Mathematics Commons^™

Beyond The Best Fit: Fitting Sir-Style Models To Data While Prioritizing Biological Meaning, Meredith L. Greer

CODEE Journal

Many students find comfort in mathematics because math classes have been a place where they can find the “right answer” to exercises. Modeling courses typically emphasize more nuance, teaching students to try modeling approaches, compare back with real-world mechanisms and data, and then refine their models, in an ongoing cycle. One topic, however, can cause students to quickly revert into “right answer” mode: fitting a model to data. Phrases such as best fit and minimize the distance suggest there is one optimal solution that can be determined by an algorithm, and these algorithms typically have no relationship to the biology …

Course Portfolio: Elements Of Physics Phys 151, Evan A. Rich

UNL Faculty Course Portfolios

This course portfolio documents the instructional design, teaching methods, and ongoing assessment efforts for PHYS 151: Elements of Physics, an algebra-based introductory physics course at the University of Nebraska-Lincoln. The course serves a broad undergraduate population, including architecture, construction management, and life science majors. The portfolio describes the teaching framework that integrates pre-lecture video preparation, active in-class engagement through iClicker questions, and collaborative weekly recitation sections, all unified around a structured six-step problem-solving approach. A central concern of the course is building students’ self-efficacy in physics, particularly among those with math anxiety or limited preparation. Two assessments are reported: a …

Assessing The Effectiveness Of Tilt-Informed Assessments In Calculus I, Samuel Horelick

Inquiry: The Journal of the Virginia Community Colleges

Transparent Design in Learning and Teaching (TILT) is widely promoted as an evidence-based framework intended to clarify expectations, promote equity, and improve student learning. While prior research reports positive outcomes across many disciplines, less is known about how transparency functions in quantitative, problem-solving courses such as calculus, where students often value efficiency and autonomy. This study examines the effects of a TILT-informed assignment redesign in two sections of Calculus I at a Virginia Community College System institution. One section completed a traditional assignment, while the other completed an equivalent task redesigned to make the purpose, task, and evaluation criteria explicit. …

A Symbolic Model Of Proof Acquisition In Act-R, Beckett Morris, Kerstin Haring

DU Undergraduate Research Journal Archive

Learning to construct mathematical proofs—formal arguments demonstrating the truth of a mathematical statement using logical deductions and previously established facts—is one of the most challenging skills in STEM education. This research aims to build the foundations for a symbolic cognitive model, using the ACT-R cognitive architecture and implementing in Python with the pyactr package, to explore how different proof strategies can be thought through with only symbols and rules. The model observes simple proofs, and its abilities are assessed based on its generalization capabilities, efficiency, and error patterns. By developing and analyzing such a model, this research provides new insights …

1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, ..., Annemarie Torresen

Masters Theses

1

I invite you to see it and feel it and sit in it and breathe it in and

hold it in your lap. Art isn’t too scary, and neither is math.

2

bouncing between bounds of a binary

bippity boppity! let’s break brains and bread

balance or belly flop, what’s mine is yours:

bumptious and bumbling and barely able

i offer it broken and let you like it that way

Machine Learning For Modeling In An Elementary Differential Equations Class, Nathan Albin, Andrew G. Bennett, Abhinav Chand

CODEE Journal

Mixing machine learning with modeling is an area of increasing importance. This paper presents a lesson where students model a spring-mass system both using traditional analysis with linear damping and using machine learning to learn the damping from real data. The machine learning is implemented in a Jupyter notebook hosted on Google Colab, allowing students to train the neural network without requiring the students to carry out coding. Students get experience with how machine learning can fail, how it can work, and the time and data requirements for machine learning to succeed, and are asked to apply this knowledge to …

Parameter Estimation In Ode Models Using Least-Squares Regression, Ulrich A. Hoensch

CODEE Journal

We present a method of estimating model parameters for non-linear ODEs using least-squares regression. The coefficient of determination can be used as a measure of model fit. The method is demonstrated using US population data to fit a logistic growth model. Also, a competing species model is used to describe the interaction of two different species of yeast.

Mississippi Early Childhood Math Resource Guide: Supporting Mathematical Development From Birth Through Age Eight, Melissa Luckett, Systems Change Lab, Mississippi State University, Social Science Research Center, Mississippi State University

Books

The Mississippi Early Childhood Math Resource Guide is a comprehensive, research-informed digital publication designed to support the development of foundational mathematical skills in children from birth through age eight. Developed by the Systems Change Lab at Mississippi State University's Social Science Research Center, the guide translates evidence-based early mathematics concepts into practical, accessible strategies for educators, families, and caregivers. 

