Science and Mathematics Education Commons^™

Codee Expects That Every Mathematician Will Do Their Odes: From The Battle Of Trafalgar To Calculus (Or Nelson To Newton), Steven Miller

CODEE Journal

Using the historical Battle of Trafalgar as a case study, we introduce students to mathematical modeling to describe and explore real-world systems. Starting with the question—how do force sizes and combat effectiveness determine which side wins?—we show how to use a blend of mathematics and computational tools to investigate the answer. Beginning by defining a simple differential equation model for combat dynamics, we analyze its behavior using differential equations and accessible algebraic techniques. We show how computational methods and simulations can support systematic, visual exploration and suggest conjectures that mathematical analysis can then establish. This material could serve as the …

Development And Validation Of An Ai-Assisted Eco-Batik Gringsing Student Worksheet, Intan Kurniawati, Arif Widiyatmoko, Bambang Subali 5, Novi Ratna Dewi

Jurnal Pendidikan dan Pembelajaran

Background: Science literacy among Indonesian students remains low, indicating a need for contextual learning resources that connect scientific concepts with students’ environments. Local cultural heritage such as Batik Gringsing, combined with artificial intelligence (AI) as a supporting tool, offers a promising context, yet their integration in a single student worksheet remains underexplored.

Objectives: This study aimed to develop and validate an AI-assisted Eco-Batik Gringsing student worksheet for science learning.

Methods: The study employed a research and development (R&D) approach adapted from the 4D model, covering the Define, Design, and Develop stages. The evaluation focused on the validity and practicality of …

Data-Driven Discovery Of Canonical Models In Undergraduate Differential Equations Education, Devon L. Garls, Raina Majumder, Scott A. Strong

CODEE Journal

Roughly a decade ago, Brunton, Proctor, and Kutz built upon the re-

sults of classical control theory, compressed sensing, and symbolic regression

to create a method for Sparse Identification of Nonlinear Dynamics (SINDy),

allowing one to infer a dynamical system from time series and bring mathe-

matical dynamics into the modern era of large data. This paper is designed for

a reader concurrently enrolled in a first course in ordinary differential equa-

tions and begins with a technical overview of least-squares regression and

finite-difference approximations to derivatives, which is enough to perform

an example hand-calculation on three data points. The …

Berlin Walls In Our Neighborhood: A Social Justice Excursion For Community College Students In Chemistry, Vuk Uskoković

Administration and Staff Articles and Research

Social inequalities, pervasive in the modern world, silently shape access to education and educational outcomes, especially in the sciences. Yet, natural science curricula rarely acknowledge these influences, often under the assumption that their commitment to objectivity must imply political and socioeconomic neutrality. This paper presents an educational initiative that addresses this disconnect by integrating elemental analytical chemistry with social justice themes. A field trip was designed for chemistry students at Fullerton College, pairing hands-on exposure to optical emission spectroscopic techniques with a socio-environmental investigation of heavy metal contamination across different neighborhoods in Orange County, California. This design deliberately tackled two …

Design Implications For Teacher-Configurable Generative Ai Writing Tools: A Participatory Design Study With Storybot, Ariel Han, Shenshen Han, Zhenyao Cai, Joey Huang, Franceli Cibrian, Kylie Peppler

Engineering Faculty Articles and Research

As generative AI (GenAI) tools become accessible, their integration into K–12 writing presents opportunities and challenges. This study partnered with 21 primary school teachers in a participatory co-design process to develop StoryBot, a teacher-configurable GenAI story-authoring platform. Teachers identified instructional needs and learning outcomes that informed system features, including genre-specific writing scaffolds, configurable prompts, and constraints on full-text generation to preserve student voice. The platform positions educators as co-designers of AI behavior rather than passive users. We conducted a pilot writing workshop with 13 youth (ages 8–12) and a focus group with six educators to examine how the platform influenced …

A Sneak Peek Into Prehistory: Curating An Interactive Fossil Display To Spark Interest In The Ua Little Rock Natural History Museum, Syd Joheim, Rene Shroat-Lewis

Research and Creative Works Expo

Arkansas does not currently have a dedicated natural history museum, creating a unique opportunity for UA Little Rock following the recent donation of an expansive fossil collection. In response, the university established a natural history museum initiative intended to benefit both the campus community and the broader public across Arkansas. This initiative provides accessible resources for learning about natural science, evolution, and the state’s prehistoric past, areas that are often underrepresented in informal science education. It also serves as a platform for outreach, student engagement, and undergraduate research, strengthening UA Little Rock’s role in science education, workforce development, and community …

