Digital Commons Network^™

Learning Through Discourse: Impacting Fractional Understanding Through Virtual Discourse, Laurie A. Gentry-Goodale

Theses and Dissertations

There is a strong need for fifth-grade students to become proficient in mathematical problem-solving using fractional computations because it will have a lasting impact on student achievement. Traditionally, mathematics is taught inside a brick-and-mortar classroom, grounded in rote memorization of facts, rules, and formulas. In recent years, more elementary students have enrolled fully in online learning environments, which emphasize on students becoming problem-solvers, specifically in fractional computation. The NCTM strongly encourages using mathematical discourse as an instructional method but employing mathematical discourse, but its applicability to online math learning is not well understood. This study addressed students' problem-solving skills, mathematical …

Designing An Educational Robotics Curriculum To Teach Mathematical Concepts While Fostering A Growth Mindset: A Self-Study, Lauren Harter

Electronic Theses and Dissertations

This study explores the development and implementation of a five-day curriculum designed to enhance students' understanding of algebraic concepts through the integration of educational robotics and growth mindset principles. The study is structured around three research questions that investigate influences on decision-making in curriculum design, the alignment of teaching intents with practices, and the impact of self-study on integrating algebra, robotics, and growth mindset principles. Findings reveal themes focused on the importance of research and collaboration, using the Understanding by Design (UbD) framework, intentional curriculum creation, starting somewhere, personal growth and self-reflection, and experiencing and embodying constructivism in action. The …

An Examination Of The Influences Of Critical Thinking Tasks On Mathematics Instruction: A Qualitative Study, Glen E. Miller

Doctoral Dissertations and Projects

The purpose of this phenomenological study will be to understand the mathematics critical thinking process for teachers in primary education in northern Virginia. The theory guiding this study is Kolb’s experiential learning theory, which applies to critical thinking processes. The central research question will be: What are the experiences of primary mathematics teachers implementing critical thinking? This qualitative hermeneutic phenomenological study aims to determine the influences of critical thinking tasks on planning and instruction. Using qualified participants from northern Virginia, this study will collect data through interviews, a focus group, and document analysis. After data collection, the data will be …

Success In Secondary Mathematics Courses, Victoria Klaas

Masters Projects

According to research, many students struggle to successfully complete required secondary mathematics courses. Not only are these courses require for students to graduate, the courses prepare students to use mathematics in their everyday lives. The demand for careers in the mathematics field continues to grow. Students will continue to miss out on careers in this field if they do not successfully complete their secondary mathematics courses. This project outlines some of the factors affecting student mathematical success and provides an Algebra II unit plan. The unit plan provides guiding lesson plans and other needed materials for teachers to help improve …

Pre-Service Teachers’ Noticing Of Students’ Mathematical Thinking When Planning, Teaching, And Reflecting On Lessons, Matthew Flores

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A central aspect of reform-minded mathematical teaching is training and developing teachers' ability to notice vital aspects in the classroom and more specifically, students’ mathematical thinking. As there is an abundance of evidence and research that support the benefits for teachers to elicit and use students’ ideas and thinking during instruction, there are just as many challenges associated with developing and mastering this skill. Specially, teachers must learn to attend to important details of students’ thinking, interpret the meaning and understanding of students’ thinking, and finally, teachers must decide how to purposefully respond to the student in a manner that …

The Integration Of Mathematical Concepts In Physics Curriculum, Paige Poindexter

Masters Projects

Research has shown that students are struggling to grasp mathematical concepts and skills, which carries over to other subjects, such as science. As the need for an improved STEM education approach continues to grow, the use of integration to guide curriculum development has proven to be effective. This project dives into the available research surrounding the overlap of subjects taught in a secondary setting, focusing on the techniques proven to improve student academic success. This project addresses the need to draw clear connections between mathematics and physics courses, with the goal of improving student scores in both areas. The result …

S–Domination Number In Graphs, Sarah H. A. Alsaebari, Ahmed A. Omran

Baghdad Science Journal

Let G (V, E) be a graph, the set D⊆ V is dominating set if each vertex v∈ V is either in D or is adjacent to a vertex in D and if there is no dominating subset of D, D will minimal dominating of a graph G. The domination number γ(G) is the minimum cardinality of all members of a minimal dominating set of a graph G. If V-D includes dominating set D' of vertices of a graph G then D' is called an inverse dominating set to D such that γ^-1(G) is the minimum cardinality of …

