations

As teachers we are tasked with ensuring that our students are equipped with the skills necessary to not only perform with proficiency on local state and national assessments but also to provide our students with opportunities to develop confidence and competence as learners of mathematics through meaningful challenging and worthwhile activities. As such many teachers have turned to technology and cooperative groups as staples in the classroom. The purpose of this study was to understand how one first-year teacher implemented what she was taught in her undergraduate coursework in teaching two specific units of instruction in two sections of high …

Beta Invariant And Variations Of Chain Theorems For Matroids, Sooyeon Lee

Electronic Theses and Dissertations

The beta invariant of a matroid was introduced by Crapo in 1967. We first find the lower bound of the beta invariant of 3-connected matroids with rank r and the matroids which attain the lower bound. Second we characterize the matroids with beta invariant 5 and 6. For binary matroids we characterize matroids with beta invariant 7. These results extend earlier work of Oxley. Lastly we partially answer an open question of chromatic uniqueness of wheels and prove a splitting formula for the beta invariant of generalized parallel connection of two matroids. Tutte's Wheel-and-Whirl theorem and Seymour's Splitter theorem give …

Feedback In The Flipped High School Stem Classroom, Trisha Michele Gilbreath

Electronic Theses and Dissertations

This study examined how much feedback students received in the flipped high school science, technology, engineering and math (STEM) classroom. The flipped classroom is a pedagogical technique where students watch video instruction at home and complete collaborative activities in class. This technique has gained popularity in recent years, especially in STEM classrooms. The literature on the flipped classroom is inconclusive, with studies mainly conducted in higher education. Student and instructor perceptions were often studied, and those perceptions are generally positive about the flipped classroom, though there are concerns to consider. Student performance shows that the flipped classroom is at least …

An Examination Of The Relationship Among The Intentions, Features, Affordances, And Outcomes Of Saturday Academy For Math Professional Development For Mathematics Teachers, Brian Buckhalter

Electronic Theses and Dissertations

Using a design framework to connect the features of SA4M to the affordances reported, participants of SA4M deepened their content knowledge on both conceptual and skill specific levels, and expressed intentions to incorporate many of the tasks from SA4M into their practices. There are implications for those tasked with creating and evaluating professional development for teachers.

Surface Entropy Of Shifts Of Finite Type, Dennis Pace

Electronic Theses and Dissertations

Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, H_S : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface entropy is a conjugacy invariant and is a tool in the classification of subshifts. We develop a tiling algorithm related to continued fractions which allows us to prove a continuity result about surface …

T-De Vries Algebra, Nawal Alznad

Electronic Theses and Dissertations

The main point of this dissertation is to introduce the action on de Vries algebra by a topological monoid and we denoted the resulting category by dVT. In order to reach our goal, we started with introducing new proofs for some well known results in the category of flows. Then, we studied the Generalized Smirnov's Theorem for flows. After we studied the new category (dVT), we were able to provide a new way to construct the Čech-stone flow compactification of a given flow. Finally, we developed the co-free T-de Vries algebra for a special case.