Sustainable Landscaping And Sustainability Education On A College Campus: A Case Study In Place-Based, Collaborative Ecosystem Science, Christine S. O'Connell, Shannon Hahn, Evelyn Jauregui, Michael V. Frazier, Anika R. Bratt, Mary A. Heskel, Megan Butler, Christie M. Manning

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Sustainability education on college campuses can leverage interdisciplinary collaborations between facilities services, sustainability offices, environmental studies researchers, and students to provide hands-on opportunities for place-based learning. In an effort led by student researchers that could be replicated in academic practice at other academic institutions, we collaborated across campus groups to improve campus landscaping and turfgrass management. Turfgrass is an ideal cover for high-traffic areas and recreation, but is energy intensive to maintain, inefficient at carbon sequestration, and requires fertilizing which contributes to nutrient pollution. Here, we outline a student-led research effort that combined experiential learning, using a college campus as …

The Use Of Gadgets And Learning Motivation Among Grade Xi Students In Biology Learning At Sma Negeri 5 Palu, Yulia Citra, Mohammad Jamhari, Masrianih Masrianih, Lestari M.P Alibasyah, Mursito S. Bialangi, Yulia Windarsih

Jurnal Pendidikan Sains

This study aims to describe the profile of gadget use and learning motivation among Grade XI students in biology learning at SMA Negeri 5 Palu and to explore students’ and teachers’ experiences of gadgets as learning support tools and potential sources of digital distraction. A qualitative descriptive design was employed, supported by descriptive questionnaire profiling. A total of 74 students completed a 50-item questionnaire on gadget use and learning motivation, while 10 students and two biology teachers participated in semi-structured interviews. Questionnaire data were analyzed using frequencies and percentages, while interview data were analyzed thematically. The descriptive findings showed that …

Differential Equation Modeling For Sustainable Resource Management: A Steady-State Optimal Harvesting Approach, Iordanka N. Panayotova, Aleksei Talonov

CODEE Journal

Mathematical models based on differential equations provide a powerful framework for connecting real-world data to informed decision-making. In this work, we present a student-accessible project that uses an optimal-control framework to study the sustainable management of biological resources.

Motivated by fisheries management, we examine a predator--prey system in which harvesting decisions must balance ecological and economic considerations. The model is formulated as an optimal control problem that seeks to maximize the total discounted net revenue from harvesting. Rather than solving for the complete time-dependent harvesting trajectory, we restrict the analysis to positive controlled coexistence equilibria and characterize an interior stationary …

Broadening The Community Of Nudibranch Enthusiasts Through Multilingual Educational Programming To Increase Climate Advocacy Engagement, Richelle Li Tanner, Cintya Felix Mendivil, Ashley Lam, Lorena Muñoz, Micah Kim, Elena G. Morales Poot, Gabrielle Keeler-May

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

Environmental literacy and advocacy for environmental protections are essential components of responsible stewardship. For coastal communities, stewardship requires knowledge of ocean processes and the biological communities living within these ecosystems. While many studies highlight difficulties in engaging American audiences in environmental concern and stewardship due to hyper-individualistic societal values, tidepooling is one recreational pathway to coastal community engagement that strengthens sense of place, and therefore, responsibility to protect natural resources. We sought to broaden the tidepooling community to include more diverse voices through a participatory science program with inland city-dwelling, multilingual, and non-English speaking adults. Using nudibranchs as an environmental …

Cultivating Collaboration In Biomolviz: Key Attributes For Building A Stem Educator Community Of Practice, Pamela S. Mertz, Charmita Burch, Roderico Acevedo, Josh T. Beckham, Didem Vardar-Ulu, Kristin M. Fox, Lauren A. Genova, Rachel M. Mitton-Fry, Swati Agrawal, Daniel R. Dries, Kristen Procko

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

BioMolViz is an educational community of practice (CoP) focused on creating resources to improve biomolecular visual literacy instruction and assessment. The community of life science instructors developed in three phases, beginning with a small Core Team that emerged from a conference session and established the domain of interest for the CoP. In-person workshops, supported by short-term funding, drove the initial expansion of the community and the development of shared activities in Phase 2. This CoP was sustained through intentional choices about how members interact, collaborate, and share work. As the community matured in Phase 3, it was supported by longer-term …

