Digital Commons Network^™

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 …

Implementing A Multi-Tiered System Of Supports, Hayley Vander Wal

Master of Education Program Theses

This action research project examined the implementation of a multi-tiered system of supports in a math classroom at a private, Christian suburban school in central Iowa. The researcher utilized the four essential indicators of MTSS to support a small group of four students who were the participants in her study. The intervention targeted the seventh grade math skills of simplifying expressions and solving equations using various methods. Analysis of the triangulated data showed growth in each of the students at varied amounts. Findings of the study suggest that students need consistent, protected Tier 2 intervention to make the most significant …

Aleks In High School Mathematics Classrooms: Exploring Teachers’ Perceptions And Use Of This Tool, Tristan Kumor, Lida Uribe‑Flórez, Jesús Trespalacios, Dazhi Yang

Educational Technology Faculty Publications and Presentations

There has been a limited amount of research that has attempted to determine teaching strategies using adaptive learning systems. Most studies have attempted to measure success of the use of these technologies based on improvements in students’ test scores but have lacked to provide any information regarding the pedagogy implemented while using the tool or teachers’ perceptions of it. A basic qualitative study was conducted where five Chicagoland high school mathematics teachers, who used the Assessment and Learning in Knowledge Spaces (ALEKS) system, were interviewed three times during one academic school year. This study asked participants to share first-hand experiences …

Understanding Student Perspectives On Higher-Level Mathematics Courses At A Higher Level Institution On The U.S.–Mexico Border, Diego Rivera

ANTH 4306/6306 Anthropology of Borders

This project explores students' perspectives on mathematics courses at a higher-level institution along the U.S.–Mexico border. Traditional mathematics instruction is often delivered from an objective standpoint, but this study investigates how students perceive courses like college algebra and calculus when taught using a practical approach that incorporates their cultural background and personal knowledge. The study involves interviews with three students from the University of Texas Rio Grande Valley (UTRGV), majoring in Statistics, Biomedical Science, and Engineering. The paper includes detailed descriptions of the students and their responses, concluding with insights derived from the interviews.

The Mathematics Of Financial Portfolio Optimization Incorporating Environmental, Social, And Governance Score Information, Ian Driskill

Master's Theses

We numerically investigate the effects that Environmental, Social, and Governance (ESG) scores have on portfolio optimization with Modern Portfolio Theory assumptions and how ESG scores correlate with the market returns of a rated company's stock. Additionally, we review and analyze a research paper published in the Journal of Financial Economics regarding ESG investing titled “Responsible investing: The ESG-efficient frontier” by Pedersen, Fitzgibbons, and Lukasz. Our overall goal is provide insight for socially responsible inclined investors, to help them understand what ESG scores tell us and how those scores may effect their overall investment returns."

New Algorithms For The Multiplication Table Problem, Evan Blom

Undergraduate Honors Thesis Collection

In 1955, Paul Erdős initiated the study of a function that counts the number of distinct integers in an (n × n) multiplication table. That is, he studied M(n) = |{i · j, 1 ≤ i, j ≤ n}|. Much research has been done in regards to both asymptotic and exact approximations of M(n) for increasingly large values of n. Recently, Brent et. al. investigated the algorithmic cost in computing this function. Instead of computing M(n) directly, their approach was to compute it incrementally. That is, given M(n−1), they could quickly compute M(n) using another function δ(n) to count the …

Mathematics Majors In Medical School Admissions: A Comparative Evaluation Of Mcat And Gpa Performance, Morgan Baker

Theses/Capstones/Creative Projects

Choosing a major as an incoming undergraduate student can be very stressful. This study investigates the differences in success that come with choice of undergraduate major, particularly focusing on the performance of mathematics majors. A large majority of medical school applicants come from a biological sciences background. Despite this preference, there is evidence that students from nontraditional majors produce higher Medical College Admission Test (MCAT) scores and superior grade point averages (GPAs). Utilizing data visualization and analysis through R programming, this research examines public data from the Association of American Medical Colleges (AAMC) to understand the benefits of pursuing a …

