1. History

BRICKS AND BLOCKS OF ULTRA MATHEMATICIANS — Satish C. Bhatnagar <satish.bhatnagar@unlv.edu>

The humanistic approach to any aspect of mathematics adds a refreshing dimension. It is especially pertinent from the pedagogical angle. The session on the Unspoken History of Mathematics is a perfect platform to raise such questions and generate new lines of thinking. For the sake of simplicity, I have defined bricks and blocks of mathematics as a set in the complement of a set of hard core theorems, propositions, lemmas, corollaries, definitions, problems etc. In this paper, I explain bricks and blocks by taking the example of the most celebrated theorem, Fermat’s Last Theorem (FLT). After more than 350 years, its proof was ultimately put to rest in 1994 by Andrew Wiles (b.1953 - ). The nuts and bolts or bricks and blocks of FLT, with a focus on Wiles, are his wife and children, schools and colleges he attended, institutions he worked, his students, classmates, neighbors, friends, colleagues, supervisors, and any tangible factors. They are generally invisible, unheard, and unspoken!

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1. Teaching Logic

Logic First: Making Logical Arguments and Writing Proofs as Separate Learning Tasks — Jennifer Aust <jaust@utsouthern.edu>

Mathematics majors with limited writing skills often struggle with the double hurdle of learning to formulate logical arguments and learning to write precisely and concisely to communicate mathematics effectively. I will introduce a pedagogical tool (which I call a Proof Outline) that provides a tabular format for logical arguments. The purpose of the tool is to separate the task of formulating the logical argument from the task of writing that argument in paragraph form, allowing students to make progress on logical reasoning and argument construction regardless of their skill level with mathematical writing. I will share examples that highlight the tool's purpose and lessons learned from using the tool in upper-level mathematics courses for several years.

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1. Spoon!

3-D Grationality — Kevin Jaimes-Villagomez <mkx764@vols.utk.edu>

This project extends the concept of grationality from regular polygons to regular polyhedra. In two dimensions, grationality arises naturally from area scaling and geometric manipulations. In three dimensions, we introduce structural and arithmetic constraints, since only five regular polyhedra exist and volume scales differently than area. By defining a nice polyhedron as a regular polyhedron with natural-number side lengths, and calling an integer 𝑚 > 3 3D‑Grational when a polyhedron with 𝑚 vertices can be broken into 𝑚 smaller congruent copies, we analyze how these solids behave. These definitions and constraints highlight the fundamental differences between 2D and 3D behavior, reveal new geometric handicaps, and creates conjectures about which vertex counts can support grationality in three dimensions.

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1. Practical AI

97D40 Transforming College Algebra Through ALEKS, Adaptive Learning, and Artificial Intelligence — Nelly Belinga <nbelinga@ung.edu>

College Algebra is a gateway course that presents significant challenges, such as varying student preparedness and math anxiety. This session explores the potential of ALEKS, an adaptive learning platform, integrated with artificial intelligence (AI), to enhance student engagement and learning outcomes. By examining classroom implementation and data-driven practices, this presentation demonstrates how ALEKS offers personalized learning paths, real-time diagnostic insights, and efficient remediation. It will also address AI's role in adaptive sequencing, feedback, and supporting equitable instruction. Participants will leave with actionable strategies for leveraging ALEKS to foster deeper mathematical understanding in College Algebra while aligning with desired learning outcomes.

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1. Recreational

A (Nearly) Infinitesimally Quick Introduction to the Surreal Numbers — Jeff Clark <clarkjeffrey1961@gmail.com>

Almost all of our math classes make use of the real numbers as well as subsets (the rational numbers, the integers, the natural numbers) and occasionally supersets (the complex numbers). John Horton Conway, in his research on game theory, came up with the notion of Surreal Numbers, an ordered field that contains the real numbers and much more, including positive numbers smaller than every positive real numbers (positive infinitesimals) and numbers bigger than every positive real number (positive infinite numbers). This talk will introduce the main concepts behind the Surreal Numbers, including their connection to game theory and how the real numbers are themselves defined.

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1. Spoon!

A Magic Carpet Ride through Irrationality — Jeneva Clark <dr.jenevaclark@utk.edu>

Stanley Tennenbaum proved the irrationality of $\sqrt{2}$ using Carpets Theorem with square carpets, and others (myself, Conway, and Miller) have tried to generalize this proof by using triangular and pentagonal carpets. Although those families of proofs used simple tools, a.k.a. “spoons,” in this talk, I am going to try to “spoonify” this even more. I’ll prove the irrationality of $\sqrt{3}$ and $\sqrt{5}$ using only square-shaped carpets. This work extends the previous findings for grationality and opens up the possibility of more research into families of irrationality proofs.

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1. History

A Mathematical History of Solitary Waves — Ryan Thompson <ryan.thompson@ung.edu>

In 1834, a Scottish engineer named John Scott Russell witnessed something he did not expect: a single wave rolling down a narrow canal without changing its shape. Intrigued, he chased it on horseback and later described it as a “wave of translation.” At a time when waves were thought to quickly spread out and disappear, Russell’s moving bump of water seemed almost impossible. His observation raised a lasting question: how can a wave travel long distances without breaking apart? Decades later, this mystery found a mathematical explanation. In the late nineteenth century, Diederik Korteweg and Gustav de Vries wrote down an equation for shallow water waves that allowed such stable traveling waves to exist. Their equation showed that two competing effects, one that tries to spread the wave out and one that tries to steepen it, can balance perfectly. The story did not end there. Over the twentieth century, mathematicians and physicists refined these ideas, searching for better ways to describe water waves and other wave phenomena. Important insights were provided by Gerald Whitham, who emphasized how simple wave patterns can slowly change as they move. The journey continues into the 1990s with a new chapter written by Roberto Camassa and Darryl Holm. Their Camassa–Holm equation predicts solitary waves with sharp crests, called “peakons,” revealing that even stranger wave shapes can arise from the same shallow water setting that inspired Russell’s canal experiment. This talk follows the path from a man on horseback chasing a wave to modern mathematical equations, illustrating how a simple physical curiosity grew into a rich theory of solitary waves and nonlinear equations.

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1. Recreational

A Tale of Two Card Games: EvenQuads and Projective SET — Timothy Goldberg <timothy.goldberg@gmail.com>

The games Projective SET and EvenQuads are both inspired by the famous SET game, but in different directions. The SET game is a model for the affine finite geometry AG(n,3), and Projective SET is so-named because it is a model for the projective finite geometry, PG(n,3). On the other hand, EvenQuads is a model for the affine finite geometry AG(n,2). Despite their apparent differences, there is an interesting way to play Projective SET within EvenQuads, and hence a mathematical connection between properties of the two, which are of interest in algebraic coding theory. In this talk, I will introduce the two games, show how to play one game within the other, and describe some of the mathematics involved in each. Time permitting, I will discuss some connections to coding theory.

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1. Recreational

Apollonius and the Hyperbolic Circle — andrew simoson <ajsimoso@king.edu>

Given distinct planar points $A$ and $B$ and a real number $k$, called the _index_, Apollonius long ago showed that the locus of all points $P$ for which $k$ is the ratio of the distances from $P$ to $A$ and from $P$ to $B$ is a circle. The puzzle we present is this one: Given a circle $\mathcal Q$ in the hyperbolic disk whose diameter $CD$ lies along the real axis, how may we recover $\mathcal Q$ as a circle of Apollonius? That is, what are $A$, $B$, and $k$? The beauty of this puzzle is that $B$ is the hyperbolic center of $\mathcal Q$.

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1. Practical AI

Comparing the Student Success of Alternate Assessments to Traditional Exams in Undergraduate Mathematics — Lily Devlin <devlinlr@appstate.edu>

In this classroom action study, we compare an alternate assessment method to traditional exams in order to determine if there is a less stress-inducing way to assess students' understanding of the concepts in an undergraduate college algebra course. Grades on both alternate assessments and traditional exams, as well as the students’ perception of the assessment we're collected from three different sections of the course. This presentation will share the alternative assessment design, the methodology of the study, and the analysis of student data.

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1. History

Connections Between Numerical Systems across North America: From Alaskan to Mayan Numerals — Elizabeth Baldwin <ebaldwin6@students.apsu.edu>

From two distinct areas at opposite ends of North America, Mayan and Katovik numerals share a great deal of similarities in both design and function. While Katovik numerals were only recently created in 1994, it served a purpose to its community that previously had difficulty in expressing how they had been doing math. The Mayans on the other hand had been able to calculate an accurate calendar and track cycles of the moon and the sun. Both of these systems are a form of body-counting, where they are a base 20 system, sub-base 5. These were meant to represent all of our fingers and our toes. The main difference between these two systems, is that the Mayan numerals are a near perfect system, where they changed how a place value worked in order to work with their records more accurately. Ultimately despite the difference in geography and involvement in the modern era, both of these cultures created reliable systems that help understand the world around us.

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1. History

Degrees of Defiance: Underground Higher Education — Ryan Thomas <rthomas@csuniv.edu>

Throughout history, conquering powers have sought to suppress culture as a means of control. This talk will explore underground universities as sites of intellectual resistance, focusing on clandestine efforts in occupied Poland during the Second World War. Although higher education was directly targeted by Nazi policy, Polish scholars organized secret courses, exams, publications, and degree programs, often at great personal risk. Using education itself as an act of defiance, these faculty members and students contributed to sustaining national identity and many would go on to shape postwar intellectual life.

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1. AI-Resistant

Designing AI-Resistant Mathematics Projects through Creativity, Personalization, and Mathematical Sensemaking in Liberal Arts Mathematics — Candice Quinn <cquinn@una.edu>

The rapid rise of generative artificial intelligence has intensified longstanding challenges in mathematics assessment, particularly for open-ended projects that can be easily outsourced to AI tools. Yet projects remain essential for fostering mathematical sensemaking, creativity, and positive mathematical identity, especially in liberal arts mathematics courses serving non-STEM majors. This session presents a sequence of AI-resistant mini-projects implemented in a Liberal Arts Mathematics (MA111) course. These projects are intentionally designed around personalization, invention, and reflective explanation, features that require authentic student thinking and cannot be meaningfully completed by AI alone. Examples include: (1) designing an original recursive number sequence inspired by Fibonacci-type patterns, (2) analyzing mathematical structure in a natural phenomenon of the student’s choosing, and (3) creating a personal number system with defined symbols, rules, and representations. The design framework integrates three core principles: 1. Personalization (student-chosen contexts and parameters), 2. Creation (students generate new mathematical objects or systems), and 3. Justification (written explanation of reasoning and meaning). Student artifacts and reflections indicate that these projects promote ownership, creativity, and deeper engagement with mathematical ideas while substantially reducing AI-generated submissions. Practical assignment prompts, scaffolding strategies, and grading approaches will be shared so participants can adapt AI-resistant project structures to their own courses.

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1. Teaching Logic

Discussion: Teaching Logic and Reasoning - What Next? — Andrew Miller <andrew.miller@belmont.edu>

Following the talks in our session on teaching logic and reasoning, we will pause to reflect, discuss, and brainstorm where we might go next. Audience members and presenters are invited to stay and discuss how they might use ideas from today's talks in their own classes, how they might refine those ideas, and how we might explore other ideas for teaching reasoning to students in mathematics classes.

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1. Practical AI

Exploring the Impact of Automated Assessments in a Quantitative Methods Course — Raluca Clendenen <raluca.clendenen@belmont.edu>

This is a preliminary report on a study investigating the effectiveness of self-grading Excel spreadsheets as a feedback tool in STEM education, particularly focusing on their impact on student learning outcomes, engagement, and satisfaction. By providing students with instant feedback on assignments, these self-grading spreadsheets are intended to enhance students’ understanding and mastery of mathematical concepts. The study gathers student feedback to explore their perceptions of how these tools influence their learning process, confidence, and comprehension in mathematical contexts. Giving students the tools they need to develop confidence is critical to their self-efficacy and performance. Additionally, this research identifies and addresses the challenges of designing and implementing self-grading assignments, offering insights into best practices for integrating technology-driven feedback tools in STEM education. Preliminary findings suggest that self-grading spreadsheets may serve as a valuable resource in promoting active learning, with implications for improving student engagement and satisfaction. Student quotes on the positive effects for their learning from the assignments, obtained via in-semester surveys and end-of-semester course evaluations, will be shared. References Blayney P., Freeman M. (2004). Automated formative feedback and summative assessment using individualised spreadsheet assignments. Australasian Journal of Educational Technology, 20(2), 209–231. https://doi.org/10.14742/ajet.1360 Kovačić Z., Green J.S. (2012). Automatic grading of spreadsheet and database skills. Journal of Information Technology Education Innovations in Practice, 11, 53–70. Laing G., Kirkham R., Kampen T. V. (2020). An Automated Assessment Marking Approach: Using Excel to Grade an Accounting Practice Assignment. e-Journal of Business Education & Scholarship of Teaching, 14(3), 12-24. Mays T. (2015). Using spreadsheets to develop applied skills in a business math course: Student feedback and perceived learning. Spreadsheets in Education, 8(3). Fyfe, E. R., & Rittle-Johnson, B. (2016). The Benefits of Computer-Generated Feedback for Mathematics Problem Solving. Grantee Submission, 147. https://doi.org/10.1016/j.jecp.2016.03.009 Kangaslampi, R., Asikainen, H., & Virtanen, V. (2022). Students’ Perceptions of Self-Assessment and Their Approaches to Learning in University Mathematics. LUMAT: International Journal on Math, Science and Technology Education, 10(1), 1–22. McCarron K.B., Park T., Ellis Y. (2023). Intermediate accounting students’ reaction to Excel® homework assignments with a feedback (self-check answer) function. Journal of Instructional Pedagogies, 28. LoSchiavo F.M. (2016). How to Create Automatically Graded Spreadsheets for Statistics Courses. Teaching of Psychology, 43(2), 147-152. DOI: 10.1177/0098628316636293.