The Role Of Adaptive Learning Programs In Secondary Mathematics: A Phenomenology Study, Shameka Sharae Gray

Doctoral Dissertations and Projects

The purpose of the transcendental phenomenological study was to discover the role of adaptive learning programs in closing the learning gaps in mathematics for secondary students in Georgia following the COVID-19 pandemic. The theory guiding this study was that of Bandura's theory on self-efficacy, as it highlights how an individual's experience impacts their belief in their ability to complete specific tasks. The central question in this study sought to identify the experiences of secondary math teachers who use adaptive learning programs to address learning gaps in mathematics following the COVID-19 pandemic. The participants for the study consisted of 10 to …

B-Chromatic Number Of The Graph Power Of The Star Graph, Erik Dahlen

DePaul Discoveries

In this paper we focus on the newly introduced b-colorings of a graph G. A b-coloring is a proper coloring such that for each color class, there exists at least one vertex which is adjacent to every other color. The b-chromatic number of a graph G is the largest number k such that G admits a b-coloring with k colors. This paper will introduce the b-chromatic number of some interesting graphs. Several operations of graphs are defined, and the b-chromatic number of those operations are found. All graphs in this paper are simple, connected, …

Math 75: Introduction To Linear Algebra, Sarah K. Merz

Pacific Open Texts

This text is intended to use in a first course of Linear Algebra with a prerequisite of Calculus 1. Topics covered include systems of linear equations, matrix operations and inverses, linear transformations, Markov chains, determinants, eigenvalues and eigenvectors, diagonalization, vector geometry, projections and planes, homogeneous coordinates, subspaces, spanning sets, linear independence, orthogonality, fundamental subspaces, and least squares.

Persistent Behavior In Solar Energetic Particle Time Series, N V. Sarlis, G Livadiotis, D J. Mccomas, M E. Cuesta, L Y. Khoo, C M S Cohen, D G. Mitchell, Nathan A. Schwadron

Faculty Publications

We investigate the long-term persistence of solar energetic particle (SEP) time series by means of four different methods: Hurst rescaled range R/S analysis, detrended fluctuation analysis, centered moving average analysis, and the fluctuation of natural time under the time reversal method. For these analyses, we use data sets from the Integrated Science Investigation of the Sun instrument suite on board NASA's Parker Solar Probe. Background systematic noise is modeled using cross-correlation analysis between different SEP energy channels and subtracted from the original data. The use of these four methods for deriving the time-series persistence allows us to (i) differentiate between …

Using Group Work In Mathematics To Introduce Social Justice Concepts: Curriculum To Help Students Learn About Each Other Through Mathematics, Wyatt Ehlke

School of Education and Leadership Student Capstone Projects

This curriculum addresses the research question: What are the best practices for engaging with social justice topics and goals in a modern, constructivism-based mathematics course? The paper documents the reasons why the author chose to approach this question, then consists of a literature review into the topics of constructivism, social justice, and group work. The paper then includes a plan for the construction of curriculum for a precalculus class and ends with a reflection on the curriculum itself. The project consists of a unit planner alongside five lessons, each of which has problems and activities that address this question in …

Persistent Behavior In Solar Energetic Particle Time Series, N V. Sarlis, G Livadiotis, D J. Mccomas, M E. Cuesta, L Y. Khoo, C M S Cohen, D G. Mitchell, Nathan A. Schwadron

Faculty Publications

We investigate the long-term persistence of solar energetic particle (SEP) time series by means of four different methods: Hurst rescaled range R/S analysis, detrended fluctuation analysis, centered moving average analysis, and the fluctuation of natural time under the time reversal method. For these analyses, we use data sets from the Integrated Science Investigation of the Sun instrument suite on board NASA's Parker Solar Probe. Background systematic noise is modeled using cross-correlation analysis between different SEP energy channels and subtracted from the original data. The use of these four methods for deriving the time-series persistence allows us to (i) differentiate between …

Ensuring The Effectiveness Of Reading And Mathematics Interventions, Bethany Lange

Master's Theses & Capstone Projects

With an increased pressure in standardized assessment performance, teachers have the difficult task of ensuring all students test at grade level. The goal of making a connection to each student’s learning style can be a daunting task, but positive results are possible. With research in mind, a school improvement plan was created to ensure the time spent during reading and mathematics interventions is effective. This plan creates a way for educators to assess students and develop the best plan of action for each student’s learning style.