Using Approximations Of Practice To Support Calculus Instructors’ Enactment Of Equitable Active Learning Teaching Practices, Kaitlyn Stephens Serbin, Karina Uhing

School of Mathematical & Statistical Sciences Faculty Publications

We implemented a semester-long professional development workshop series to help Calculus I and II instructors implement active learning and equitable teaching practices. The workshops actively engaged instructors in approximations of practice (Grossman et al., 2009) in which they learned to enact various teaching practices like designing tasks; eliciting, noticing, and responding to evidence of student thinking; orchestrating class discussions; fostering inclusive social norms; and equitably managing student participation. After they participated in the workshops, we interviewed the instructors about their decisions to implement the teaching practices from the approximations of practice in their teaching. We analyzed the instructors’ resources, orientations, …

Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger

CODEE Journal

Students in introductory differential equations courses often learn to associate specific equation types with familiar physical systems. While this approach supports procedural fluency, it can inhibit transfer learning: students recognize familiar forms rather than construct models from first principles. This paper presents a modeling-first instructional approach designed to help students recognize the shared structure of second-order differential equations across diverse contexts. Students derive governing equations from fundamental physical laws for multiple systems, including an Inductor, Resistor, and Capacitor (LRC) electrical circuit, a simple pendulum, and viscous pipe flow. Through guided comparison, students identify common components such as inertia, damping, restoring …

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 …

Fast-Track Ode: A Student-Centered, Game-Based Summer Differential Equations Course, Chamila D. Malagoda Gamage

CODEE Journal

This article describes a student-centered and game-based redesign of an Elementary Differential Equations course taught during a six-week summer session. In this compressed setting, students had to move through the standard course content quickly while still developing procedural fluency, conceptual understanding, and confidence with applications. To support these goals, the course used real-time feedback tools, collaborative problem solving, applications connected to students' fields, and mathematical games. The paper describes the course context, major activities, implementation details, and student feedback. Student responses suggest that the activities were well received and helped students stay engaged, participate regularly, prepare for exams, and see …

A Modeling Scenario For Cooling A Hot Vehicle In Florida, Jared Bunn, Bernadette Mullins, Elizabeth Hale, Jaeyoun Oh

CODEE Journal

This paper presents a group project assigned in a Calculus 2 course that has students work to develop, analyze, and draw conclusions about a modeling scenario for cooling a hot car. Using a modeling-first approach, instructors supported the students in class throughout the beginning of the project, enabling the groups to complete the remainder of the project on their own. Students used parameter estimation to tune their models to provided data: one for windows being up, and one for windows being down. This project provides an example of how modeling can be introduced early in a calculus course, rather than …

The Role Of Trauma-Informed Care In Supporting At-Risk Students In Alternative Education, Jar'mel D. Taylor Dr.

Transformations

Students with traumatic experiences commonly fail to meet educational goals and control their emotions while also losing their involvement in classes. Standard trauma-informed care practices remain absent from numerous alternative educational institutions, which leaves their teaching community without adequate support to help traumatized students effectively. The application of Trauma-Informed Care (TIC) strategies toward student outcomes requires investigation to develop effective educational approaches that enhance school success. The researcher used qualitative exploratory case study methodology to study TIC practices in alternative education for Black and Brown adolescent students (aged 12–18) in Washington, D.C. Semi-structured interviews and a focus group with 16 …

Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan

Transformations

This paper presents a progressive series of age-appropriate lesson plans for grades K-12 that all use the same interdisciplinary activity to educate students about Science, Technology, Engineering, Art, and Mathematics (STEAM) simultaneously. Technology from Texas Instruments (TI) was employed including a TI Nspire graphing calculator that can run Python programs, a TI Innovator Hub, and a TI Rover. The TI Rover is a small, robotic car that has sensors and is controlled by the calculator via the Hub hardware interface. A Python program was developed that uses the color sensor in the Rover to detect the color on colored paper …

From Reluctance To Resilience: The Link Between Attitude And Growth Mindset In Calculus Students, Olivia Valente, Kathryn E. Pedings-Behling, Amy N. Langville