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1. Teaching Logic

From Truth Tables to Trees: Strengthening Logical Reasoning Through Semantic Tableaux — Ashley Suominen <asuomine@scad.edu>

Logic and formal reasoning are foundational to mathematics, yet students often struggle to connect symbolic notation with conceptual meaning. This presentation explores the pedagogical value of semantic tableaux as an integrated approach that reinforces truth tables, normal forms, and tautology analysis while deepening conceptual mastery of propositional logic. Semantic tableaux offer a visual and algorithmic method for decomposing well-formed formulas into subformulas and atoms. This tree-based representation complements traditional truth-table reasoning by applying the rules for logical connectives to determine whether a statement is satisfiable. By making the logical structure visually explicit through a branching tree, this method reveals the conditions for tautologies and contradictions while naturally bridging to normal forms (CNF and DNF). In doing so, it also reinforces case-based reasoning that underpins probability models and proofs by cases. Ultimately, semantic tableaux move students beyond procedural symbolic manipulation and table-reading toward a deeper understanding of logical form, laying a rigorous foundation for advanced reasoning in mathematics and computer science.

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1. AI-Resistant

Homework-Video-Reflection System for Calculus I and DE — Shalmali Bandyopadhyay <sbandyo5@utm.edu>

Traditional homework-based assessment in undergraduate mathematics has been destabilized by AI tools, producing a familiar pattern: flawless homework, failed exams. This talk presents an integrated homework-video-reflection system implemented in Calculus I and Differential Equations that addresses AI-assisted academic dishonesty without punitive measures. Exam problems are drawn directly from homework, making transparency itself the accountability mechanism

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1. Practical AI

How Alternative Assessment Can Change the AI Conversation — Kristi Rittby <kerittby@peace.edu>

What if, instead of trying to prevent students from using AI, we designed assessments that require collaboration with it? At a small liberal arts college, mathematics assessment for non-majors was reimagined through alternative grading and structured revision cycles. When assessment shifts from point accumulation to iterative feedback and proficiency-based revision, students begin to use AI not to produce answers, but to ask better questions, test ideas, and clarify their thinking. This session explores the evolving partnerships between students, instructors, and AI in redefined learning spaces, striving to increase a sense of belonging. Let’s explore redesigning assessment to sustain rigor, preserve human connection, and invite authentic mathematical curiosity in the age of generative AI.

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1. History

Inspired by Notable Women in Math: An Assessment in Abstract Algebra — Denise Rangel Tracy <rangel.tracy@fmarion.edu>

In this talk, I will describe a project based assessment created for an abstract algebra course that centers the mathematical work of women algebraists highlighted in the Association for Women in Mathematics (AWM) EvenQuads playing card project. Rather than presenting algebra as a finished body of results, this assignment invited students to explore topics such as geometric group theory, elliptic curve groups, and tropical algebra through the work of mathematicians whose contributions are often absent from traditional undergraduate coursework. Students completed individualized structured problem sets connected to each honoree’s research area, developed a short biography, and gave a presentation linking the mathematics to the mathematician’s contributions. I will discuss the goals of the assignment, share examples of the algebraic tasks designed for the project, and reflect on how integrating these mathematicians into assessment broadens the historical narrative students encounter in upper level mathematics.

