Mathematics Commons^™

Test Retakes In Introductory Math Courses, John Hird, Chris Mcclain

2026 Scholarly Teaching Conference: Poster Session Papers

In this poster, we describe the implementation of an exam retake model using specifications grading for math courses taken by non-STEM majors. This system was implemented by two faculty members over three years in two sequential courses. During that time, we tried several versions of allowed retakes, with varying restrictions on partial credit. Some of the challenges that we faced were scaling the system for use by different faculty members and with different courses, managing faculty workload on writing and grading multiple exams, and managing student expectations.

An Exploratory Approach For Teaching Systems Of Linear Odes With Real Repeated Eigenvalues, Biyong Luo, Li Zhang

CODEE Journal

In this paper, we present a project that aims to pique students' interest and facilitate their engagement in learning. Students will be encouraged to take an active role in their learning of systems of linear ODEs with real repeated Eigenvalues. Through discussion and completion of a set of guided questions given in the project, students will gain a deeper understanding of the topic. Also, students will use the technology tool Bluffton App to draw solution trajectories in a phase plane, and then learn necessary skills for explaining the movements of the trajectories and their long term behaviors. This project may …

Analysis Of Solutions To Research Methods: Navigating The Infinite Content Of Mathematics, Jesus Navarro

Student Scholar Symposium

In the infinite realm of mathematical research, understanding and communicating complex concepts require structured and logical approaches. However, a variety of research methods are employed in mathematical studies; these may differ in approach, historical context, and other important considerations which can contribute to confusion and a lack of effective communication. The genesis of this research began with personal confusion during my research on "Counting the Uncountable: Life in a World Without Numbers", setting the stage for the central challenge: How do mathematicians explain their research? To answer this issue, we analyzed a variety of mathematical research articles to highlight their …

From Textbook To Classroom: Gaps In Mathematical Representation And Translation In Nepali Education, Deepak Basyal

Mathematics and Statistics

Translating real-world problem contexts into mathematical symbols is a key skill in curricula worldwide. This study examines Nepali students’ abilities to translate words into symbols and how Nepali textbooks from earlier grades support the development of these skills. To investigate this phenomenon, a sequential explanatory study was conducted with a test for 10th graders and an analysis of Grades 6—9 textbooks. Results show that students struggle to convert real-world contexts into mathematical symbols, while textbooks provide limited opportunities for practice. In particular, students have difficulty translating symbols back into real-world situations, suggesting a link between textbook opportunities and achievement. These …

Connections On Manifolds: A Modern Approach To Classical Differential Geometry, Jed Allen Wilshire

Theses and Dissertations

The purpose of this thesis is to connect modern differential geometry concepts to the classical differential geometry study of surfaces, specifically spheres. This thesis will cover the topics of Riemannian manifolds, tangent spaces, vectors, vector fields, the connection of Levi-Civita, the Christoffel symbols, and Riemannian curvature. Each concept will be demonstrated on the well known unit sphere manifold.

Untitled Unmastered: Initial Conditions And Emergent Properties Of The Mathematics Classroom, Reginald L. Mcgee

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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, …

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 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 …

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 …

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 …

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.

“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 …

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, …

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, …

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, …

Algebraic Topics For Future Middle School Teachers, Leonard Van Wyk

Department of Mathematics and Statistics - Faculty Scholarship

This text contains algebraic concepts relevant to the middle school mathematics curriculum. Topics include the basics of number theory, functions, linear systems, matrices, and polynomials.

Number Talks To Promote Discourse In The Algebra 1 Classroom: A Number Talk Curriculum Development For A Unit On Quadratic Expressions, Lindsay C. Borger

Masters Theses/Capstone Projects

This project sought to develop a curriculum of Number Talks for use at the secondary level, specifically in an Algebra 1 class as a supplement to a unit on quadratic expressions. The project begins with a look at existing research on constructivism and social constructionism as well as the reforms in mathematics education informed by those learning theories. It then looks at calls for more discourse in the mathematics classroom as a part of these reform efforts, and the part Number Talks play in fostering discourse and mathematical thinking for students. The Number Talk curriculum includes a guide for implementing …

Engaging Mathematicians One Step At A Time: Math Trails, Mary L. Dalton, Jennifer Yantz

Journal of Humanistic Mathematics

Mathematics is present in everything we see and do. Sometimes we look past it, looking for some mathematical mystery when the beauty of mathematics is evident in the most obvious ways. One way to engage students to notice connections to mathematics in these everyday objects and events is to direct them in a guided math trail. A math trail is an activity where participants follow a map or guide to various locations while they are encouraged to take notice of connections to mathematical patterns and concepts in the objects around them. An important benefit is that going on a math …

An Unlikely Duo: Injecting Art Projects In The Lower-Division Mathematics Classroom, Douglas T. Pfeffer, Christina Durón

Journal of Humanistic Mathematics

Too often society has sterilized mathematics to the point that many view it as drab and deplete of aesthetic intrigue---in higher education, this is particularly true of students in the lower-division classroom. In this paper, we propose the use of art projects as a novel way to alter this perspective. Art projects function as a hands-on, active way to invite students to both identify connections between math and various non-mathematical disciplines as well as view math as overall more intriguing, inviting, and interesting. This paper details our implementation and discusses anonymously solicited survey data that highlights our successes.

Image Of Mathematics: A Case Study Of Two Women's Early Mathematics Experiences, Lili Zhou, Elizabeth Suazo-Flores, Bima Sapkota, Rose Mbewe, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

People often view mathematics as abstract, cold, and irrelevant to real life, and their school experiences likely influence such views. In this case study, we investigated the mathematics experiences of two women who participated in an afterschool girls-only STEM club 30 years ago when they were in fifth and sixth grades. We explored how the participants' early in- and out-of-school experiences informed their images of mathematics. We collected data through a survey, focus group interviews, and individual interviews. We employed oral history methods in interviews to grant participants a significant degree of freedom to retrospectively recount and reconstruct their experiences. …

Examining Student Understanding Of Series Convergence Using Script Writing, Eduardo Torres Manzanarez

Mathematics Dissertations - Archive

This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ …