Digital Commons Network^™

Teacher Observations On The Success Of Hard-Of-Hearing Students In The Middle School Mathematics Classroom: A Case Study, Hannah Abbott Mcpherson

Doctoral Dissertations and Projects

The purpose of this case study was to describe how deficits in foundational language among hard-of-hearing students influence mathematics instruction for general education middle school classroom teachers working to educate this student population in the South. The theory guiding this study was Paivio’s theory on dual coding, as it supports learning the necessary concepts needed to perform successfully in mathematics. The central research question for this study was: What are the experiences of middle school mathematics teachers working with hard-of-hearing students? Methodology defined as a descriptive case study included individual interviews, a focus group, and journal prompts to collect data …

Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya

Turkish Journal of Mathematics

This paper explores the ideals and their structural properties in two generalizations of the partial transformationsemigroup. Furthermore, principal, maximal, and minimal ideals within these semigroups are elucidated.

Oer Book Review For Calculus - Openstax Calculus, Jing Hu

Open Educational Resources Publications

This OER textbook review provides a comprehensive evaluation of the "Calculus" textbook series published by OpenStax. The reviewer, Jing Hu, an adjunct lecturer at Bentley University, highlights the textbook's strengths, including its thorough coverage of essential calculus topics, accurate and well-established mathematical principles, practical relevance, and user-friendly design. The open-access nature of the resource is seen as a significant advantage, contributing to its long-term utility and accessibility for both students and educators. Overall, the review concludes that the OpenStax Calculus textbook is a high-quality, comprehensive, and freely available resource that effectively supports the learning and teaching of calculus.

Matrix-Free High-Performance Saddle-Point Solvers For High-Order Problems In H (Div), Will Pazner, Tzanio Kolev, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

This work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in . The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis (cf. [W. Pazner, T. Kolev, and C. R. Dohrmann, SIAM J. Sci. Comput., 45 (2023), pp. A675–A702]), efficient matrix-free preconditioners can be constructed for the -block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The …

Plotting For Change: Utilizing Computer-Based Scaffolding Through Desmos To Influence High School Students’ Performance And Attitudes Toward Mathematics, Jennifer Underwood Farmer

Theses and Dissertations

The purpose of this action research was to understand the impact of computer-based instructional scaffolding in Desmos on Math 3 high school students’ performance and attitudes toward mathematics. The demand for societal mathematics literacy has increased significantly over the last decade and continues to grow. To achieve this literacy, students must reason, augment, communicate, model, and problem-solve with technology applications; development of these skills requires engagement and support through technology-rich learning opportunities.

Currently, Math 3 students are not performing at the proficient level on state exams and are displaying negative attitudes towards mathematics. Student attitudes and performance in technology enhanced …

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

Culminating Experience 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 …

The Integration Of Mathematical Concepts In Physics Curriculum, Paige Poindexter

Culminating Experience 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 …

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, …

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 …

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.

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 𝐻1𝐻1 semi-inner product and 𝐿2𝐿2 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 …

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 …

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, …

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.

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.

The Core Of It All: From The Forest To The Concrete Jungle, Ayo Andra J. Deas

Dissertations, Theses, and Capstone Projects

The Core of It All is a component of principle within Fasaha. The mission of Fasaha is to implement programming directed toward development of one’s Core through self-actualization. Self-Actualization is defined as bringing forth the total essential qualities of one’s own consciousness, character, and identity through positive behavior. Throughout this manuscript, principle is defined as the standard of natural essential qualities determining intrinsic consciousness, character and identity. Programming is defined as providing with intrinsic instructions for the automatic performance of a task.

Fasaha is a support service that enhances the existing organization’s service. Throughout this dissertation, it will be apparent …

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.

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 …

Comparing Online And Traditional Assessment Practices In Middle School Mathematics, Maxwell Krueger, Kathy Enger

Dissertations, Theses, and Projects

As a result of the COVID-19 pandemic, teachers across the world have been forced to explore different modalities of assessment, many of them virtual. Now that many of the most restricting policies for schools due to pandemic have been lifted, the use of these virtual assessments remain. Due to the recent nature of their use though means that not many studies have looked into the implications of these assessments on students let alone middle school students. This study aims to help fill in some of the gaps in this research. In this study, students will take one of two assessments …

The Effects Of A Gamified Flipped Classroom On First-Generation Low Income Student Motivation And Achievement In A Georgia High School Mathematics Class, Michael Maxwell

Learning Sciences Dissertations

Math continues to be a challenge for American high school students. The United States was placed ninth in reading and thirty-first in math literacy out of 79 nations and economies in the most recent results for international exams given to teens. Math test results were worst in states with large wealth disparity. Motivation and engagement, conceptualized as students' energy and drive to participate, learn, work efficiently, and realize their potential at school, play a significant impact in students' academic success. While the flipped classroom methodology has demonstrated some success within helping this trend, many studies indicate that additional assistance is …

Conceptual Understanding Of Linear Relationships Across Various Mathematics Courses, Melissa Manley

Theses and Dissertations

This cross-sectional study investigated the conceptual understanding of linear relationships for 195 students enrolled in a single school in a large, urban district across five mathematics courses: Grade 7 Math (n = 24), Grade 8 Math (n = 52), Geometry (n = 43), Algebra 1 (n = 31), and Algebra 2 (n = 45). The following questions guided this study: (1) What differences exist in students’ conceptual understanding of linear relationships across mathematics courses? (2) What are common strengths and weaknesses in students’ conceptual understanding of linear relationships?

An assessment was created to assess three constructs of conceptual understanding of …

The Elephant In The Classroom: Understanding Teachers’ Implicit Biases In Grading Student Work In A Mathematics Classroom, Tina Marie Medina

Electronic Theses and Dissertations

This study focused on automaticity or the choices we make without conscious thought. Specifically, the study examined how math teachers improved their understanding of the practice and evolution of culturally responsive teaching by analyzing the lived experiences and metacognition of practicing middle school teachers as they assess student work in mathematics. The potential impact of implicit stereotypes, instructor expectations, assessment design, cultural considerations, and other variables on the grading process was investigated. The purpose of this case study was to uncover teachers’ implicit biases as it relates to grading student work in a middle school math class.

This qualitative study …