Interview With Lee Zyrus Hernandez, Lee Zyrus Hernandez, Diego Rivera

ANTH 4306/6306 Anthropology of Borders

The interview with Lee Zyrus Hernandez explores the potential impact of incorporating Borderlands culture into higher-level mathematics education. Rivera seeks to understand if a practical approach, utilizing the cultural knowledge of Borderlands people, could enhance students' experiences with mathematical courses like college algebra and calculus at the University of Texas Rio Grande Valley (UTRGV). Hernandez, a student with a background in applied statistics and data science, reflects on his experiences with math education, including dual enrollment courses and studies in New York and Atlanta. He discusses the lack of cultural relatability in his math education and expresses support for incorporating …

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 …

An Analysis Of Instructor Feedback, Olga Hawranick

Boise State University Theses and Dissertations

Carless & Boud (2018) capture the definition of feedback best as “a process through which learners make sense of information… use it to enhance their work or learning strategies (p.1).” This definition goes beyond feedback solely being the role of instructors and highlights the student component in making sense of the feedback which we reference in this study as “actionable feedback.” Are instructors providing meaningful feedback to their students to encourage revision? Past studies offer inconsistent results on most features of feedback and little is known about how some of these factors benefit students’ interactions with feedback.

This study aims …

Using Tensile And Compressive Stress Superposition During Incremental Forming To Manipulate Martensitic Transformation In Ss304, E M. Mamros, F Maab, A E. Tekkaya, Brad L. Kinsey, J Ha

Faculty Publications

Single point incremental forming (SPIF) is a flexible manufacturing process that has applications in industries ranging from biomedical to automotive. In addition to rapid prototyping, which requires easy adaptations in geometry or material for design changes, control of the final part properties is desired. One strategy that can be implemented is stress superposition, which is the application of additional stresses during an existing manufacturing process. Tensile and compressive stresses applied during SPIF showed significant effects on the resulting microstructure in stainless steel 304 truncated square pyramids. Specifically, the amount of martensitic transformation was increased through stress superposed incremental forming. Finite …

Using Tensile And Compressive Stress Superposition During Incremental Forming To Manipulate Martensitic Transformation In Ss304, E M. Mamros, F Maab, A E. Tekkaya, Brad L. Kinsey, J Ha

Faculty Publications

Single point incremental forming (SPIF) is a flexible manufacturing process that has applications in industries ranging from biomedical to automotive. In addition to rapid prototyping, which requires easy adaptations in geometry or material for design changes, control of the final part properties is desired. One strategy that can be implemented is stress superposition, which is the application of additional stresses during an existing manufacturing process. Tensile and compressive stresses applied during SPIF showed significant effects on the resulting microstructure in stainless steel 304 truncated square pyramids. Specifically, the amount of martensitic transformation was increased through stress superposed incremental forming. Finite …

An Expansive Framing Intervention And Its Influence On Nursing Students' Perceptions Of Value For Mathematics, Kimberly Evagelatos Beck

All Graduate Theses and Dissertations, Fall 2023 to Present

Nurses regularly use mathematics on the job, yet they often do not view their work as mathematical. This may indicate a lack of transfer from the nursing school mathematics context to nursing practice. Further, nursing students often perceive very little usefulness and relevance for learning mathematics beyond simple calculations. Expansive Framing (EF) is a theory and instructional technique that has been shown to foster transfer by establishing intercontextuality, or connections made between disparate contexts. This research explored whether creating intercontextuality created through broad framing also improved perceptions of mathematics value and transferability, and how intercontextuality functioned as the driver of …

How Relational Instruction And Caring Learning Environments Relate To Mathematics Self-Concept: A Multilevel Investigation Of The High School Longitudinal Study Of Data, Sandra J. Miles

All Graduate Theses and Dissertations, Fall 2023 to Present

The purpose of this research is to look for ways mathematics teachers can increase their students' mathematics self-concept (i.e., achievement, confidence, and interest). Many students avoid taking upper-level mathematics classes or pursuing careers in science, technology, engineering, or mathematics (STEM). However, the need for STEM professionals in the workforce will increase in future years and there is a projected shortage of students who will be trained to fill the demand. This research proposes that mathematics teachers can actively work to improve their students' self-concept by providing a caring and emotionally supportive learning environment as well as providing instruction that builds …

Using Probability Theory To Calculate The Odds That Either Candidate Wins The 2024 Presidential Election, Andrew Ruggero

Department of Applied Mathematics & Statistics Faculty Publications

In the U.S., where the electoral college is used to determine the votes of an election, calculating the odds of a president winning is not as simple as looking at the total vote percentages. With each state not exactly having a proportionally linear amount of votes per its population, the total percentage doesn’t mean much. As such, in order to calculate these odds, we must look at a variety of winning combinations per each candidate. First, we must take into account that swing states are the only ones that matter. Defined as a 5% difference between the two main candidates, …

