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2026

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Sumthin: A Context-Dependent African American Vernacular English Word For Variables, Mark Apedo Jan 2026

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.

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The Math Teaching Atlas: Trails, Anchors, And Compass In Action, Ivan Z. Feng Jan 2026

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.

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Reminiscences Of My Past Life As A High School Math Teacher, Wayne Nirode Jan 2026

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.

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Creating Art With The Generalized Pythagorean Theorem, Ángel Colín Jan 2026

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.

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Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca Jan 2026

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 …

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Invitations To Stem: Activities For Building Community And Enthusiasm From A First-Year Seminar, Dusty Grundmeier, Shanelle Davis Jan 2026

Invitations To Stem: Activities For Building Community And Enthusiasm From A First-Year Seminar, Dusty Grundmeier, Shanelle Davis

Journal of Humanistic Mathematics

We reflect on and analyze a first-year seminar designed as an invitation to Science, Technology, Engineering, and Mathematics (STEM) fields. We present sample activities designed to develop mathematical and scientific problem-solving skills while also building community and enthusiasm. Through solving mathematical puzzles, project-based learning, and reflective activities, students develop a supportive and welcoming STEM-focused community and identity. Along with sample activities, we share our goals, challenges, and student feedback. Finally, we suggest some guiding principles for designing and choosing problems for similar STEM enrichment activities and seminars.

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Partnering With Students To Create A Positive Image Of Mathematics, Manmohan Kaur Jan 2026

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 …

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Why Read The Classics (Of Mathematical Proofs)?, Cosimo Perini Brogi Jan 2026

Why Read The Classics (Of Mathematical Proofs)?, Cosimo Perini Brogi

Journal of Humanistic Mathematics

Inspired by Italo Calvino’s (almost) homonymous writing, this short essay suggests a formal perspective to complement the typical categorisation of classical results in mathematics on aesthetic bases. The traditional proof that √2 is not a rational number provides a simple example of proof mining. When studied through the tools of logic, that proof has also led to designing new systems for formal proving based on cyclic proofs. This example thus supports the central thesis of this essay that reading the classics of mathematical proofs enables us to acquire a taste for mathematical beauty and can open new directions in mathematics …

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A Mathematician Expresses Grief, Richard Delaware Jan 2026

A Mathematician Expresses Grief, Richard Delaware

Journal of Humanistic Mathematics

A famous Scottish mathematician of the eighteenth century shares a tragic sorrow.

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How (And Why) To Start A Math Circle At The County Jail, Aram Bingham Jan 2026

How (And Why) To Start A Math Circle At The County Jail, Aram Bingham

Journal of Humanistic Mathematics

Math circles are a common form of outreach usually run by professional mathematicians as enrichment for K-12 students or teachers. As a setting to stimulate interest and develop positive socialization around mathematical practice, a regular math circle can also be an effective bridge to higher education in carceral settings for both facilitators and participants. This article describes my journey through starting and running math circles in county jails, with a view towards the expansion of mathematics education as another tool for the dismantling of mass incarceration.

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Making Mathematical Art Via The Harmonic And Perturbed Harmonic Functions, Mehmet Pakdemirli Jan 2026

Making Mathematical Art Via The Harmonic And Perturbed Harmonic Functions, Mehmet Pakdemirli

Journal of Humanistic Mathematics

Starting from the definition of a harmonic function series, we define a new series which we call the perturbed harmonic function series. We explore the relationship of the new series with the Weierstrass and Riemann fractal functions as well as its convergence and differentiability properties. We then illustrate the potential of the harmonic functions in generating complex figures that sometimes resemble natural objects, with explicit numerical examples.

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A Note On Modeling Prejudice, Alan Lockard, Edwin Harcourt Jan 2026

A Note On Modeling Prejudice, Alan Lockard, Edwin Harcourt

Journal of Humanistic Mathematics

We model prejudice in the context of an iterated prisoner’s dilemma tournament. Prejudice here is defined as the inability to distinguish amongst members of an identifiable group. We run a computer simulation where agents of one of two groups with defined strategies are randomly matched against each other. The agents either cooperate with or defect against the agent they are matched with. Our focus is on agents who play an unprejudiced version of the Tit-for-Tat strategy (cooperate with any player in the first encounter, and then apply the same strategy [defect or cooperate] that the opposing player played against them …

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How Did Cauchy Prove His Integral Theorem? A Historical Reconstruction For Education Research, José Gerardo Piña-Aguirre, Rosa María Farfán Márquez Jan 2026

How Did Cauchy Prove His Integral Theorem? A Historical Reconstruction For Education Research, José Gerardo Piña-Aguirre, Rosa María Farfán Márquez

Journal of Humanistic Mathematics

In his article “Mémoire sur les Intégrales Définies, prises entre des limites imaginaires” of 1825, Cauchy proves that the integral of a complex function f defined on complex numbers is independent of the path of integration if the function f remains finite and continuous along the chosen path. In contemporary literature that analyzes the mathematics of Cauchy, the specific mathematical process that allowed Cauchy to prove this result is not explicitly presented. The purpose of this manuscript is to communicate a symbolic-algebraic derivation that justifies the narrative argument used by Cauchy to support his proof, thus hopefully filling this gap. …

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Gold And Silver In Balance: Khayyam’S Mathematical Analysis Of Binary Alloys, Yousef Yassi, Reza Yassi Jan 2026

Gold And Silver In Balance: Khayyam’S Mathematical Analysis Of Binary Alloys, Yousef Yassi, Reza Yassi

Journal of Humanistic Mathematics

The history of titration dates back to Archimedes who established that an object submerged in a liquid displaces an amount of liquid whose weight is equal to the buoyant force acting on the object. Since then, many scientists and engineers have tried to optimize his approach or devise new instruments for titration purposes. Omar Khayyam (1048–1123), in addition to designing a hydro-static balance, developed mathematical approaches for titration of binary alloys, that is, alloys made up of only two elements. Here we explore the different versions of Khayyam’s work on titration given by various sources. We also compare the accuracy …

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A Just Balance And The Teaching And Learning Of Mathematics, Marshall Gordon Jan 2026

A Just Balance And The Teaching And Learning Of Mathematics, Marshall Gordon

Journal of Humanistic Mathematics

Society’s response to the question of what is worth sharing and how it best can be provided as conceived by the educational establishment shapes the education of every individual in school. As the classroom experience is a commitment to the future of society, it is good and just for society to support the educational development of each person in order that all can participate productively. In this way a “just balance” is established. In the particular case of educating students in mathematics, however, there is apparently an unjust balance, for despite the considerable time and effort students and teachers in …

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Polygonal Number Similarity, Gunhan Caglayan Jan 2026

Polygonal Number Similarity, Gunhan Caglayan

Journal of Humanistic Mathematics

This note takes an exploratory approach to define and then visualize the notion of polygonal number similarity between pairs of k-gonal numbers Pk(αn) and Pk(n) , where α is an integer scale factor of 2 or greater.

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Translating Trattato Dell'alcibra Amuchabile, Olympia Nicodemi Jan 2026

Translating Trattato Dell'alcibra Amuchabile, Olympia Nicodemi

Journal of Humanistic Mathematics

We present a detailed look at one small section of a premodern algebra manuscript from circa 1365 C.E. The manuscript, Tratatto dell’Alcibra Amuchabile (Anonimo), is written in the Tuscan vernacular, with no symbols, no punctuation, and wildly inconsistent (pre-printing press) spellings. We present some of the hurdles to translating this “rhetorical algebra” followed by an annotated translation of one of its algebra rules, Rule 5, through which we learn the methods and mindset of algebra that preceded and seeded the breakthroughs in algebra of the 16th century. We also point to some of the significant differences between algebra then …

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Mathematics And Ethics: Narratives And Conversations, David Pritchard Jan 2026

Mathematics And Ethics: Narratives And Conversations, David Pritchard

Journal of Humanistic Mathematics

We provide an eclectic overview of various narratives that mathematicians use to describe mathematics. We discuss some of the ethical issues and approaches that each narrative tends to emphasise, and how these can lead to productive conversation in the absence of a universally agreed philosophical or ethical framework. We also discuss the dangers of a deficit model of ethical engagement, and other threats to conversation.