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1. Spoon!

Kitchen Physics: Teaching Quantum Mechanics & General Relativity With Spoons. — Jonathan Clark <jclark@tnwesleyan.edu>

Advanced physics utilizes mathematical concepts which are often inaccessible to both undergraduate and unprepared graduate students. In keeping with the theme of teaching with spoons, this talk will illustrate examples of presenting advanced modern physics concepts with only using low-level tools accessible to typical math or science majors. In particular, we will derive gravitational time dilation without using the differential geometry of general relativity, we will solve the quantum harmonic oscillator without using Schrödinger's equation, and we will present a conceptual proof of Bell's theorem using only Venn diagrams. The intent of this talk is to inspire physics teachers to try utilizing spoons in their classrooms to illustrate otherwise unavailable content using more accessible intuitive tools.

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1. History

Latin America's Hidden Contributions to Mathematics — Zachery Keisler <zkeisler@saludaschools.org>

In this talk, we’ll trace the development of mathematics in Latin America, using precise examples to anchor a broader story. We’ll start with the Mayans' vigesimal positional numeral system—remarkable for its early and systematic use of zero—which enabled sophisticated calendrical calculations and astronomical observations. Fast forward to the present, and we encounter the work of Carolina Araujo in birational geometry, particularly her contributions to the theory of Fano manifolds and rational curves within Mori theory. These cases serve as guideposts for a deeper discussion spanning Indigenous mathematical traditions, the influence of colonial-era education, and the emergence of active research communities in Mexico, Brazil, and Argentina. By sharing these stories, we’ll see how Latin American mathematics has been shaped by creativity, exchange, and resilience, and why its contributions matter in today’s global mathematical landscape.

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1. Recreational

Manimating Formal Definitions and Theorems — Robert DeYeso III <robldeye@gmail.com>

We use the community version of Manim (created and popularized by Youtuber 3Blue1Brown) to animate mathematical concepts and theorems that are traditionally very difficult to convey. Examples include animations of the derivative, the $\varepsilon$-$\delta$ definition of the limit, and the fundamental theorem of calculus. If time permits, we will play with an interactive example where students can dynamically adjust animations of integrals.

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1. Practical AI

Mastery Based Assessment in a Remedial Math Course — Sarah Eskew <sarklock@utsouthern.edu>

We will discuss how the remedial math course at our university was converted to mastery based assessment. This will include how we decided on the learning targets, how we handle the logistics of additional attempts, and what is mastery graded and what is not. Initial reactions from student surveys will also be included.

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1. History

Mathematics Behind African Art — Kari Mays <mays_kari@hcde.org>

Mathematics, at its heart, is African. Unfortunately, much of ancient African traditions and customs have been lost due to colonization and slavery, including their knowledge and practice of mathematics. However, artifacts uncovered by archeologists confirm the understanding of math principles by African artisans. African art holds the secret behind the history of mathematics in Africa. With a focus on Sona sand drawings, this presentation will explore the beauty of mathematics that can be pulled from the ancient customs of the Tchokwe people of Angola. By exploring the work of Paulus Gerdes, a mathematician known for his work with the Tchokwe people, a discussion of mirror curves and symmetry arises from the analysis of the Sona sand drawings. He takes the patterns created by these curves to make what he coins as Lunda-designs. In this presentation, you will learn how to create your own Lunda-design and learn why they are mathematically beautiful.

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1. Spoon!

N Our 2D Era — Cara Admiraal <c.admiraal@yahoo.com>

In our previous work, we explored the higher dimensional analogues for Primitive Pythagorean Triples (PPTs) both algebraically and geometrically. In this session, we take a curiosity driven exploration of primitive Pythagorean results in two dimensions, emphasizing the recognition of patterns within differently defined collections of PPTs and observing predictable frequencies and occurrences of non-PPTs. What possible connections exist between this creative exploration and the higher dimensional analogues?