Organized by developmental stages, the guide integrates learning domains, age-appropriate math skills, and everyday instructional practices to promote the use of "math talk" and embedded learning opportunities across settings. It incorporates activities, instructional strategies, and resources aligned to support both formal …

Conceptualizing A Responsive Design Pedagogy To Support Teachers' Responsiveness To Students' Mathematical Ideas Through Making, Denish Ogweno Akuom

Theses, Dissertations and Culminating Projects

This study develops Responsive Design Pedagogy (RDP), a conceptual and analytic model of teacher responsiveness in design-based environments, to account for how responsiveness emerges through interactions among students, tools, and tasks. Although responsiveness has been widely studied in mathematics education, limited attention has been given to responsiveness within mathematical design activity and to how teachers attend to the multiple modes through which students express their mathematical ideas. Addressing these gaps, this qualitative study examined one teacher’s enactment of responsiveness in a Learning-by-Design classroom where students designed and used 3D-printed mathematical tools. Data sources included classroom video, student design artifacts, teacher …

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

Exploring The Evolution Of Preservice Elementary Teachers' Mathematics Identity And Possible Selves: A Multi-Case Study Approach, Christa R. Mawn

Theses, Dissertations and Culminating Projects

This study explores the nature of preservice elementary teachers’ mathematics identity and possible selves and identifies shifts in their mathematics identity or possible selves over the course of a place value unit during the semester during a course on mathematics content for elementary teachers. Drawing on narrative identity and possible selves theory, this qualitative multi-case study examined the mathematics identity and possible selves of preservice elementary teachers enrolled in a mathematics content course. Course assignments were used as data sources and included written narratives, future-oriented reflections, drawings, and course artifacts. Individual cases were analyzed, and were followed by a cross-cases …

Emergent Storylines That Influence Positions And Mathematical Status In Collaborative Small-Group Proof Activity, Brittney M. Ellis, Tenchita Alzaga Elizondo

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we used positioning theory to examine storylines that emerged in students’ discourse as they collaborated on a proof construction task. We purposefully selected a case of group work from an inquiry-oriented introduction to proof course as prior analyses showed it was highly collaborative (Alzaga Elizondo, 2022), yet power dynamics seemed unbalanced. We hypothesized that positioning theory could provide a useful lens to interrogate such power dynamics. Through this analysis, we identified several implicit storylines that influenced the interaction related to the nature of proofs, the nature of mathematics, writing proofs, the role of an external authority, …

Instructors' Lived Experiences Of Using Authentic Assessments In College Calculus Courses Across The United States: A Phenomenological Study, Christy Hart Kains

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the lived experiences of instructors with authentic assessments in college calculus courses across the United States. The theory guiding this study was Astin’s student involvement theory, which provided a framework to study the involvement of students in higher education. The central research question for this study was: What are the lived experiences of instructors who utilize authentic assessments in college calculus courses across the United States? This study used a qualitative design following the transcendental phenomenological approach of Moustakas. The sample included 12 instructors from two-year and four-year colleges in …

Exploring The Thinking Processes Of Female Students In Solving Number Pattern Problems Based On Self-Directed Learning, Lailia Maghfiroh, Yayan Eryk Setiawan, Sikky El Walida

Jurnal Pendidikan Sains

Problem solving in mathematics requires integrating conceptual understanding, procedural knowledge, and logical reasoning. This qualitative exploratory case study investigates the intuitive and analytical thinking processes of two female students with contrasting levels of Self-Directed Learning (SDL) in solving number pattern problems. Data were collected through written problem-solving tasks and semi-structured interviews and analyzed descriptively. In this case study, the student with high SDL tends to use analytical thinking, including systematic data organization, strategic planning, and reflective evaluation, while the student with low SDL tends to rely on intuitive thinking, using rapid pattern recognition and prior experience without systematic verification. These …

Development Of Problem-Based Teaching Modules On Linear Systems Of Equations And Inequalities To Improve Mathematical Problem-Solving Skills, Elsya Suharnita, Kartini Kartini, Sehatta Saragih

