Mathematics Commons^™

Expanding Ode Examples: Introducing Gene Regulation Dynamics Through Hill Functions, Maila Hallare, Jane M. Santamore

CODEE Journal

Gene regulation is a fundamental biological process that controls gene expression. It can explain phenomena such as cell differentiation, circadian rhythms, disease progression, and metabolic control, among many others. Despite their importance in mathematical biology, gene regulation models are rarely featured in traditional ODE textbooks, which focus mainly on examples from engineering, physics, chemistry, and population biology. This article introduces gene regulation dynamics as a valuable addition to ODE curricula, presenting the models from a mathematical perspective and building on properties of the Hill function. These models deepen the understanding of biology-inspired ODE applications, provide accessible research opportunities for students, …

Italian Mathematics Prison Teachers’ Perspective On The Teaching/Learning Of Mathematics In Prison School, Andrea Maffia, Luca Decembrotto, Chiara Giberti, Federica Mennuni, Gabriella Pocalana, Silvia Regola, Agnese Telloni

Journal of Prison Education Research

Teaching in the prison context is characterized by a high complexity level; it is a multifaced activity influenced by several factors depending on the specific context. We present a preliminary but overall picture of schooling in Italian prisons by considering teachers’ reflections regarding their experiences in teaching mathematics in correctional facilities. To address the gap in the current literature on this issue, we conducted a SWOT analysis on the reflection provided by a group of nine Italian mathematics teachers who teach in different prisons and with different experiences and backgrounds. Their reflection allowed us to identify and describe six theory-driven …

Follow Me Into Math: Near-Peer Influencers Take The Stage, Aaron T. Wilson, Sergey Grigorian, Mayra Ortiz Galarza, Xiaohui Wang

School of Mathematical & Statistical Sciences Faculty Publications

Young people like to be entertained, and to entertain others. What if students were to invest enough of their time and effort into learning topics from our mathematics courses to become experts in the eyes of their peers? In this study we positioned college students and high school students as mathematical performers on the stage in front of their nearpeers, for whom they became math influencers, developing and presenting MathShows. The paper shows readers how we positioned students on the stage, using a 7-step MathShow Design Process informed by a Neer-peer Mathematical Mentoring framework. Of import for educators, researchers and …

Growth Mindset In The Mathematics Classroom: Studying The Effects Of A Growth Mindset Intervention On High School Students In A Geometry Classroom, Katelyn Strauss

Mathematics Graduate Theses

Having a growth mindset is crucial to being successful in a mathematics classroom. However, many students believe themselves to be either “mathematics people” or “not mathematics people”. When students believe they are not a mathematics person, they are far less likely to engage in material where they face struggles, and thus they miss out on valuable learning. A review of the literature has show that students have been able to shift their mindset from fixed to growth through a series of interventions. I used a unit in Geometry to see how a growth mindset intervention would affect the mindset of …

(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution, Priyadharshini R., Shalini K., Hemalatha R., Sangeetha S.

Applications and Applied Mathematics: An International Journal (AAM)

The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use …

The Calvin University Math Department History 1920-2020, Michael Stob

University Histories

No abstract provided.

The 3d Double Spherical Pendulum: Modeling, Analysis, And Simulations, Alexander Gofen

CODEE Journal

This paper presents an inquiry-based research project that develops and analyzes the system of ordinary differential equations governing the motion of the 3D double pendulum, blending computational experiments with applied and theoretical mathematics. We formulate the Lagrangian for the three-dimensional double spherical pendulum and use Maple to derive the four coupled ordinary differential equations (ODEs) in angular variables; for completeness, we also present an equivalent Cartesian formulation. We then compare and visualize the models using the Taylor Center high-order Taylor-series solver, which delivers high-accuracy trajectories and real-time animations in 2D and anaglyph 3D (red/blue). We place the system in context …

Project-Based Learning With Odes: Modeling Straw Rocket Motion With Air Resistance, Viktoria Savatorova, Ethan Dyer, Aleksei Talonov

CODEE Journal

This paper presents a hands-on project that guides students through building and validating a mathematical model of projectile motion. The project starts with the idealized case of motion under gravity without air resistance and then introduces air drag : first as a linear force, and then as a nonlinear quadratic force, with the Reynolds number providing the justification for the quadratic model. Students perform experiments with vertical and angled launches, capturing and analyzing motion data using video analysis software. Vertical launch data allows parameter estimation via least squares fitting of the nonlinear drag model, yielding values for initial velocity and …