Journal of Educational Research and Practice

Many postsecondary students enter general education mathematics courses with negative attitudes, shaping their willingness to engage with the content. This study explores the relationship between students’ attitudes towards mathematics and their growth mindset, revealing effective strategies to enhance learning experiences, particularly for students who are reluctant learners. The research investigates two questions: (1) How do students’ Attitude Toward Mathematics Inventory (ATMI) scores and Growth Mindset Scale (GMS) scores relate? and (2) Do gender or course modality affect this relationship? This study addresses a gap in literature by examining how enjoyment, motivation, self-confidence, and perceived value connect with growth mindset. The …

Numbers, Patterns, And Memories: Early Experiences Of Mathematicians And Mathematics Education Researchers, Constantinos Xenofontos

Journal of Humanistic Mathematics

This paper offers a reflective analysis of early mathematical experiences shared by fifty-six mathematicians and mathematics education researchers, including my own, as part of Cambridge Mathematics’ “Seven Questions with . . . ” interview series. Drawing on thematic analysis, I identify five key patterns across participants’ recollections: the context of early mathematical engagement, the influence of significant others, emotional responses, shifts in mathematical thinking, and mathematics as a social or competitive experience. Many accounts emphasise informal, everyday encounters with mathematics—often preceding formal education—as central to developing interest and confidence in the subject. The findings challenge the notion of innate mathematical …

Impact Of Covid-19 Pandemic On Mathematics Achievement And Problem-Solving Ability: Insights From Secondary Schools In India, Laishram Nirtish Singh, Anand Jyoti Sanasam, Jocyline Thokchom, Ningombam Cha Cogent, Laisom Sharmeswar Singh

Journal of Humanistic Mathematics

The COVID-19 pandemic disrupted students’ engagement with mathematics. This study aims to contribute to our understanding of the extent of this disrupting by examining differences in mathematics achievement and problem-solving ability between adjacent cohorts who learned Class 8 under different schooling conditions in India: Group A (pandemic-exposed Class 8 cohort) and Group B (post-reopening Class 8 cohort). Using a descriptive design in a natural setting, we selected a stratified sample of 1,200 students from Class 9 and Class 10 across 21 secondary schools in Manipur, India. The sample was stratified by gender, family type, school type, and locality to ensure …

A Professional Development Course On Data-Driven Dynamical Systems At A Primarily Undergraduate Institution - Part B: Professional Development Framework And Institutional Implementation, Alessandro M. Selvitella, Jeffrey R. Anderson

CODEE Journal

This paper presents the professional-development and institutional-implementation component of a three-paper program on introducing data-driven dynamical systems into undergraduate ordinary differential equations instruction at a primarily undergraduate institution. The companion paper \cite{SelvitellaAnderson2026} develops the mathematical and computational content, including regression, regularization, Dynamic Mode Decomposition, Sparse Identification of Nonlinear Dynamics, and a Van der Pol oscillator activity. The present paper asks a complementary implementation question: what departmental structures, graduate teaching assistant roles, professional-development activities, and course-support pathways are needed for such materials to become teachable within local undergraduate settings?

We describe a three-phase professional-development model for graduate teaching assistants in the …

Surveying First-Year Stem Students’ Self-Reported Knowledge, Skills, And Attitudes Towards Teamwork, Gregory R. Goldsmith, Camilla Acosta

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

The ability to work in a team is cited as a key outcome for many undergraduate Science, Technology, Engineering, and Mathematics (STEM) programs, both as a method for improving learning and as a highly desired trait for employers. Despite a growing focus on teamwork, our ability to design appropriate teamwork curriculum is limited by our poor understanding of what students arriving at university know about teamwork, what teamwork skills they consider themselves to possess, and their attitudes towards teamwork. We delivered a mixed-methods survey to first-year STEM undergraduate students (n = 205) to benchmark knowledge, skills and attitudes towards …

Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett

CODEE Journal

As data-driven methods are increasingly used in science and engineering, students benefit from learning to integrate machine learning techniques with traditional mathematical modeling. We present a hands-on extra-credit assignment for an undergraduate ordinary differential equations (ODE) course that enables students to compare classical analytical methods with data-driven approaches on the same physical system. Using a coupled-pendulum system---two pendulums connected by a spring---with real experimental data acquired via video tracking of a real physical setup, students work through three models in a guided Jupyter notebook with all code provided. First, they fit a neural network with Fourier features as a purely …

A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis, Paige Zhu, Padmanabhan Seshaiyer