"Who Wrote The Epistle, God Only Knows": A Statistical Authorial Analysis Of Hebrews In Comparison With Pauline And Lukan Literature, Benjamin J. Erickson

Senior Honors Theses

The authorship of Hebrews has been a point of contention for scholars for the past two millennia. While the epistle is traditionally attributed to Paul, many scholars assert that it carries thematic, structural, and stylistic differences from the remainder of his extant epistles; therefore, many other possible authors have been proposed. Of these, only Luke has other New Testament writings. Therefore, this project conducts a statistical comparison of Hebrews to the Pauline and Lukan corpora using stylometric authorial analysis methods. This analysis demonstrates that Hebrews is stylistically closer to Lukan literature than Pauline (but not to a significant degree), and …

Skeletal 2-Groups And Category Theory, Nicholas Small '25, Alexander Stepanov '26, Haley Waiksnis '25

Mathematics & Computer Science Student Scholarship

Nicholas Small ’25, Mathematics and Computer Science major
Alexander Stepanov ’26, Mathematics and Studio Art major
Haley Waiksnis ’25, Mathematics major
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Autonomous Remote Erosion Monitoring Using Computer Vision, Emily Gelchie '24, Gabriel Benz '25

Mathematics & Computer Science Student Scholarship

Emily Gelchie ’24, Computer Science major
Gabriel Benz ’25, Computer Science major
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science

Media Portrayals Of Mathematics And Mathematicians: An Annotated Bibliography Of Published Journal Articles, Sarah O'Connor '26

Education Student Scholarship

Sarah O'Connor ’26, Mathematics major
Faculty Mentor: Dr. Kevin O’Conner, Secondary Education and Dr. Olga Limnios, English

Avatars Runnin' On Dunkin, Keelin Robbins '26

Mathematics & Computer Science Student Scholarship

Keelin Robbins ’26, Computer Science major, Finance minor
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science

Returning To School After A Pandemic And The Lived Experiences Of Rural High School Mathematics Teachers On Student Success, Joshua Saúl Silva

Dissertations

Purpose: The purpose of this qualitative phenomenological methodology investigation was to examine and describe rural mathematics teachers’ lived experiences on the effects of the COVID-19 global pandemic on freshman students returning to school after being online for 2 years through the lens of Bandura’s theory of self-efficacy and serves as part of a thematic dissertation with each researcher focusing on different educators in the K-12 school system.

Methodology: Through qualitative methodology utilizing one-on-one interviews of nine rural high school freshman mathematics teachers with 5 or more years of experience before, during, and after the COVID-19 global pandemic, data was analyzed …

Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Alexander Navarro

Honors Theses

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

Parents' Experiences At A Mathematics Workshop Focused On K-2 Content, Abigail W. Wilkerson

Honors College Theses

Parents’ beliefs towards math have been shown to impact their children’s academic achievement in the subject (Elliott & Bachman, 2018; Maloney et al., 2015). With the constant changing of math standards, the math taught in today’s schools may be different from the way parents were taught math. This change can lead to feelings of discomfort or nervousness when the subject is brought up. A parent workshop geared towards helping parents better understand the way math content is being taught can help them to feel more comfortable with math and more prepared to help their children. To help combat this issue, …

An Analysis Of Orientation And Preceptorship Influence On Nurse Job Satisfaction Across Two States., Kathryn Robinson, Robert Cavanaugh, Rebecca Dias, Alexandra Peary, Ryan Johnson, Vikram Rao, Breac Baker, Kelley Strout, Rhonda Board, Brianne Olivieri-Mui

Faculty Publications

A large public nursing data set was used to determine whether orientation and/or preceptor programs impact job satisfaction among registered nurses in Maine and Massachusetts. There was no association between orientation and preceptor programs and satisfaction, nor evidence that new nurse status modified the relationship. There is a need for evaluation of orientation and preceptor programs' structure and effectiveness, and innovation is needed in promoting job satisfaction, thereby increasing nurse retention.