Traffic Prediction For Research And Education Networks: Anomaly-Aware Deep Learning And Benchmarking, Mohammad Arafath Uddin Shariff

School of Computing: Dissertations, Theses, and Student Research

Research and Education Networks (RENs) and High-Performance Computing (HPC) environments are critical infrastructures for modern scientific discovery, demanding sustained high-throughput and low-latency data transfers. Unlike commercial networks, RENs exhibit unique traffic characteristics, including predominant “elephant flows,” inherent burstiness, and complex temporal-spatial dynamics often decoupled from human-driven cycles. Traditional traffic forecasting methods, tailored for commercial Wide Area Networks (WANs), consistently fail to capture these distinct REN dynamics, leading to inefficient resource management and potential impediments to scientific progress.

This thesis addresses this critical gap by developing and validating a robust, scalable, and anomaly-aware traffic forecasting framework specifically tailored for REN/HPC networks. …

Let’S Teach More Accurate And Inclusive History! The Case Of Islamic Contributions To Mathematics And Science, Nuh Aydin

Journal of Humanistic Mathematics

Schools commonly teach a history of mathematics and science that is Eurocentric. This selective version of the history of science, called Classical Narrative by some, is rooted in colonial times and mindset, and has reinforced certain negative opinions about other cultures. It ignores or downplays contributions to mathematics and sciences from non-western civilizations, and falsely attributes many scientific discoveries to European scholars. Medieval Islamic Civilization, which had strong connections to Renaissance Europe, serves as a clear example of how this narrative is distorted. Based on research on primary sources since the middle of the 20th century, we now know that …

From Shudu [Sudoku 數獨] To Dushu [Learning Of Mathematics 讀數]?, Man Keung Siu

Journal of Humanistic Mathematics

The puzzle game Sudoku has been popular for over two decades, and even at one time became a craze for the public. This paper will briefly describe what the game is, a little bit of its history, and how to play it, but will leave the details to the many published books about the game. Some interesting and difficult mathematical problems relevant to the game will be highlighted, again leaving the detailed discussion to specific books published on this issue. The main point the paper tries to focus on is a discussion on the cognitive and the psychological aspects of …

Examples Of Mathematics Personified, Amenda N. Chow

Journal of Humanistic Mathematics

Synesthesia is a cognitive condition in which multiply senses are stimulated at once. There are different types of synesthesia. For example, in a documented study [9], a person with synesthesia when considering the number three associates it as a male and a jerk. This association is persistent, always the same and automatic. Presented here are a variety of examples about mathematics in personified form. These examples focus on using personification as a way to better understand and appreciate mathematics.

Math Anxiety And Shame Exemplified On The Reality Show Survivor, James Drimalla, Dru Horne

Journal of Humanistic Mathematics

In an episode of season 45 of the reality show Survivor, three contestants competed in a challenge involving mathematics. In their reflections and responses to the challenge, the contestants discussed feelings of anxiety, fear, and shame. In this article, we describe (a) the challenge, (b) the three contestants’ attempts to complete the challenge and their responses to the challenge, (c) responses to the challenge in the media, and (d) relevant details of our personal experiences and related backgrounds. We then discuss themes of math anxiety, shame, and virtues, and encourage leaders in mathematical spaces to place a higher value on …

Introducing The Linear Poem, Cristian Ramirez Rodriguez

Journal of Humanistic Mathematics

In this article I introduce the linear poem, a poetic form I developed in fall 2023 as a pedagogical tool for high-school students. The linear poem is a poem which represents an integer valued linear function, treating the line numbers as inputs and the linguistic units in a line as outputs. Two examples of linear poems are given as well as the steps taken to produce them. By interpreting poetic forms as integer-valued functions as is done in this article, interdisciplinary pedagogy can be achieved, allowing educators and students to express mathematical ideas such as slope-intercept form in a creative …

