Digital Commons Network^™

An Invitation To Gauge Theory, Oscar I. Hernandez

Mathematics and Statistics

We introduce the audience to the mathematics of gauge theory. We begin by formalizing the intuitive concepts of smoothness, tangency, symmetry, constancy, and parallelism. Building up to a theory of parallel transport in associated fiber bundles, we study principal connections in principal bundles as well as the related notions of curvature and holonomy. In particular, we conclude with a non-abelian Stokes's theorem which recasts holonomy in terms of curvature.

Navigating The Multiple Roles Of Mathematics Graduate Teaching Assistants In Pursuit Of Racial Equity, Access, And Justice, Kristyn Lue

Exploring How We Teach

• Mathematics Graduate Teaching Assistants (GTAs) play a large role in the socialization of undergraduate students of Color and thus have an impact on their sense of belonging and retention in the STEM fields.
• GTAs occupy a unique role as agents of mathematics socialization, as they are also undergoing their own socialization as doctoral students; in many ways, these roles and this socialization processes constrain GTAs in ways that can be detrimental and marginalizing to students of Color.
• Without being aware of the ways in which systemic racism and white supremacy operate in mathematics spaces, GTAs play a role in upholding …

Students From Any Major Can Learn Valuable Career Skills In Data Science Course, Ohio University College Of Arts & Sciences

All Forum Articles

No abstract provided.

Problem Solving Like A Mathematician: Disciplinary Literacy Instruction In Elementary Mathematics, Charlotte Frambaugh-Kritzer, Stephanie Buelow

Reading Horizons: A Journal of Literacy and Language Arts

This study aims to grow the literature by examining the how of disciplinary literacies (DL) elementary mathematics instructional practices in teacher education, which is under-reported. Using qualitative case study methods, we examined how one cohort of elementary preservice teachers (PTs) enacted the DL instructional practices in their field practicum K–6 classrooms. Using a social constructivism perspective, we combined directed content analysis with real-time dialogue and the writing process as analytical tools to examine our data. Data sources included observation notes from the mathematics methods course, observation notes from the field practicum, and multiple artifacts (e.g., post observation oral and written …

The Relationship Between Motivation, Academic Achievement, And Engagement In Mathematics Using Digital Game-Based Learning: An Explanatory Sequential Mixed Methods Study, Amy Rose Morgan

Boise State University Theses and Dissertations

Digital game-based learning (DGBL) has unique factors that can engage students in the learning process. It has been shown that incorporating DGBL into mathematics can help bridge the learning gap, differentiate instruction, and engage students (Yang et al., 2018; Hulse et al., 2019; Chen et al., 2012; Naik, 2017). This study examined how students’ prior engagements are related to their academic achievement as well as investigated students’ motivation while utilizing DGBL in mathematics. An explanatory sequential mixed methods design was utilized to collect the quantitative data followed by the qualitative data. There were eighteen middle school participants in grades six …

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

In Mathematics, As In Art, Andrew Granville

Journal of Humanistic Mathematics

The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?

Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield

Journal of Humanistic Mathematics

Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …

Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler

Journal of Humanistic Mathematics

Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …

Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel

Journal of Humanistic Mathematics

Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.

Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.

Faculty Submissions

Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”

In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and …

Effective Strategies For Students With Learning Disabilities In Algebra, Leeann Calvert

LC Journal of Special Education

It has now become crucial to develop strategies and methods to effectively educate students with learning disabilities in mathematics. Strategies that target and improve student’s problem solving ability should positively impact their overall math performance, grades, graduation rates, and postsecondary success (Montague, Enders, & Deitz, 2011). This paper will review research-based practices in algebra employed to successfully educate upper middle and high school students with learning disabilities and provide a summary of those practices which are effective and useful.

Reconstructing Historical Earthquake-Induced Tsunamis: Case Study Of 1820 Event Near South Sulawesi, Indonesia, Taylor Jole Paskett

Theses and Dissertations

We build on the method introduced by Ringer, et al., applying it to an 1820 event that happened near South Sulawesi, Indonesia. We utilize other statistical models to aid our Metropolis-Hastings sampler, including a Gaussian process which informs the prior. We apply the method to multiple possible fault zones to determine which fault is the most likely source of the earthquake and tsunami. After collecting nearly 80,000 samples, we find that between the two most likely fault zones, the Walanae fault zone matches the anecdotal accounts much better than Flores. However, to support the anecdotal data, both samplers tend toward …

Implementation Of A Tier Ii Math Intervention Program, Taylor Torres

Master's Theses & Capstone Projects

The impact of COVID-19 has been detrimental to student success. School closings reduced learning for all students but especially for primary students who missed critical foundational skills. Tier II math interventions within the MTSS framework show evidence of growth for students of all ages and needs. This research-based approach is a logical response to combatting the damage caused by the pandemic. Several successful research studies on mathematics intervention will provide promise of replication in other schools. This school improvement plan will outline actions toward implementing Tier II math interventions in a rural Iowa elementary school.