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Emergent Collective Argumentation Types In A Socio-Critical Mathematical Modeling Activity, Ayse Ozturk, Ozgul Kartal Jan 2026

Emergent Collective Argumentation Types In A Socio-Critical Mathematical Modeling Activity, Ayse Ozturk, Ozgul Kartal

Journal of Humanistic Mathematics

Socio-critical mathematical modeling encourages students to employ mathematics as a tool for social inquiry and action, promoting critical thinking and social awareness. While research on collective argumentation in mathematical modeling exists, its connection to socio-critical modeling remains underexplored. This study addresses this gap by examining the types of collective argumentation that emerge during small-group and whole-group discussions as students navigate different phases of the modeling process. Using an adapted version of Toulmin’s argumentation model and a framework for socio-critical modeling phases, this study analyzes classroom discussions in which high school students engage in a modeling task focused on fair raise …

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A Schur-Fire Way To Make Matrix Products Coincide, Keith Copenhaver, Josh Hiller, Christopher Sciortino Jan 2026

A Schur-Fire Way To Make Matrix Products Coincide, Keith Copenhaver, Josh Hiller, Christopher Sciortino

Journal of Humanistic Mathematics

When are the Schur product and the matrix product of two matrices the same? With the help of Morpheus (from The Matrix) and more, we explore this question and find both mathematical answers and math-memes.

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Exploring The Dynamics Of Romantic Relationships Through The Lens Of Prem Rog, Umang Jain, Dheeraj Sharma, Pranay Goswami, Kuldeep Malik Jan 2026

Exploring The Dynamics Of Romantic Relationships Through The Lens Of Prem Rog, Umang Jain, Dheeraj Sharma, Pranay Goswami, Kuldeep Malik

Journal of Humanistic Mathematics

Romantic relationships are dynamic events that begin, grow, and frequently remain for a long time in a stagnant or fluctuating state until possibly dissipating. Although they are unquestionably the most significant dynamic events in our lives, dynamic systems theory has only recently included them in its formal framework. Without a mathematical model, it would be impossible to analyze and comprehend the dynamics because, in general, love stories are too brief to allow things to stabilize and are affected by the ups and downs of the surrounding community. In this paper, we set up models made up of four ordinary differential …

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The More Things Change..., Mark Huber, Gizem Karaali Jan 2026

The More Things Change..., Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Jan 2026

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Ai Teaching Assistants In Higher Education: A Case Study In Pedagogical Integration And Support Jan 2026

Ai Teaching Assistants In Higher Education: A Case Study In Pedagogical Integration And Support

Journal of Economics and Finance Education

This case study examines the implementation of three customized AI teaching assistants in a graduate quantitative methods course for adult learners. Designed to provide timely, course-specific support, the AI tools enhanced student engagement, upheld academic integrity, and aligned with pedagogical principles such as constructivist learning and formative assessment. The assistants were evaluated on the accuracy of their responses and compliance with behavioral requirements. Student feedback indicated improved learning and reduced frustration. This study offers a replicable model for responsibly integrating AI in higher education to support diverse learner needs and promote academic success.

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The Abcs Of Modified Bond Duration And Wxyzs Of Bond Convexity Jan 2026

The Abcs Of Modified Bond Duration And Wxyzs Of Bond Convexity

Journal of Economics and Finance Education

By breaking the mathematical derivation of Macaulay Duration, Modified Duration, and Bond Convexity into smaller easily calculated component parts, a more manageable means of calculation for these bond measures emerges for the student. Further, an Excel spreadsheet or an algorithm within a programming language can also be implemented using these smaller component calculations. The Excel template provided can be made into an assignment or used as a resource for the student.