Jurnal Pendidikan Sains

This study addresses the low mathematical problem-solving competency among Indonesian students, as evidenced by the PISA 2018 results that showed 71% failed to meet the minimum mathematical competency level. This study aims to develop a problem-based learning (PBL) module for systems of equations and inequalities content to improve Phase E students' mathematical problem-solving abilities. Using the ADDIE (Analysis, Design, Development, Implementation, Evaluation) model, this study involved expert validation, a small group trial with 12 students, and field implementation using a posttest-only control group design with 24 students in the experimental group and 25 students in the control group. The results …

Cognitive Conflict In Iconic Visual Representations: Comparing Conventional And Ai Approaches, Endrayana Putut Laksminto Emanuel, Herfa Maulina Dewi Soewardini, Radhitya Duta Pradana, Sikky El Walida

Jurnal Pendidikan Sains

Background of study: The rapid integration of Artificial Intelligence (AI) in higher education has transformed mathematical problem-solving practices, yet it introduces potential discrepancies in students’ visual understanding, particularly in geometric contexts, leading to commognitive conflicts in visual mediators. Aims and scope of paper: This study aims to analyze and compare the sources of commognitive conflict in iconic visual representations when students solve flat shape problems using conventional methods versus AI-assisted approaches. Methods: A qualitative design was employed involving 20 first-year mathematics education students divided into two groups (AI-assisted and conventional). Data were collected through students’ written work and semi-structured interviews …

Math 242: Elements Of Probability And Statistics (Syllabus), Ahmad Almomani Ph.D.

School of Arts & Sciences

This syllabus was developed by SUNY Geneseo Professor Ahmad Almomani during the spring 2026 semester.

Course Objectives:

Upon successful completion of Math 242, R/Elements of Probability and Statistics, a student will be able to: 

• Organize, present and interpret statistical data, both numerically and graphically; 
• Use various methods to compute the probabilities of events; 
• Analyze and interpret statistical data using appropriate probability distributions, e.g. binomial and normal. 
• Apply central limit theorem to describe inferences; 
• Construct and interpret confidence intervals to estimate means, standard deviations and proportions for populations; 
• Perform parameter testing techniques, including single and multi-sample tests for means, standard deviations …

Statistical Investigation Project, Ahmad Almomani Ph.D.

School of Arts & Sciences

The assignment was developed by SUNY Geneseo Professor Ahmad Almomani for the course, MATH 242: Elements of Probability and Statistics in the spring 2026 semester.

The objective for this assignment is that students will apply statistical methods to analyze real-world data and communicate meaningful conclusions.

A Systematic Review Of Mathematical Interpretations Of The Weton Marriage Tradition Within Islamic Cultural Contexts, Ratna Damayanti, Surya Sari Faradiba

Jurnal Pendidikan Sains

This study is grounded in the limited integration of mathematics, culture, and religion within academic discussions of local traditions, particularly the weton marriage calculation practice. It aims to explore the mathematical concepts embedded in weton calculations and to analyse these practices from an Islamic law perspective within an interdisciplinary framework. The study employs a Systematic Literature Review (SLR) method following the six-stage PRISMA 2020 protocol, including the formulation of research questions, development of a search strategy, application of inclusion and exclusion criteria, study selection, quality assessment, and thematic synthesis. Data were collected from Google Scholar and Garuda using the keywords …

Measuring What Matters: Specifications Grading And Latin* Students’ Mathematics Identity, Luis Miguel Fernández, Mayra Ortiz Galarza, Cristina Villalobos, Martha Asare

School of Mathematical & Statistical Sciences Faculty Publications

This study examined Specifications Grading, an alternative grading system emphasizing clearly defined learning outcomes and revision, and mathematics identity among 846 Latin* Calculus I students at a Hispanic-Serving Institution. Mathematics identity, comprising competence/performance, recognition, and interest, was measured at the beginning and end of the semester. Repeated-measures analyses indicated stable competence/performance and recognition alongside declines in interest. Specifications Grading was associated with increased mathematics identity, and multilingual students experienced smaller declines than their peers overall.

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Este estudio examinó la calificación por especificaciones, un sistema de evaluación alternativo que enfatiza resultados de aprendizaje claramente definidos y oportunidades estructuradas de revisión, …

Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures., Giovanni Giuseppe G.G. Nicosia Prof.