Unlocking Math Minds: Using Inquiry-Based Instruction To Increase Student Engagement And Learning In A Third Grade Classroom, Eric Swendseid

School of Education and Leadership Student Capstone Projects

This paper and supporting website include research and strategies to answer the research question, How can the implementation of inquiry-based math instruction increase student engagement and learning success in a third grade classroom? Inquiry-based learning is a process where the students are involved in their learning. The classroom is student-centered, not teacher-centered. Using the student-centered or inquiry-based approach, students do not learn through transmission. Instead, they collect information and synthesize the information they find through critical thinking skills. The learning process is considered to be higher-order learning. The research presented in this paper focuses on guided inquiry within a mathematics …

Temporal Sentiment Mapping System For Time-Synchronized Data, Jiachen Ma

Dissertations (1934 -)

Temporal sentiment labels are used in various multimedia studies. They are useful for numerous classification and detection tasks such as video tagging, segmentation, and labeling. However, generating a large-scale sentiment dataset through manual labeling is usually expensive and challenging. Some recent studies explored the possibility of using online Time-Sync Comments (TSCs) as the primary source of their sentiment maps. Although the approach has positive results, existing TSCs datasets are limited in scale and content categories. Guidelines for generating such data within a constrained budget are yet to be developed and discussed. This dissertation tries to address the above issues by …

Incremental, Spaced Repetition And Studymate Flashcards: The Impact On College Student Memorization Of Measurement Conversion Standards, Patricia A. Bromer

Theses and Dissertations

The purpose of this action research was to evaluate the impact of and student perception of incremental, spaced repetition of StudyMate electronic flashcard use on memorization of measurement conversion standards for an online Mathematics in Health Sciences course. Online college classes require more self-direction and usually do not allow for partner or group work. These characteristics of online classes may hinder students’ ability to memorize crucial information, increasing their cognitive load and leading to feelings of inadequacy. This mixed methods study assessed the impact of incremental, spaced repetition of StudyMate flashcard use on college math students’ memorization of measurement conversion …

An Examination Of Attachment And Aspirations In Diverse Rural Youth: The Role Of Peers And Teachers, Gresi Bonomo Irdam

Theses and Dissertations

This dissertation consists of three studies that examined diverse rural youths’ educational and rural aspirations. These studies have the potential to inform rural communities, educators, and parents by providing novel understandings of how peers and teachers in mathematics and science classrooms influence diverse rural youths’ rural attachment, and aspirations (i.e., educational, rural residential, community, and proximity). Thus, the purpose of this dissertation was to investigate rural teachers and their diverse students from White, African American, Hispanic, and Native American backgrounds. In particular, the studies within this dissertation examine how teachers’ social connectedness to their rural communities relates to their teacher …

Kaley Norris Gets Career, Life Experience During Keybanc Summer Internship, Ohio University College Of Arts & Sciences

All Forum Articles

No abstract provided.

25 Arts & Sciences Faculty Promoted, 15 Granted Tenure, Ohio University College Of Arts & Sciences

All Forum Articles

No abstract provided.

Understanding College Students' Use Of Written Feedback In Mathematics, Erin Loraine Carroll

Theses and Dissertations

Many teachers want to help their students develop a growth mindset about their ability to do mathematics. Research has shown, however, that teachers simply do not know how to promote growth mindsets in their classrooms. Existing research suggests that one way teachers can support students' development of a growth mindset is through the written feedback they provide students. This study combines the research done on students' mindsets and written feedback to examine the interaction between student mindset and written feedback by analyzing written feedback provided to students in a College Algebra class and how students used that feedback based on …

22 Arts & Sciences Professors Awarded Faculty Fellowship During 2022-23, Ohio University College Of Arts & Sciences

All Forum Articles

No abstract provided.

Factors On Memory Retention: Effect To Students’ Academic Performance, Sheena Mae T. Comighud

International Journal of Business and Technology

Abstract.This paper examined the factors contributory to memory retention affecting the academic performance in Mathematics of Grade 7 students of Kalumboyan High School, Bayawan City Division for SY 2019–2020. The study made use of the descriptive-correlational research design. The questionnaire covered five areas: motivational practices and experiences, goal setting and accomplishments, personalized learning, teaching strategies and learning activities, and educational resources and learning devices. The respondents of the study were the 160 Grade 7 students. The study utilized percentage, mean, weighted mean, and Spearman’s rank correlation coefficient. The salient findings revealed that the extent of students’ perception on factors contributory …

Teachers' Experiences In Implementing Technology-Rich Curriculum For Student Achievement: A Phenomenological Study, Dorrothe Jean

Doctoral Dissertations and Projects

The purpose of this phenomenological study is to describe how premillennial teachers at East Orange Public School (EOPS, a pseudonym) respond to technology-rich curriculum. Twelve elementary school premillennial teachers will participate in the study focused on one central research question and three sub-questions: (a) What is the lived experience of elementary teachers implementing technology-rich mathematics curriculum? (b)How do elementary school teachers perceive their preparedness for teaching in a classroom where technology-rich math curriculum has been implemented? (c)How do elementary school teachers describe their transitions from a premillennial curriculum to a millennial curriculum where it has been implemented? (d) How do …

Ramsey Theory, David Lai

Master's Theses

The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and semicirculant graphs. Then, generalizing the Ramsey number to graphs other than complete graphs, we flesh out the missing details in the literature on a theorem that completely determines the generalized Ramsey number for cycles.

Effectiveness Of A Program Based On Stem In Developing Critical Thinking Skills In Mathematics Among Eleventh Grade Scientific Students In Gaza, Mohammed Asqule, Rana Ziada

An-Najah University Journal for Research - B (Humanities)

The study aimed to investigate the effectiveness of a program based on STEM approach in developing critical thinking skills in Mathematics for the students in GAZA. To achieve the study objectives, the researchers adopted the experimental approach. A program based on STEM, teacher guide has been prepared. To verify the effectiveness of the program, the study tool was a critical thinking skills test. This test has undergone pre and post application on a sample consisted of a group of (86) female students selected from Al-Zahraa Secondary School. The study results revealed that there were statistically significant differences at the level …

Power Of Yet: The Integration Of The Culturally Responsive Literature With The Productive Struggle In Mathematics, Kathleen Crawford-Mckinney, Asli Ozgun-Koca, Kristy Rebar

Michigan Reading Journal

We used a children's book with three groups of students (ages 6-9) to foster mathematical engagement through read alouds. We will share lessons learned from this experience as we integrate children’s literature with mathematics through the lens of Power of Yet.

Optimal Race Strategies For Cyclists, Brendan Perez, Drew Altringer, Evan Fisette

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

For competitive cyclists, each course presents a unique set of factors and, in turn, leads to difficulty in choosing a racing strategy. Some courses confront cyclists with drastic changes in elevation while others are of a more consistent grade. Similarly, curvature varies from course to course.

Further, riders vary in their areas of strength. A rider’s power curve maps their instantaneous power output 𝑃 in W/kg over the amount of time that the rider can sustain that power level in seconds. The shape of a rider’s power curve indicates their riding style.

In this paper, we model the optimal …

Optimizing Forest Harvest Cycles For Carbon Sequestration, Alex Landry, Margaret Lippsmeyer, Casey Wong

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Our mathematical model aims to depict optimal harvest times for different types of forests based on the value they provide for carbon sequestration. We have developed three different models for the main forest types throughout the world, boreal forests, temperate forests, and tropical forests. For the model, we implemented a manipulated sine function for one period. By using a manipulated sine function, we are able to model the amount of carbon dioxide a tree is able to sequester over its lifetime as well as show the release of carbon dioxide back into the atmosphere when the tree dies and decomposes …

The Stem Trail: Alaska Native Undergraduates Find The Right Path In Higher Education, Olga J. Skinner

Indigenous Studies

The goals of this research are twofold. (1) This research explores decision making and college experiences of Alaska Native undergraduates pursuing degrees in the science, technology, engineering, and mathematics (STEM) fields, and (2) this research, using participant observation explores the Indigenous metaphor of "the trail" to frame student persistence towards their degrees. Twelve participants, representing various STEM fields, Alaska Native cultures, and K12 schooling experiences, shared their motivations and aspirations through interviews and photographs. Key findings indicate the significant role that Indigenous Knowledge plays in influencing student decisions around majoring in STEM degrees. Findings also illuminate the variety of K12 …