Science and Mathematics Education Commons^™

Pedagogical Moves For Provoking Prospective Teachers’ Intellectual Needs While Connecting Abstract Algebra And Secondary Mathematics, Kaitlyn Stephens Serbin, Estrella Johnson, Sthefanía Espinosa

School of Mathematical & Statistical Sciences Faculty Publications

Researchers have exhibited ways in which prospective secondary mathematics teachers can connect content from abstract algebra with secondary mathematics in ways that reshape their understanding of secondary mathematics and thereby support their teaching of that content. However, there has been very little research done on what mathematics teacher educators can do in the classroom to help prospective teachers make connections between abstract algebra and secondary algebra in ways that support such reshaping. This study focuses on a mathematics teacher educator who guided a class of prospective teachers to connect properties of algebraic structures with equation-solving procedures by directing their focus …

A Conceptual Framework For Cognitive Engagement And Human Agency In Ai-Mediated Learning, Sam Rhodes, Zuhal Yilmaz, Terrie Galanti, Younggon Bae, Victoria Delaney, Zareen Gul Aga, Stephen Hutt

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of this chapter is to propose a conceptual framework that unpacks AI use in instructional practice across three interrelated dimensions: human agency, cognitive demand, and AI orchestration. We ground this work in historical perspectives on technology's mediating role in education. We then propose the conceptual framework and three characterizations of the use of AI in school instruction: cognitive load reducer, cognitive capacity builder, and cognitive companion. We then illustrate a worked example of each, including a curricular example and sample student prompts, and conclude with questions that educators might ask themselves as they consider if and how to …

Analysis Of Students' Problem-Solving Skills In Work And Energy Based On Gender, Miftahuljannah Muslimin

Jurnal Pendidikan Sains

This study analyzes students’ problem-solving skills on Work and Energy using a quantitative descriptive design, profiling performance across five indicators without causal claims. Participants were 85 students from SMA Negeri 1 Barru, South Sulawesi (30 males, 55 females) who answered five essay items scored on useful description, physics approach, specific application, mathematical procedure, and logical progression. Overall means were 57.73 (females) and 60.73 (males); an independent t-test showed p = .333 > .05 with Cohen’s d = 0.22 (small), indicating no meaningful overall difference. By indicator, ANOVA showed no gender differences (α > .05) except for logical progression (p = .029). …

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 …

Fermented Foul Play: A Real-World Forensic Scenario To Enhance Student Engagement And Understanding Of Instrumentation And Analytical Data Analysis, Abigail Hoermann, Laci Joy Walmer, Matthew J. Goss

Student Scholar Symposium

A forensic-style investigation was introduced in an upper-level instrumental analysis course to foster collaboration and application of theoretical concepts in a laboratory setting. Students were provided with kombucha samples collected from a simulated crime scene and tasked with determining ethanol concentrations using Gas Chromatography–Mass Spectrometry (GC-MS). By independently preparing serial dilutions, establishing calibration curves, and interpreting mass spectra, they practiced quantitative analytical techniques and engaged in evidence-based problem solving. Notably, Sample C demonstrated elevated ethanol levels (6.4% v/v), suggesting possible adulteration and deepening the forensic narrative. Through this scenario-driven format, students strengthened both their technical competencies and their ability to …

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 …

Education In The Planetarium: A Practical Approach, Matthew Fyfe

Honors Projects

This project proposes live planetarium programming built within the 5E instructional model. It creates a practical application of this with lesson modules surrounding topics in observational astronomy. Specifically, there are investigations into instrumentation through CCD cameras and data collection and processing through spectroscopy and photometry with light curve folding with activities highlighting each. Each module is broken down into segments corresponding to the learning cycles of the 5E model, and as they are self contained in this way can be used piecemeal in different combinations.

Developing Accessible Narrative-Based Stem Learning Software For K-6 Braille Display Users, Dylan Ravel, Daniel Tsivkovski, Brandon Foley, Maryam Etezad, Franceli Cibrian, Ariel Han, Rajeev Joshi

Student Scholar Symposium Abstracts and Posters

This research develops a free, accessible web application that enables K-6 students who are blind or visually impaired (BVI) to learn STEM concepts using refreshable braille displays. Currently, most online learning tools are not designed for BVI students, creating a significant educational barrier.

The application interfaces with commercial braille displays and uses narrative-based learning to make STEM content approachable and engaging. By presenting material as interactive stories, students can connect with concepts while developing braille reading skills. The curriculum design prioritizes accessibility through the Accessible Rich Internet Applications (ARIA) standards and screen reader support.