Mathematical Merit, Sarah Moss

The Voice

No abstract provided.

Evaluation Of Inner Products Of Implicitly Defined Finite Element Functions On Multiply Connected Planar Mesh Cells, Jeffrey S. Ovall, Samuel E. Reynolds

Mathematics and Statistics Faculty Publications and Presentations

In recent years, there has been significant interest in the development of finite element methods defined on meshes that include rather general polytopes and curvilinear polygons. In the present work, we provide tools necessary to employ multiply connected mesh cells in planar domains, i.e., cells with holes, in finite element computations. Our focus is efficient evaluation of the ��1��1 semi-inner product and ��2��2 inner product of implicitly defined finite element functions of the types arising in boundary element based finite element methods and virtual element methods. Such functions are defined as solutions of Poisson problems having a polynomial source term …

Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser

Electronic Theses and Dissertations

This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.

We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …

Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk

Electronic Theses and Dissertations

The universal 2-parameter vertex algebra W_∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W_∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …

Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker

NEXUS: The Liberty Journal of Interdisciplinary Studies

Discoveries of equations for irrational numbers are not new. From Newton’s Method to Taylor Series,there are many ways to calculate the square root of two to arbitrary precision. The following method is similar in this way, but it is also a fascinating derivation from geometry that has applications to other irrationals. Additionally, the equation derived has some properties that may lead to fast computation. The first part of this paper is dedicated to deriving the equation, and the second is focused on computer science implementations and optimizations.

Effects Of Single-Session Practice Structure On Motor Skill Acquisition And Alpha And Beta Eeg Oscillations, Aubrey Porter, Ronald Victor Croce, Wayne Smith

Faculty Publications

Background: Although it is known that practicing a motor skill updates the associated internal model, it is still unclear as to how cortical oscillations linked with the motor skill change under differing practice schedules. The current study investigated α- and β-power changes associated with motor skill acquisition. Objectives: Firstly, we investigated the behavioral effects of practice on motor learning and retention during repetitive (RP) and variable (VP) practice schedules on an anticipation timing task. Secondly, we investigated changes in cortical α (10 - 13 Hz) and β (15 - 30 Hz) event-related synchronization and desynchronization (ERS/ERD) under RP and VP …

Effects Of Single-Session Practice Structure On Motor Skill Acquisition And Alpha And Beta Eeg Oscillations, Aubrey Porter, Ronald Victor Croce, Wayne Smith

Faculty Publications

Background: Although it is known that practicing a motor skill updates the associated internal model, it is still unclear as to how cortical oscillations linked with the motor skill change under differing practice schedules. The current study investigated α- and β-power changes associated with motor skill acquisition. Objectives: Firstly, we investigated the behavioral effects of practice on motor learning and retention during repetitive (RP) and variable (VP) practice schedules on an anticipation timing task. Secondly, we investigated changes in cortical α (10 - 13 Hz) and β (15 - 30 Hz) event-related synchronization and desynchronization (ERS/ERD) under RP and VP …

Khovanov Homology And Legendrian Simple Knots, Ryan J. Maguire

Dartmouth College Ph.D Dissertations

The Jones polynomial and Khovanov homology are powerful invariants in knot theory. Their computations are known to be NP-Hard and it can be quite a challenge to directly compute either of them for a general knot. We develop explicit algorithms for the Jones polynomial and discuss the implementation of an algorithm for Khovanov homology. Using this we tabulate the invariants for millions of knots, generate statistics on them, and formulate conjectures for Legendrian and transversely simple knots.

Infographic: Finding The Digital Learning ‘Sweet Spot’, Andrew Broadley

Teacher infographics

According to mathematics performance data from the OECD's PISA 2022 report, students that spend time at school learning on digital devices outperform students that don't. But how much time is too much time? In today’s infographic, we look at student mathematics scores across the OECD and Australia by hours spent on digital learning at school.