An Analysis Of Orientation And Preceptorship Influence On Nurse Job Satisfaction Across Two States., Kathryn Robinson, Robert Cavanaugh, Rebecca Dias, Alexandra Peary, Ryan Johnson, Vikram Rao, Breac Baker, Kelley Strout, Rhonda Board, Brianne Olivieri-Mui

Faculty Publications

A large public nursing data set was used to determine whether orientation and/or preceptor programs impact job satisfaction among registered nurses in Maine and Massachusetts. There was no association between orientation and preceptor programs and satisfaction, nor evidence that new nurse status modified the relationship. There is a need for evaluation of orientation and preceptor programs' structure and effectiveness, and innovation is needed in promoting job satisfaction, thereby increasing nurse retention.

Dimer Models And Local Systems, Haolin Shi

Yale Graduate School of Arts and Sciences Dissertations

In this thesis we study several generalizations of the dimer model to higher rank geometric settings.The dimer models, first studied as a toy model in statistical mechanics, exhibit beautiful mathematical structures. It can be exactly enumerated and its probabilistic properties can be studied algebraically. It is also related to geometry and topology. Many versions and generalizations of the dimer model have been studied. Some examples are double dimer models on surfaces. We generalize double dimer models to $n$-dimer models and prove many classical results still hold. Boundaried double dimer models have been extensively studied on the disk. We generalize such …

Two Topics On Quantizations Of Quiver Varieties, Yaochen Wu

Yale Graduate School of Arts and Sciences Dissertations

This dissertation is devoted to the study of two topics on quantizations of quiver varieties, combining the works of the author during his PhD. The first topic concerns graded Poisson deformations of quiver varieties. We provide algorithms to compute the Namikawa-Weyl group of the affinization of a smooth Nakajima quiver variety from the quiver combinatorial data. This extends a result of [MN19] for quiver varieties associated to Dynkin quivers. The second topic concerns the classification of Harish-Chandra bimodules over the quantizations of flower quiver varieties, i.e. the quiver with one vertex and ≥ 2 edge-loops. We show that if the …

On Schrödinger Equations With Non-Perturbative Potentials, Adam Black

Yale Graduate School of Arts and Sciences Dissertations

This thesis consists of four parts, each studying a different class of Schrödinger equations. Though the setting and relevant questions vary between chapters, a theme that runs through all of them is the study of a Hamiltonian with a potential that is not small enough to be treated perturbatively. Indeed, in all of the Schrödinger equations below, the potential is, in some sense, large enough that it may affect the asymptotic behavior of the system.In Chapters 2 and 3, we investigate the scattering theory of Schrödinger operators with potentials that have anisotropic decay. More specifically, we assume that the potential …

Dynamics Of Diagonal Flows In Anosov Homogeneous Spaces, Michael Chow

Yale Graduate School of Arts and Sciences Dissertations

In this thesis, we prove some dynamical and geometric properties of diagonal flows on \emph{Anosov homogeneous spaces}, generalizing classical results for the geodesic flow on closed hyperbolic surfaces. Let $G$ be a connected semisimple real algebraic group and $\Gamma$ be a Zariski dense Anosov subgroup of $G$. On the Anosov homogeneous space $\Gamma \backslash G$, we consider a \emph{one-parameter diagonal flow} $a_{t\v}$ ($t \in \R$) parameterized by a family $D_\Gamma \cong \R^{\rankG-1}$ of directions $\v$. We prove that $a_{t\v}$ is \emph{locally mixing} with respect to the \emph{Bowen--Margulis--Sullivan measure} $\BMS$ with recurrence rate proportional to $1/t^{(\rankG-1)/2}$. More generally, our results apply …

Caminatas Comunitarias Para Enseñar Matemáticas En La Costa Caribe Colombiana: Un Enfoque Rural, Ricela Feliciano-Semidei, Kevin A. Palencia Infante, Jonathan A. Cervantes Barraza

Faculty Books & Book Chapters

Este libro recopila la experiencia vivida por docentes de matemáticas e investigadores que participaron del proyecto Pedagogías basadas en la comunidad rural para la enseñanza de las matemáticas en áreas rurales de la costa caribe colombiana. Los autores contextualizan estas experiencias para que puedan ser replicadas por otros docentes. Para lograrlo, se guía al lector con teorías educativas, políticas educativas, reflexiones y ejemplos alineados al currículo colombiano actual. Los ejemplos sirven de modelo y motivación para crear otras lecciones utilizando estas teorías. Este libro invita a los lectores a transformar las experiencias de los estudiantes de áreas rurales en recursos …