Exploring Commutativity In A Hindi Language Classroom, Kumar Gandharv Mishra

Journal of Humanistic Mathematics

Commutativity is an important concept in mathematics. However, not much emphasis is given to it in the elementary or secondary school curriculum, as there is a lack of interesting noncommutative examples at this level. Since most examples of binary operations provided deal with numbers, commutativity appears trivial. In this article we offer an interesting example of noncommutativity that is familiar to Indian school children from a different context. Students in India study a chapter based on the joining of vowels in Hindi grammar. This process is analogous to producing commutative as well as noncommutative operations. When we bring in mathematical …

Memes As An Effective Approach To Increase Public Engagement With Mathematical Concepts, Juan M. Romero, Carlos Trenado

Journal of Humanistic Mathematics

A meme is a graphical concept or cultural item that is disseminated via the Internet, often through social media platforms. Memes serve as a mechanism for replicating cultural traits by incorporating aspects of cultural mutation and evolution. The potential of memes in learning and education has been emphasized in several recent studies. The present article examines the impact of memes in increasing public engagement with mathematics and mathematical concepts. By focusing on memes that exhibit specific attributes—such as emotional facial expressions of recognizable human characters and dialogues emphasizing the usefulness or beauty of a mathematical concept—we observe a significant increase …

Graphical Timetables As A Real-Life Example Of Different Representations Of Functions, Olav G. Imenes

Journal of Humanistic Mathematics

This paper examines 203 pre-service teachers' reactions and learning when they were introduced to a real-life situation in which it is natural to publish officially both graphs and tables of a given function: the situation of operating a railway. I found that almost all the pre-service teachers managed the easiest tasks, like calculating speeds, distances, and time for train represented by graphs. However, the more complicated tasks, which required interpretations of the graphs and tables, such as planning for a delayed train, finding which trains were locals, freight trains etc., were more difficult for them to grasp. There were few …

A Proposal To Explore Geometry With Geogebra: Graphical Exploration And Formal Demonstration Of The Collinearity Of The Barycenters Of A Polygon, Saulo Mosquera Lopez, Marlio Paredes, Walter Castro

School of Mathematical & Statistical Sciences Faculty Publications

This paper illustrates an example of a mathematical activity that teachers and students can replicate to create an experience that resembles professional mathematical activity. We extend the property “Consider a triangle ABC, any straight line and let A’, B’, C’ be the reflections of the points A, B, C on the straight line then the barycenters of the triangles ABC, A’BC, AB’C and ABC’ are collinear and the line of collinearity is perpendicular to the straight line” for any quadrilateral. It is proved that there are four additional triangles, for a total of eight, whose barycenters are collinear and that …

The Other Side Of The Equation: De-Simplification, A Prerequisite For Calculus, Stephen L. Brown

ACMS Conference Proceedings 2005

No abstract provided.

Predictors Of Nursing Students' Stress, Anxiety, And Depression During The Covid-19 Pandemic In A Hispanic-Serving University In South Texas: A Cross-Sectional Study, Maria I. Diaz, Eleftherios Gkioulekas, Nancy Nadeau

School of Mathematical & Statistical Sciences Faculty Publications

Background: In nursing education, there have been several studies on the impact of the COVID-19 pandemic on the ability of nursing students to cope while in nursing school.

Purpose statement: The goal of this study is to assess undergraduate nursing students' support mechanisms as predictors of stress, anxiety, and depression during the COVID-19 pandemic within a Hispanic-serving institution in South Texas.

Methods: Across-sectional design was used in this study. An online survey using self-reported questionnaires was used to gather data from an undergraduate nursing student cohort during the Fall 2021 semester. Linear regression was used to identify the predictors of …

“What Makes It Eigen-Esque-Ish?”: A Form-Function Analysis Of The Development Of Eigentheory Concepts In A Quantum Mechanics Course, Megan Wawro, Kaitlyn Stephens Serbin

School of Mathematical & Statistical Sciences Faculty Publications

Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how “eigen” develops over time in one quantum mechanics course by analyzing form-function relations (Saxe, 1999) for eigentheory concepts over 22 class sessions. We share results concerning our microgenetic and ontogenetic analyses of the creation of form-function relations and their shifts over time by characterizing the continuity and discontinuity of the various functions and forms associated with concepts …

Understanding Student And Teacher Perceptions Of A Checking For Accuracy Method In Algebra Class, Abigail A. Jameson