CODEE Journal

Chronic post-surgical pain (CPSP) is a common and often overlooked complication following surgical correction of idiopathic scoliosis, impacting long-term patient wellbeing despite improvements in surgical outcomes. This project introduces a novel epidemiological framework to model the progression of CPSP using a compartmental structure. By applying a coupled system of nonlinear differential equations, we simulate pain trajectories over time and assess the effectiveness of surgical interventions. The model is implemented for a single-cohort population and extended to a two-cohort design to compare outcomes between Posterior Spinal Fusion (PSIF) and Vertebral Body Tethering (VBT) procedures. Further stratification by patient age enables us …

Trattato Dell’Alcibra Amuchabile (Anonimo): A Guided Translation, Gary Towsley, Olympia Nicodemi

Geneseo Authors

The Trattato dell’Alcibra Amuchabile is a pre-modern algebra text from c. 1365. It is written in a Tuscan dialect of Italian and is situated in the abbacus school tradition, schools that taught the mathematics needed for a mercantile society. Like all the algebra written in Italy at the time, it was inherited from al-Khwarizmi and, like his, written with no symbols—no x’s, y’s, plus signs, etc. It was what is sometimes called “rhetorical algebra.”  There is very little source  material available in English from this important era in the history of algebra. This book helps fill that gap. …

Centering Culture, Language, And Identity In A History Of Mathematics Course For Preservice Teachers, Luis Miguel Fernández, Tenchita Alzaga Elizondo

School of Mathematical & Statistical Sciences Faculty Publications

This article presents the redesign of an undergraduate History of Mathematics course for preservice teachers at a Hispanic-Serving Institution. Grounded in Community- and Family-Centered Pedagogy (CFCP) and Marshall’s framework for culturally sustaining mathematics teaching, the course intentionally moved beyond Eurocentric narratives to center students’ linguistic, familial, and cultural resources as integral to mathematical meaning-making. Two core assignments anchored the redesign: (1) evolving Padlet reflections that connected global mathematical histories to students’ family and community practices, and (2) bilingual Cuentos Matemáticos that wove mathematical concepts with personal and cultural narratives in English and Spanish. Selected student reflections illustrate how these experiences …

Toward A Didactical Phenomenology For The Completeness Axiom, Sean Larsen, Tenchita Alzaga Elizondo, Kristen Vroom, Stephen Strand Ii

School of Mathematical & Statistical Sciences Faculty Publications

The study is part of an instructional design project focused on introductory real analysis. The goal of the project is to develop a theoretically grounded and empirically supported instructional approach that builds on students’ experiences in the calculus sequence to engage them in the reinvention of the rigorous foundations of the calculus. An essential aspect of this foundation is the completeness of the real numbers. Drawing on the didactical phenomenology heuristic from the theory of Realistic Mathematics Education (RME), we conducted an iterative instructional design study focused on the completeness axiom. The work proceeded in two phases. First, we conducted …

The Impact Of Madden-Julian Oscillation On Rainfall Variability In South Sulawesi And Its Implications For Science Education, Misbahuddin Mansur, Pariabti Palloan, Agus Susanto

Jurnal Pendidikan Sains

This study examined the relationship between the Madden–Julian Oscillation (MJO) and rainfall variability in South Sulawesi Province, Indonesia, using daily rainfall observations from 24 stations during 1990–2020. A quantitative observational design based on long-term climatological time-series analysis was employed. MJO activity was identified using the Real-time Multivariate MJO (RMM) index, while rainfall variability was analyzed through rainfall anomalies, rainfall frequency, and spatial patterns across Seasonal Zones (ZOM). The results indicate that active MJO phases were generally associated with wetter conditions and higher rainfall frequency, whereas suppressed phases corresponded to drier conditions. Rainfall responses varied considerably among regions, with coastal areas …

From Cork To Coasting: A Multi-Stage Ode Model Of Water-Rocket Flight, Viktoria Savatorova, Patryk Kustra, Ethan Dyer, Connor Carlson, Aleksei Talonov

CODEE Journal

Water rockets provide an affordable and engaging context for exploring applications of differential equations. Motivated by outreach activities conducted with undergraduate students, we develop a four-stage mathematical model of vertical water-rocket flight that is suitable for use in an ODE or mathematical modeling course. The model includes the cork-release phase, water-thrust propulsion, air-thrust propulsion with compressible and potentially choked flow, and the final ballistic stage with quadratic drag. While retaining key physical features, the model can be formulated as a system of ordinary differential equations that can be integrated numerically using tools familiar to students. We compare model predictions with …