Numeracy

Several ancient languages use linguistic structures to differentiate between singular, dual, and plural forms that are used when one, two, or many objects are referenced. (Some languages go further, adding a trial form to differentiate two from three.) In many modern languages, numerals are used to convey precise number. After reviewing a range of ways languages express number (including the interesting case of Pirahã which does not express precise number), the paper concludes with a proposed developmental path for the expression of quantity in languages.

Demystifying Hardware Formal Verification For Undergraduate Education: A Risc-V Processor Case Study With Coursework Implementation, Riley A. Peters

Master's Theses

Hardware verification engineers apply formal methods to prove that a digital device always behaves according to its specification. This differs from traditional functional verification, in which engineers establish correctness by repeatedly sending test inputs to the device and comparing the outputs against a reference model. With the growing complexity of integrated circuits, the demand for digital verification engineers with formal methods experience has continued to increase. However, California Polytechnic State University: San Luis Obispo's current curriculum lacks dedicated material to prepare students for these roles.

This thesis seeks to address the lack of formal methods material through two efforts. First, …

The Butterfly Effect In Economics: Exploring Chaos With A Simple Financial Model, Sandy Hs Herho

CODEE Journal

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and …

Poems For A Calculus Class (After Reading Midlife Calculus And At The Dimensional Border), Kevin Farey

Journal of Humanistic Mathematics

This poetry folder is made up of two short trios. The first begins with “Methods,” a thirteen-line poem by Britt Kaufmann, and continues with two thirteen-line responses to it. The folder’s second half consists of three (non-thirteen-line) responses to a collection of thirteen-line-almost-sonnets by Philip Fried, who had in turn been inspired, during the pandemic, by Edwin Abbot’s Flatland.

Both Kaufmann and Fried are authors of previous JHM poetry folders. Poems from Kaufmann’s book Midlife Calculus appeared in the January 2025 issue and poems from Fried’s series At the Dimensional Border appeared in the July 2024 issue. In addition, …

Sumthin: A Context-Dependent African American Vernacular English Word For Variables, Mark Apedo

Journal of Humanistic Mathematics

If mathematics is a language, then African American Vernacular English (AAVE) could hold the key to a fascinating understanding of the evolution of algebra from human speech in North America. The use of the pronoun something (sumthin) to depict an unknown amount of money that varies implies that algebra developed as a logical necessity in human communication. Exploring this phenomenon and leveraging it to demonstrate the concept of algebra could enhance the comprehension of the subject among speakers of AAVE.

The Math Teaching Atlas: Trails, Anchors, And Compass In Action, Ivan Z. Feng

Journal of Humanistic Mathematics

This paper advocates a shift grounded in mathematical reasoning: teach and write math through explicit routeways rather than narratives, anchor new ideas to familiar concepts on a roadmap, and use motivation and concrete examples as a compass and simulation for discovery.

Reminiscences Of My Past Life As A High School Math Teacher, Wayne Nirode

Journal of Humanistic Mathematics

In this article, I reflect on my twenty years as a high school math teacher. I describe four distinct phases of my career in five-year increments. I aim to make public both what makes teaching high school students rewarding and what makes it difficult. Also, my writing illuminates how indelible the first five years were to my development as a teacher. I hope that this brief memoir helps early-career teachers see past the tumultuous beginnings while also inspiring veteran teachers to reflect on their own careers.

Creating Art With The Generalized Pythagorean Theorem, Ángel Colín

Journal of Humanistic Mathematics

The Pythagorean Theorem and its generalizations have been widely studied. In this article we focus on one particular generalization that asserts that the area of a polygon with one side the hypotenuse of a right triangle is the sum of the areas of similar polygons whose corresponding sides are the other two sides [4]. Using this theorem together with interactive software or simply pencil and paper, we create some visually enticing artwork. This activity, we believe, can contribute positively to geometry teaching at all academic levels.

Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca

Journal of Humanistic Mathematics

We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …

Partnering With Students To Create A Positive Image Of Mathematics, Manmohan Kaur

Journal of Humanistic Mathematics

In a 1989 paper, Barbeau states, “Probably no area of human activity is as afflicted as mathematics with a gap between the public perception of its nature and what its practitioners believe it to be.” Decades later, the situation is much the same. With the technical advances in the contemporary world, mathematics affects our day-to-day activities in essential ways such as e-commerce and credit card security. Mathematical problem solving intrinsically requires creative and critical thinking. However, mathematics is often perceived as uninventive, sterile, static, and removed from human needs and culture. This paper describes how mathematicians can own the image …