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1. Practical AI

Our class SI is the "infamous" AI — Rodica Cazacu <rodica.cazacu@gcsu.edu>

It is well known that one big issue students have in math classes is related to solving word problems. So, what can we do in a class like Quantitative reasoning or Mathematical Modeling, where most of the problems they have to solve are word problems? How many examples could an instructor show their students to make sure they understand how to approach such problems? This presentation will look into how I use the AI in my Quantitative Reasoning classes as a tool that will help my students understand the process of solving word problems, creating examples and understanding the mathematical logic while applying it in real life. I will talk about what I call Unit Workshops, where my students work in groups to discuss different methods, they find using the AI and compare them to what we worked in class before, looking for errors that may affect the results and/or interpretation of the results. All these workshops are guided, and each group must write a report.

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1. AI-Resistant

Promoting Genuine Engagement through an AI-Resistant Assignment: Evidence from Student-Created Video Solution Homework in Undergraduate Mathematics — Wonjin Song <wsong@ung.edu>

The rapid advancement of artificial intelligence has created new challenges for mathematics educators seeking assignments that promote authentic student engagement rather than AI-assisted completion. This study examines student-created video solution homework as an AI-resistant assignment in undergraduate mathematics. Implemented across four undergraduate mathematics courses, the assignment required students to explain their problem-solving processes verbally and visually. Classroom-based empirical evidence was collected through two measures: (1) comparisons of exam performance by video homework completion and quality, and (2) a student perception survey. Across courses, students who consistently earned full-credit video scores demonstrated higher average exam performance than peers with incomplete or lower-quality submissions. Survey responses further indicated that students perceived improvements in conceptual understanding, organization of reasoning, and confidence in explaining mathematics. Together, these findings suggest that structured video explanation assignments can promote genuine engagement and deeper learning while serving as a practical AI-resistant assessment strategy in undergraduate mathematics.

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1. Recreational

Quad-packing in the game EvenQuads — Taiki Aiba <taiba3@gatech.edu>

_EvenQuads_ is a _SET_-like card game published by the AWM whose goal is to find "quads", which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry $AG(6,2)$, and a quad in the card game corresponds to a plane in $AG(6,2)$. An interesting puzzle is to consider what the largest number of quads is that we can possibly pack into a specified number of cards/points, if we are allowed to choose them however we wish. In this talk, we will explain the rules and geometric underpinnings of EvenQuads, and describe some current work and open questions about quad-packing.

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1. Practical AI

Some AI solutions to a math professor's problems — Nick Kirby <kirbyn@apsu.edu>

The use of AI in the professor's office can be a source of great fun or great aggravation. This presentation shares specific, prosaic problems that were solved well by generative AI. In particular, we will explore three distinct success stories: 1. Administrative efficiency: building LaTeX files for class notes; 2. Assessment design: using AI to generate diverse, standards-aligned exam questions; and 3. Programmatic visualization: using AI-assisted coding to build Mathematica animations of poles of Padé approximants. The presentation will also candidly address the dead ends of generative AI, discussing failed attempts at posing research-level open problems and the frustrations of iterative assignment design.

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1. Practical AI

Standards-Based Grading: First Day Activities to Promote Student Buy-In — Rachel Epstein <rachel.epstein@gcsu.edu>

Standards-Based Grading (SBG) has many potential benefits for students, since it gives them multiple opportunities to demonstrate their understanding and doesn’t penalize taking longer to learn something. However, since most students have only experienced points-based grading in math courses, they are often wary of and confused by SBG. In this presentation, I’ll discuss how I introduce SBG on the first day of class, using small group discussions to help them identify issues with traditional grading and understand the benefits of SBG. This presentation is intended to be useful both for those already using SBG and those interested in learning more about it.

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1. Recreational

Tangles and computational algebraic geometry — Doug Torrance <dtorrance@piedmont.edu>

A simple closed space curve that is comprised of quarter circles of fixed curvature with continuous tangents is known as a Tangle, after the popular fidget toy. We show that all Tangles of a given length n (or n-Tangles) correspond to the solutions of a particular system of polynomial equations. Using the software platform Macaulay2, we prove the nonexistence of 5-Tangles and describe all 6-Tangles.

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1. Spoon!

Tennenbaum's Spoon — Jake Mealey <mmealey@vols.utk.edu>

Mathematician Stanley Tennenbaum demonstrated a geometric proof of the irrationality of the square root of 2 in the 1950s using a lesser known theorem called Carpets Theorem. Using a “spoon”, I plan to show Tennenbaum’s proof in an easy to understand light. However, to avoid steering away from the more mathematical aspects of such a proof, I will show the core algebra and math as well. Both of these points of view will be viewed from a geometric lens just as Stanley Tennenbaum did.

