Digital Commons Network^™

A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.

Doctoral Theses

Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …

Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.

Doctoral Theses

The main focus of this thesis is secret sharing. Secret Sharing is a very basic and fundamental cryptographic primitive. It is a method to share a secret by a dealer among different parties in such a way that only certain predetermined subsets of parties can together reconstruct the secret while some of the remaining subsets of parties can have no information about the secret. Secret sharing was introduced independently by Shamir [139] and Blakely [20]. What they introduced is called a threshold secret sharing scheme. In such a secret sharing scheme the subsets of parties that can reconstruct a secret …

Linear Inverse Problems And Neural Networks, Jasjeet Dhaliwal

Master's Theses

We investigate two ideas in this thesis. First, we analyze the results of adaptingrecovery algorithms from linear inverse problems to defend neural networks against adversarial attacks. Second, we analyze the results of substituting sparsity priors with neural network priors in linear inverse problems. For the former, we are able to extend the framework introduced in [1] to defend neural networks against ℓ0, ℓ2,and ℓ∞ norm attacks, and for the latter, we find that our method yields an improvement over reconstruction results of [2].

Blue Red Hackenbush Spiders, Ravi Cho

Master's Theses

One of the goals of Combinatorial Game Theory is to find provable winning strategiesfor certain games. In this paper, we give winning strategies for certain spider positions played using the rules of Blue Red Hackenbush and a variant. Blue Red Hackenbush and its variants are played on a graph of a bLue and Red edges that are connected to a vertex called the ground. We will represent the ground as a horizontal black line. In this paper, we study spider graphs played under two different variants: Blue Red Hackenbush and Reverse Blue Red Hackenbush. Both variants are played by two …

Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker

Dissertations and Theses

In this work, the finite element method and the FEAST eigensolver are used to explore applications in fiber optics. The present interest is in computing eigenfunctions u and propagation constants β satisfing [sic] the Helmholtz equation Δu + k²n²u = β²u. Here, k is the freespace wavenumber and n is a spatially varying coefficient function representing the refractive index of the underlying medium. Such a problem arises when attempting to compute confinement losses in optical fibers that guide laser light. In practice, this requires the computation of functions u referred to as …

Factors That Contribute To Motivation And Student Achievement As Adolescents Transition From Elementary To Middle School Or Junior High In One Urban District In The Rio Grande Valley, Lizette Villarreal Longoria

Theses and Dissertations

This study will examine factors that contribute to the decline in achievement scores in reading and mathematics when students transition from elementary to their first year in middle school or junior high school. It will test the hypothesis that motivation is not a function of mentors, academic support, teams, parental involvement, transition experience, math perception, and reading perception for students transitioning from elementary to middle school or junior high school. In this quantitative research study, data will be collected using a multiple linear regression analysis to examine the factors that contribute to motivation and the achievement score decline in reading …

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 …

Numerical Cognition And Autism Spectrum Traits In Adults, Benjamin Covington

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Evidence suggests that individuals with high-functioning autism spectrum disorder (ASD) may be particularly inclined toward math proficiency, especially in adulthood. There is also evidence, however, that many of those with an ASD struggle in math as children compared to their typically-developing peers. These ostensibly inconsistent findings may indicate that individuals with an ASD struggle with number sense, a precursor to formal math, rather than with formal math per se. This account is compatible with evidence of a specific form of neural dysregulation, excitatory/inhibitory imbalance, in ASD that results in reduced signal-to-noise ratios (SNR) for processes that occur in downstream …

The Impact Of A K-8 Stem Program On Grades And Student Choice Of Stem And Advanced Mathematics And Science Coursework In High School, Astrid Rodrigues

Dissertations

The demands of today’s workforce call for schools to prepare their students to have problem-solving skills and be critical thinkers and collaborative colleagues. Science, Technology, Engineering, and Mathematics (STEM) learning has been known to cultivate, excite, and promote critical thinking and problem-solving skills in students from an early age.

This study explored the high school course selection of students who had participated in a compulsory Kindergarten to 8^th grade (K-8) STEM program, called Project Lead the Way (PLTW), while in middle school. Specifically, the study compared the number of STEM and advanced mathematics and science courses that students who …

Properties Of Curriculum-Based Measurement For Mathematics : An Investigation Of The Average Growth, Variability, And Precision Of Three Forms, Arianna Doss

Legacy Theses & Dissertations (2009 - 2024)

CBM for mathematics assesses growth in accuracy and fluency of basic math skills using content from a student’s curriculum. CBM for mathematics can include single-skill measures (SSM), skill-based measures (SBM), and general-outcome measures (GOM). Past research on growth rates in CBM for mathematics has focused on GOMs and has relied on estimations of weekly growth rates, but more information on expected growth rates and their precision for these measures is needed for practice. The current study addresses this gap in the literature by examining weekly growth rates and their precision for one SSM containing multiplication problems, one SBM containing addition …

Teachers’ Perceptions Of Teaching Mathematics Online In Elementary Schools In Al Ain., Kamar Fayez Kamar

Theses

Online learning is an active method of learning in our lives, and it has been implemented in all the schools in the United Arab Emirates (UAE). Many methods such as platforms, online educational websites, and other applications were used by teachers to support online learning, and to be able to assist students to achieve their goals and accomplish what is required from their curriculum. The main objective of this study is to examine teachers’ perceptions toward teaching mathematics using online learning in elementary schools. Data was collected from 90 (n= 90) elementary teachers in Al Ain City, UAE, during the …

Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.