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An Empirical Implementation Of A Two-Standard-Deviation Investment Signaling Framework Across Multiple Asset Classes Jan 2026

An Empirical Implementation Of A Two-Standard-Deviation Investment Signaling Framework Across Multiple Asset Classes

Journal of Economics and Finance Education

This paper presents a pedagogically driven application of a quantitative investment signaling model based on two standard deviation bands. Deviations beyond the two standard deviation range are interpreted as potential mean reversion signals, triggering tactical shifts in asset allocation or trading actions. Students construct the models in Excel using live market data, overlaying asset returns against calculated deviation bands to inform decisions. The firsthand approach emphasizes applied learning and critical thinking, with students analyzing model results and presenting empirical findings. Evidence suggests this experiential method significantly enhances student engagement, comprehension, and retention of investment strategy concepts across diverse financial settings

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Coase, Thaler, And Behavioral Economics: Methodological Considerations Jan 2026

Coase, Thaler, And Behavioral Economics: Methodological Considerations

Journal of Economics and Finance Education

In their experiments to measure the endowment effect in market settings, Kahneman, Knetsch, and Thaler (1990; hereafter KKT) assessed the assumption of zero transaction costs associated with the Coase theorem. Their study recruited a sample of advanced undergraduate economics students who were placed in a market setting using coffee mugs as real-world goods, under conditions in which there were zero transaction costs. Their results suggested that an endowment effect lowered trading volume, which should not have occurred if Coase theorem worked in practice. We reexamine the research design employed by KKT, as well as their study’s statistical analysis and results.

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Analysis Of Coverage Of Tuberculosis Prevention Therapy (Tpt): Literature Review, Septia Rahmalina, Ede Surya Darmawan Jan 2026

Analysis Of Coverage Of Tuberculosis Prevention Therapy (Tpt): Literature Review, Septia Rahmalina, Ede Surya Darmawan

Journal of Indonesian Health Policy and Administration

Tuberculosis Preventive Therapy (TPT) is a crucial intervention for tuberculosis (TB) control, particularly among high-risk groups such as household contacts of TB patients and people living with Human Immunodeficiency Virus (HIV). Despite being recommended by the World Health Organization (WHO), TPT implementation still faces challenges at the primary care level. This study employed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) method to review 11 articles published between 2021 and 2025 that were relevant to TPT implementation in various high-TB burden countries, including Indonesia. The main barriers identified were input (logistics, training), process (tracing, education, monitoring), and output …

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Student-Faculty Partnerships In Mathematics Undergraduate Coursework, Alyssa G. Cavazos, Luis Miguel Fernández, Isabel Amaro, Elianna Olivo, Cristina Villalobos Jan 2026

Student-Faculty Partnerships In Mathematics Undergraduate Coursework, Alyssa G. Cavazos, Luis Miguel Fernández, Isabel Amaro, Elianna Olivo, Cristina Villalobos

Writing and Language Studies Faculty Publications

This study examines how student–faculty partnerships are experienced within undergraduate mathematics coursework at a majority Hispanic Serving Institution (HSI). Drawing on the Student as Partners (SaP) theoretical framework and using an interpretive phenomenological research design, we examined the lived experiences of student and faculty partners who participated in a series of professional development sessions on student-faculty partnerships and equitable teaching and learning practices in mathematics courses. Findings indicate that student partners’ lived experiences in the partnership program contributed to the development of sense of belonging, self-efficacy, and awareness of the need to link real-world and culturally responsive applications to mathematics …

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Microplastics In St. John, United States Virgin Islands Sediments: Methodological Approaches And Variability Of Microplastics Concentrations And Accumulation Rates, Henry B. Arbaugh, Sarah C. Gray, Dimitri Deheyn Jan 2026

Microplastics In St. John, United States Virgin Islands Sediments: Methodological Approaches And Variability Of Microplastics Concentrations And Accumulation Rates, Henry B. Arbaugh, Sarah C. Gray, Dimitri Deheyn

Theses

Sediment samples were collected from a near shore and reef site in Coral Bay, St. John, United States Virgin Islands (USVI) from 2007-2016, using tube sediment traps. These samples provide an opportunity to study microplastics (MPs) in an area where no previous MP studies have been performed. Most sedimentary MP studies utilize benthic samples which can only measure MP concentrations (#MP/g or #MP/mL sediment), while sediment traps can provide MP accumulation rates (#MP/cm2/day) as a function of time. However, the methods used for extracting MPs from benthic samples have not been tested using sediment trap samples whose characteristics, …

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