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1. Practical AI

Using AI to Enhance Mathematics Classes and Departmental Functions — Julie Barnes <jbarnes@email.wcu.edu>

As teachers, we are always looking for ways to work smarter, not harder, and AI can assist with that.  In this talk, we look at a collection of ideas from AI used in calculus and introduction to proof classes.  These ideas include some nuts and bolts topics like creating review sheets with solutions, writing creative word problems with useful diagrams, and generating a large collection of possible exam questions to choose from.  We will also look at some more artistic ideas, like developing an image for the class's Canvas tile, generating playing cards about historical mathematicians, and creating a slide show about departmental graduates.  

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1. Teaching Logic

Using Authentic and AI-Generated Debate to Teach Logic and Argumentation — Andrew Miller <andrew.miller@belmont.edu>

At Belmont University, our Global Honors Program curriculum includes a Mathematical Inquiry Seminar as the only required mathematics course for students in this program. Since its inception, this course has included a unit on logic, argumentation, and critical thinking. We share recent course activities that attempt to bridge the gap between mathematical approaches to logic and real-world argument analysis. These include discussing authentic debates hosted by the nonpartisan, nonprofit organization Open to Debate and arguments created with the assistance of generative AI tools.

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1. AI-Resistant

Using Oral Exams to Enhance Conceptual Understanding — Chris Cyr <chris.cyr@covenant.edu>

It is often said that the best way to understand something is to try to explain it to someone else. Based on this, would asking our students to explain important course concepts in their own words be an effective learning technique? To test this hypothesis, a few years ago I introduced oral exams as an alternative assessment method in some of my upper-division courses. In this talk, I will describe how I conduct oral exams in my Real Analysis and Abstract Algebra courses, giving examples of the types of questions I ask, criteria for evaluation, strategies for alleviating student anxiety, and some benefits of assessing students using this method.

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1. Teaching Logic

Using Specifications Grading in a Transition Math Course. — Jeff Hildebrand <jhildebr@ggc.edu>

A course to introduce mathematics majors to upper level mathematics courses requires the students to develop familiarity with and the ability to use many mathematical tools. Because of this, the course lends itself to the use of specifications grading. This talk will discuss one attempt to implement this method of grading and describes some of the benefits and the drawbacks found will teaching the courses with this approach.

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1. AI-Resistant

Visual Algebra, Intro to Proofs, and other AI-resistant upper-division math courses — Matthew Macauley <mattmacauley@gmail.com>

Before AI, my students submitted weekly homework sets written by hand. Today, they use LaTeX to write and typeset their own professional-looking textbooks. Somewhat ironically, the emergence of AI has helped them strengthen, rather than weaken, their mathematical writing skills. I'll tell you all about this, and more. If time permits, I will show you how I have AI-proofed my abstract algebra class by infusing hundreds of visual elements, along with feedback from former students who have gone on to PhD programs. For those unable to attend, additional details and materials are available on my course webpages.

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1. Spoon!

When are Two Polygons Fold-Congruent? — Elena Ruiz <ellie.c.ruiz@gmail.com>

Hilbert's Third Problem, presented in 1900, asked: given two polyhedra of equal volume, are they scissors-congruent? That is, can one always be cut into a finite number of pieces and be reassembled into the other? In two dimensions, it is clear that two polygons have equal area if they are scissors congruent, but the converse was proved in 1807. The parallels between flat origami and polygonal decomposition suggest a common framework, which motivates us to define a notion of fold-congruence. We pose the question: are two polygons of equal area always fold-congruent? In this talk, we discuss preliminary investigations into this seemingly difficult question.

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1. Recreational

Wreath Cards & Cube Rotations — Stephen Davis <stdavis@davidson.edu>

As part of her 2025 MAA-SE plenary talk, Catherine Hsu introduced cards that represented elements of the group $S_2\wr S_3$ for a game similar to SET. We call these cards *Wreath cards* and pull out the 24 cards (the $\mathcal{R}$ deck) that correspond to the group of rotations of a cube. We propose a ``game" to express a drawn card from the $\mathcal{R}$ deck as a product with factors chosen from three designated generators for $\mathcal{R}$. The player is also challenged to physically manipulate a cube to demonstrate the product.

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