Masters of Education in Teaching and Learning

Mathematics encompasses learning from one’s mistakes and developing accuracy with problem-solving. This action research study analyzed the classroom teacher’s and students' perceptions of a checking for accuracy math method that was implemented in an eighth-grade algebra classroom. Additionally, the researcher wanted to understand how the participants felt about the accuracy method and its influence on students’ attitudes toward math and mastery of math concepts. Student surveys, individual teacher (with student artifacts) and student interviews and focus groups (with individual artifacts) were the qualitative data collected using the constant comparative method. Descriptive statistics was used to collect quantitative data with calculated …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict A. Cristobal

Department of Mathematics: Dissertations, Theses, and Student Research

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Equity Vs. Excellence: Dichotomy Or Duo?, Nadjia I. Logans

Honors Program: Senior Projects (Public)

In this thesis, I investigate recent changes in mathematics education and how these developments connect to the principles of equity and excellence. I place a special focus on “active learning” methods. My methodology primarily consisted of interviews with educators, along with analyzing literature from math education researchers. I first define and explain the motivations behind active learning instruction methods. Next, I explore not only how instructors define equity and excellence but how educators perceive the role of the two principles within education. Finally, I challenge the pervasive media portrayal of equity and excellence as being mutually exclusive. Instead, I find …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict Arroyo Cristobal

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

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn

All Dissertations

This dissertation examines the lived experiences of 11 Black college mathematics students at their predominantly white institution (PWI) through the lens of Black Critical Theory (BlackCrit) to counter deficit narratives about the racial achievement gap (RAG) in mathematics education courses. Deficit narratives often attribute disparities between Black and white students’ mathematical performance to assumed deficiencies in Black students’ abilities rather than systemic inequities, historical marginalization, and ongoing anti-Blackness in educational settings (Cobb & Russell, 2015; Kress, 2021). Using multiple case studies, this study explores how anti-Blackness manifests in mathematics classrooms, how students navigate tensions between multiculturalism, neoliberal educational policies, and …

2025 Acssc Program, Acssc Planning Committee

Annual Celebration for Student Scholarship and Creativity

No abstract provided.

Shaping Mathematics Identity: An Exploratory Study On Specifications Grading In Calculus I At A Hispanic-Serving Institution, Luis M. Fernandez, Kaitlyn Stephens Serbin, Cristina Villalobos, Shaghayegh Azadi Setayesh, Guillermo Garza

School of Mathematical & Statistical Sciences Faculty Publications

Calculus I courses play a pivotal role in shaping students' STEM pathways, making it essential to adopt pedagogies that foster both achievement and mathematics identity development, particularly among underserved groups such as Hispanic students. This study explores the impact of Specifications Grading, an alternative assessment method where students meet specific course learning objectives through multiple attempts, on students’ mathematics identity development. Through a comparative case study of two Calculus I students at a Hispanic-Serving Institution, one enrolled in a specification graded course and the other in a traditionally-graded course, we examine shifts in their self-perceptions of competence, interest, recognition in …

Reinventing Mathematics Learning: An Exploration Of Undergraduate Mathematics Learning Post-Pandemic, Morgan R. Balesano

Honors Scholar Theses

In response to the COVID-19 pandemic, beginning in March 2020 nearly all secondary and undergraduate mathematics students were forced to adapt to new methods of learning and testing. As a result, the current experience for these mathematics students has changed vastly, as have the opinions and preferences of these students in terms of their learning. This study aims to identify instruction and testing resources and methods that students prefer and those that students find less beneficial in their current, post-pandemic educational experience. The past few years have seen a focus on the direct impacts of online learning during the pandemic, …

Exploring Teacher Knowledge In Meeting The Expectations Of Integrated Content Language Development In Mathematics: A Descriptive Case Study, Carrissa Rozelaar-Miller

Doctoral Dissertations and Projects

The purpose of this descriptive case study was to discover how knowledge is applied to meet the expectations of integrated content and language development in mathematics for Title I elementary teachers at an urban school district in the central United States. Halliday’s theory on systemic functional linguistics guided the research as it relates to the function and purpose of language through meaning and social interaction in different genres. The central research question was: How do Title I elementary teachers apply specific integrated content and language development knowledge in mathematics? The participants consisted of 10 teachers with at least three years …