The goal is to provide BVI …

(R2084) Clarification Of Mathematical Criteria For Conservative Forces And Vector Fields With A Point Singularity In Engineering Studies, Nelli Aleksandrova

Applications and Applied Mathematics: An International Journal (AAM)

The paper deals with a comprehensive analysis of existing mathematical criteria for conservative vector fields including algebraic and geometrical interpretation of Extended Green’s Theorem. Special attention is devoted to the fields containing a point singularity, which represents the primary challenge both in teaching Calculus and in carrying out scientific research in general in computer engineering. Examples of real-world physical fields such as gravitational, electric and magnetic ones are used to appreciate the proposed clarification while teaching various interchangeable disciplines such as mathematics, physics and engineering. Other examples from scientific research literature are provided as well to support the necessity of …

Investigating Programming Behaviors To Understand Student Engagement And Experience In Introductory Programming Courses, Marcus Eugene Gubanyi

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

Introductory programming courses are foundational to developing students’ problem-solving abilities and shaping their persistence in computing pathways. Engagement with programming tasks plays a central role in student learning and experience. Many research measures, including self-reports and code submissions, offer only a limited view of student engagement with programming tasks. This dissertation leverages programming process data, consisting of keystrokes and compilation events, to capture the programming process as it unfolds and to investigate observable programming behaviors. Guided by educational theories, three studies examine how students’ programming behaviors vary across instructional and assessment contexts, how they relate to motivational profiles, and how …

Design And Evaluation Of Gamified Kahoot Modules For Improving Engagement And Conceptual Understanding Of Introductory Physics Students, Yaritza Villarreal

Theses and Dissertations

This study investigates the effectiveness of gamified learning modules in enhancing the engagement and conceptual understanding of introductory physics students. The first phase of this study focused on the design and development of gamified learning modules for selected topics in introductory physics. The modules were developed by integrating principles of Backward Design, following an escape-room theme with interactive scenarios, and incorporating classic game elements (e.g., points and leaderboards).

The second phase examined the effectiveness of the gamified Kahoot modules using a pretest-posttest control-group design. Sixty-eight (68) students were equally randomly assigned to the control and experimental groups. The experimental group …

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.

A Comparative Evaluation Of Feedback Strategies For Enhancing Student Software Test Suite Writing Outcomes, Ashton Alonge

Master's Theses

Background and Context

Software testing is a fundamental component of computer science education, forming the basis for students’ ability to ensure program correctness and reliability. Despite its importance, many students struggle to design test cases that effectively expose faults and achieve meaningful test coverage. Traditional instructional approaches often emphasize code coverage metrics such as line or branch coverage, but these metrics may not adequately capture the quality of student tests. Mutation analysis, which measures how well tests detect small, artificial faults (mutants) introduced into the program, offers a potentially richer measure of test effectiveness. However, little is known about how …

Exploring The Impact Of Statistics Course Modality On Student Learning: A Mixed Methods Approach, Becky Kelleman

Electronic Theses and Dissertations

The importance of statistical literacy has become increasingly evident, as individuals grapple with interpreting statistics to inform critical decisions. Despite the recognized significance of statistical literacy, challenges persist in both educators’ and students’ efforts to navigate the complexities of statistics education. The purpose of this study is to explore the impact of different course modalities on undergraduate students’ academic performance in introductory statistics courses. Using Social Cognitive Theory (SCT) as a theoretical framework, this research aims to shed light on the complex dynamics influencing statistical literacy attainment. By addressing gaps and inconsistencies in the current literature, this study seeks to …

[Project Insight] Modeling Social Isolation: A Data-Driven Index Function Design And Implementation, Jeremis Morales-Morales

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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 …

Challenges In Developing Physical Intuition In College General Physics Courses, Vasiliy S. Znamenskiy, Rafael Niyazov

Open Educational Resources

Many students can memorize formulas but struggle to feel what a newton, joule, or volt means; they treat formulas as plug-and-chug templates rather than descriptions of relationships among physical quantities. This presentation introduces three types of learning activities: (1) text-free (“no-text”) problems, in which carefully designed visuals replace prose to convey relationships and constraints; (2) anti-problems, which begin with a mathematical expression and ask students to imagine a physical situation it could describe; and (3) lab games that turn routine measurement into purposeful play, emphasizing estimation, scaling, and unit sense. We provide ready-made, Brightspace-compatible assessments alongside low-tech implementation options. The …

Citytech Algebra Based Physics Exam1 (Brightspace Quiz), Vasiliy S. Znamenskiy, Rafael Niyazov