A Thesis, Or Digressions On Sculptural Practice: In Which, Concepts & Influences Thereof Are Explained, Set Forth, Catalogued, Or Divulged By Way Of Commentaries To A Poem, First Conceived By The Artist, Fed Through Chatg.P.T., And Re-Edited By The Artist, To Which Are Added, Annotated References, Impressions And Ruminations Thereof, Also Including Private Thoughts & Personal Accounts Of The Artist, Jaimie An

Masters Theses

This thesis is an exercise in, perhaps a futile, attempt to trace just some of the ideas, stories, and musings I might meander through in my process. It’s not quite a map, nor is it a neat catalogue; it is a haphazard collection of tickets and receipts from a travel abroad, carelessly tossed in a carry-on, only to be stashed upon returning home. These ideas are derived from much greater thinkers and authors than myself; I am a mere collector or a translator, if that, and not a very good one, for much is lost. I do not claim comprehensive …

A Brief Introduction To General Topology, Richard P. Millspaugh

Open Educational Resources

The material in this text is intended to be accessible to undergraduates who have had an introduction to elementary set theory and proof techniques. It includes sufficient material from general topology to prove the two main topological results found in a standard first semester calculus course: the Intermediate Value Theorem and the Extreme Value Theorem. This material can be found in Chapters 2 through 6 and makes up the bulk of the text. Rather than approaching these topics through use of the standard euclidean metric, it defines the standard topology on R in terms of the usual order on R. …

Valid Confidence Intervals For Μ,Σ When There Is Only One Observation Available, Anirban Dasgupta, Stephen Portnoy

Mathematics and Statistics Faculty Publications and Presentations

Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation X ∼ N(µ, σ2). Here we extend this result to obtaining 1-sample confidence intervals for σ and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (2019) to allow a sample of size m from a multivariate normal distribution where m may be less than the dimension.

Some Hypergeometric Identities And Related Leonard Pairs, Taiyo Summers Terada

Dissertations and Theses

The notion of a Leonard pair was introduced by Terwilliger in 2001 to simplify Leonard's theorem, which classifies the orthogonal polynomials in the terminating branch of the Askey-Wilson scheme. In the same year, Kresch and Tamvakis made a conjecture about a certain ₄F₃ hypergeometric series while studying the arithmetic analogues of the standard conjectures for the Grassmanian G(2,n). The ₄F₃ series appearing in their conjecture is closely related to a family of orthogonal polynomials in the Askey-Wilson scheme. Consequently, the theory of Leonard pairs provides a useful framework for understanding their conjecture.

In …

An Intertaxon Dissimilarity For Level-1 Phylogenetic Networks From Rooted Triples, Noah Palmer

Mathematics and Statistics

An important problem in evolutionary biology is how to infer the evolutionary history of a set of taxa in the presence of hybridization. In this work, we present an important first step in the establishment of an algorithm for the inference of a level-1 species network under the Network Multispecies Coalescent Model using rooted triples. In particular, we define a new intertaxon dissimilarity, dRT , which can be directly computed from the topology of the rooted triples displayed on a network, and might be estimated from data. In our main result we prove that this dissimilarity is equivalent to an …

Struggling To Be Positive Problem Solvers – A Study On The Relationship Of Elementary Mathematical Self-Concept, Gender, Learner Identification, And Productive Struggle Trajectories On Constructed Response Questions When Being Taught With A Standardized Curriculum, Kali D. Rogers

LSU Doctoral Dissertations

Mathematical word problems are some of the most difficult problems for students to solve due to their complexity and relationship to real-world situations (Şahin et al., 2014; Verschaffel et al., 2020). With math being known for right-or-wrong answers, these open-ended questions cause much confusion and frustration, specifically for students of various subgroups. In the last several decades, educational teaching expectations have shifted from engaging, self-created learning to robotic and redundant curriculum expectations that induce a ‘teaching to the test’ environment (Shafiyeva, 2021). Mathematics is the powerhouse of where students can experience and succeed with productive struggle learning that teaches the …

Analysis And Computation Of Constrained Sparse Coding On Emerging Non-Von Neumann Devices, Kyle Henke

Mathematics & Statistics ETDs

This dissertation seeks to understand how different formulations of the neurally inspired Locally Competitive Algorithm (LCA) represent and solve optimization problems. By studying these networks mathematically through the lens of dynamical and gradient systems, the goal is to discern how neural computations converge and link this knowledge to theoretical neuroscience and artificial intelligence (AI). Both classical computers and advanced emerging hardware are employed in this study. The contributions of this work include:

1. Theoretical Work: A comprehensive convergence analysis for networks using both generic Rectified Linear Unit (ReLU) and Rectified Sigmoid activation functions. Exploration of techniques to address the binary …