Doctoral Theses

No abstract provided.

The Importance Of Math Fact Automaticity, Jessica Olson

School of Education and Leadership Student Capstone Projects

The retention of math facts is a critical step when it comes to solving mathematical equations. The website I designed for my project addresses this topic. It focuses on giving students, teachers and parents the research, tips and resources they need to be successful. Research shows that automaticity with math facts can lessen the academic load of students and also be a predictor of future math success. Using strategies such as interleaving, engaging with manipulatives and learning mnemonic devices has been shown to positively affect one’s recall of basic facts. However, drilling and mindless repetition has a much more negative …

Personalized Geometry Instruction: A Mixed Methods Action Research Study Implementing An Adaptive Web-Based Learning Environment To Support High School Students’ Geometry Problemsolving Skills, Catherine D. Jordan

Theses and Dissertations

The purpose of this action research study was to evaluate the implementation of an adaptive web-based learning environment to personalize geometry instruction and practice for high school students at a private school in North Carolina. This study was guided by the following three research questions: (1) How and to what extent does implementing personalized geometry instruction and practice through an adaptive web-based learning environment affect high school students’ knowledge of geometry? (2) How does using personalized geometry instruction and practice through an adaptive web-based learning environment affect students’ motivation to learn geometry as well as their mathematics self-efficacy, anxiety, and …

Developing Mathematical Thinking In High Schoolers Through “Curricular Thinking Tasks”, Michaela Weispfennig

School of Education and Leadership Student Capstone Projects

A review of the literature and reflection on personal experience show a need to rethink the way we teach and learn mathematics. A traditional math class relies on direct instruction and emphasizes decontextualized procedures and algorithms. This type of instruction does not work well for the majority of students, nor does it prescribe to the goals of math education in our modern world. We don’t need “human computers'' like we did before the internet. Instead, the primary goal for most high school math students is to develop the mathematical thinking skills needed to tackle new problems. Inspired by Peter Liljedahl’s …

Developing A Deep Understanding Of Multiplication And A Growth Mindset In 5th Grade Students From Marginalized Groups, Rachael Johnson

School of Education and Leadership Student Capstone Projects

Traditionally mathematics has been taught with a focus of rote memorization of basic facts and procedures. Research has found that this often leaves students without the conceptual understanding behind procedures. This can prevent students from making the connections necessary to transfer their knowledge to other situations. It has also become clear that students from marginalized groups often score much lower on high stakes tests than their white counterparts. This project involved creating a multiplication unit that uses number talks, strategies from cognitively guided instruction as well as ideas on culturally relevant teaching. The goal of this project was for students …

Some Topics In Leavitt Path Algebras And Their Generalizations., Mohan R. Dr.

Doctoral Theses

The purpose of this section is to motivate the historical development of Leavitt algebras, Leavitt path algebras and their various generalizations and thus provide a context for this thesis. There are two historical threads which resulted in the definition of Leavitt path algebras. The first one is about the realization problem for von Neumann regular rings and the second one is about studying algebraic analogs of graph C ∗ -algebras. In what follows we briefly survey these threads and also introduce important concepts and terminology which will recur throughout.

Scaling Limits Of Some Random Interface Models., Biltu Dan Dr.

Doctoral Theses

In this thesis, we study some probabilistic models of random interfaces. Interfaces between different phases have been topic of considerable interest in statistical physics. These interfaces are described by a family of random variables, indexed by the ddimensional integer lattice, which are considered as a height configuration, namely they indicate the height of the interface above a reference hyperplane. The models are defined in terms of an energy function (Hamiltonian), which defines a Gibbs measure on the set of height configurations. More formally, letÏ• = {Ï•x}x∈Z dbe a collection of real numbers indexed by the d-dimensional integer lattice Z d. …

On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.

Doctoral Theses

This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …

Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.

Doctoral Theses

A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …

Examining The Use Of Culturally Relevant Pedagogy In Undergraduate Mathematics Learning Modules With Students Of Color, Thomas A. Mgonja

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In mathematics, Students of Color have persistently performed lower than their White counterparts, thus creating a need to explore instructional methods that could reduce performance disparities. This study investigated culturally relevant pedagogy (CRP) to understand how it might support students’ mathematics learning in undergraduate mathematics learning modules. The overarching research question focused on how CRP in undergraduate mathematics Learning Modules supported students’ mathematics learning. There were also two main questions that focused on participants’ evaluations of the CRP modules and how those evaluations were reported based on subgroups (Students of Color and White). The researcher employed a sequential explanatory mixed-methods …

Game Based Intervention To Develop Early Childhood Mathematical Understanding And Decrease Gaps Related To Socioeconomic Status, Lydia Flynn

Boise State University Theses and Dissertations

Early mathematical understanding is important for later success in mathematics. Game based interventions can be a successful means by which to help young students to improve their mathematical understandings. The purpose of this study is to examine whether a math game that was to be played at home improved the mathematical understanding of kindergarten students. Kindergarten students, from rural Idaho, were assigned to a group that played math games (n = 15) or a control group that did not (n = 13). The intervention group was given a simple math game and instructed to play 20 times in a …

Partial Representations For Ternary Matroids, Ebony Perez

Electronic Theses, Projects, and Dissertations

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a …

The Role Of Self-Efficacy And Academic Mindset On Middle School Math Achievement For At Promise Youth: An Explanatory Study, Michael Lockwood Mansfield

Dissertations

California’s accountability system has blended its focus on noncognitive factors of achievement as well as evidence of academic growth. School districts are becoming increasingly interested in developing noncognitive factors in their students to help increase student achievement. With the wide variety of mandates and responsibilities schools are shouldering, it will be important to continue developing methods to increase all school accountability metrics in relation with each other. This research aims to explore the relationship between noncognitive factors and mathematics achievement as measured by the Northwest Evaluation Association’s Measure of Academic Progress assessment (MAP). This study surveyed 8th graders throughout a …

Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.

Doctoral Theses

This thesis comprises four essays on social choice theory. The first three essays/chapters consider models where voters follow “non-standard” rules for decision making. The last chapter considers the binary social choice model and analyzes the consequences of a new axiom. The first chapter introduces a new axiom for manipulability when voters incur a cost if they misreport their true preference ordering. The second chapter considers the random voting model with strategic voters where standard stochastic dominance strategy-proofness is replaced by strategy-proofness under two lexicographic criteria. The third chapter also considers the random voting model but from a non-strategic perspective. It …

#Blackgirlmathmagic: A Mixed Methods Study Examining African American Girls In Standardized Mathematicstesting, Rakeema Thomas Toussaint

LSU Doctoral Dissertations

Black women have been making successful strides in mathematics for decades; however, they continue to be underrepresented in mathematics and other STEM fields. According to Young et al. (2017), Black girls and women perform lower in mathematics than all other racial gender groups except for Black males. Considering the stakes for Black girls and women in mathematics, this study sought to address this group's challenges early in their secondary education experiences, focusing on standardized testing.

The purpose of this explanatory-sequential mixed-methods study was to determine how different mathematics item types impacted the performance of African American girls, especially multiple-select multiple-choice …

Designing A Professional Development Series For Educators On The Benefits Of Mathematical Manipulatives For Elementary Students’ Understanding And Mindset, Emily Geraghty

School of Education and Leadership Student Capstone Projects

Research has shown that manipulative use has a positive impact on elementary students’ understanding and mindset during their mathematics instruction. Yet, some K-5 educators are not aware of the benefits or do not know how to effectively implement manipulatives in their classrooms. This led to the creation of a professional development series. The goal of the project is for K-5 educators to learn about the benefits of manipulatives on students’ understanding and mindset through active learning, practice and application. This is made possible through slides, videos, discussion and example lessons that utilize manipulatives. By participating in the professional development series, …

Implementing Math Discourse And Rich Math Tasks To Develop Mathematical Thinking, Heather Berry

School of Education and Leadership Student Capstone Projects

Math is more than quick computation and the pursuit of correct answers. Math is sense-making. For students to thrive as problem solvers and critical thinkers in the classroom and beyond, attention must be paid to the development of their mathematical thinking. Mathematical thinking refers to the abilities to efficiently distinguish amongst specific procedures and flexibly formulate and represent strategies to suit a situation. It also includes the capacity to explain, analyze and justify one’s thinking with an understanding of self as an effective learner of math (Baroody et al., 2007; Boaler, 2018; Katz, 2014; Schoenfeld, 2016). This capstone project uses …

Combining Cognitively Guided Instruction With Required Mathematics Curriculum To Improve Overall Number Sense And Problem Solving Skill, Anna Becker

School of Education and Leadership Student Capstone Projects

Elementary school mathematics instruction often moves quickly from one to one correspondence to algorithms and rote exercises, leaving students with procedural knowledge but lacking in number sense and problem solving skills. Teachers follow the required curriculum to ensure success on assessments but skip over important instructional time that leads to number sense and a deeper understanding. Bringing Cognitively Guided Instruction into the classroom will improve students’ problem solving skills while also strengthening their number sense. This project provides educators with a full unit of detailed lesson plans for the kindergarten classroom. It also includes an outline of another unit with …

Fostering Critical Thinking Skills, And Engagement To Produce Better Retention Of 4th Grade Math, Christine Prostrollo

School of Education and Leadership Student Capstone Projects

My research question for this capstone project is: Which instructional approach best fosters critical thinking skills, engagement, and long-term retention in mathematics to best prepare 4th-grade students for the 21st century? My research suggests that a mathematics curriculum that best fosters these areas of learning would likely be the most successful at preparing our students for 21st-century learning. The various instructional approaches discussed in this literature review all have their strengths and weaknesses. Because of this, a combination approach of inquiry and direct instruction while focusing on the development of critical thinking skills, engagement, and long-term retention should be the …