Open Educational Resources

This Brightspace-based Exam 1 assesses foundational concepts in algebra-based physics through short, auto-graded items designed to provide clear feedback. The exam targets core learning outcomes from the opening units of the course: measurement and unit analysis, significant figures, one-dimensional kinematics with constant acceleration (relationships among 𝑥, 𝑣, 𝑎, 𝑡), and basic problem-solving with proportional reasoning. Question formats include numerical entry multiple choice focused on common misconceptions, and brief conceptual prompts that test qualitative understanding before calculation. The item set emphasizes translating among verbal descriptions, diagrams, formulas, and graphs; checking the reasonableness of results; and communicating precision. Randomized parameters and pooled …

Revisiting The Spin–Lattice Relaxation Of Homonuclear In-Phase And Antiphase Nmr Magnetization, Lauren M. Kehoe, Zachary G. Mayes, Kelsey E. Brakensiek, Emma L. Ellis, Adam J. Alderfer, Lingyu Chi, Klaus Woelk

Chemistry Faculty Research & Creative Works

Hyperpolarization techniques such as dynamic nuclear polarization (DNP), chemically induced dynamic nuclear polarization (CIDNP), and parahydrogen-induced polarization (PHIP) enhance the sensitivity of NMR spectroscopy and MRI, but the associated antiphase magnetization patterns often relax faster than those of conventional in-phase signals. This study analyzes the spin–lattice relaxation matrix for single-quantum transitions in an isolated, weakly coupled two-spin AX system to identify eigenvectors and eigenvalues that govern the time evolution of in-phase and antiphase longitudinal magnetization. The analysis predicts that AX antiphase magnetization, such as that generated by PHIP hydrogenations in high magnetic field, can relax up to twice as fast …

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 …

Unified Study Of The Classical Hall Effect, Carter J. Reed, Javier E. Hasbun, Wyatt E. Ackerman, L Ajith Desilva

Georgia Journal of Science

Germanium (Ge) samples with different doping types, acceptors (p-type) and donors (n-type), were studied to investigate charge carrier behavior. Carrier concentrations were found to be 1.16×10^21 m^(-3) for the p-type sample and 7.337×10^20 m^(-3) for the n-type sample. These experiments were conducted for the standard Hall effect (Hall voltage versus low magnetic field (B) values) as well as conductivity and Hall voltage versus temperature for different B-fields. The measurements versus temperature at zero-field allow us to obtain band gap ( Eg). While we investigate the conductivities for n-type and p-type doped samples, we also study the conductivity of an undoped …

Potential Pitfalls In Visual Models Of Tipping Points - And How To Fix Them, Jonathan Dechert, Svetlana Gurevich, Stefan Heusler

Northeast Journal of Complex Systems (NEJCS)

Visual models play a crucial role in both science and science communication. However, the distinction between mere analogies and mathematically sound graphical representations is not easy and can be misunderstood not only by laypeople but also within academic literature itself. Moreover, even when the graphical representation exactly corresponds to the mathematical model, its interpretation is often far from obvious. In this paper we discuss the potential landscape visualization commonly used for tipping points in the context of nonlinear dynamics and reveal potential pitfalls, in particular when distinguishing bifurcation induced tipping (B-tipping) from noise-induced tipping (N-tipping).

We propose new visualization techniques …

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 …

It’S A Lightboard … And A Glassboard!, Craig Looney

Physics Faculty Publications

In this poster I present an innovative lightboard-glassboard design concept and prototype. The device, when not in use as a lightboard, is positioned against a wall in a low-profile configuration and used as an illuminable office glassboard. For video production, the device – supported and guided by a robust anti-tip rail system – is safely rolled away from the wall and used as a lightboard. This device has several advantages over traditional mobile lightboard designs including ease and reliability of setup, elimination of storage and transport issues, usability in modest-sized offices, and functionality as an illuminable glassboard when not in …

Farming With Data: Tracing Critical Tensions Using Data Science For Food Justice, Marc Sager, Maximilan Sherard, Anthony Petrosino

Publications

In this manuscript, we explore the intersection of artificial intelligence (AI) and equitable learning in higher education, focusing on data science as a subset of AI and social justice as the core theme of equity. Our investigation sheds light on the nuanced tensions inherent in employing data science for social justice. Rooted in situated perspectives of learning and consequential learning, our study employs an instrumental case-study methodology and analysis techniques from interaction and conversation analysis. Collaborating with three undergraduate students and an urban farm, the students used data science practices to highlight inequities surrounding food justice and access to food. …