Abstract for 22224

Loci of Equal Viewpoints for Two Ellipses

Author: Wei-Chi Yang

Affiliation: Radford University

In this presentation, we will talk about what A.I. can or cannot answer for the problems we discussed in this paper and related applications. We are given two ellipses, denoted by E₁ and E₂, respectively. Point A is outside these two ellipses. We draw tangents from A to the two curves, E₁ and E₂, respectively. The angle between these tangents is the angle we see these two ellipses at from point A. We investigate the locus of the set of all points where this angle is the same for both ellipses. The original locus problem discussed in this paper is simple, and the algebraic partial solution provided by most students in Section 1.2 is accessible but incomplete. It is indeed virtually impossible to study the locus problem without the help of a computer algebra system. The locus is invariant under the rigid transformations. We shall see how a uniform shear transformation will affect the locus discussed in this paper.

Abstract for 22237

Understanding Geometric Pattern and its Geometry, Part 13 – Tetradecagonal geometric patterns

Authors: Miroslaw Majewski

Affiliations: New York Institute of Technology, Abu Dhabi Campus

Abstract: Depending on the region, we may deal with geometric patterns constructed in geometries obtained from different regular polygons. Thus, we have hexagonal patterns created using the geometry of a regular hexagon, octagonal patterns created using the geometry of a regular octagon, decagonal patterns, and patterns in mixed symmetries – dodecagonal and hexagonal, or nonagonal. For example, in Istanbul and Edirne, we find a large group of Ottoman decagonal designs. In Mughal India, we deal with simple octagonal or hexagonal designs. At the same time, in Cairo, we will find patterns created on regular dodecagon as a main geometric shape.

Surprisingly, we find very few patterns based on the geometry of the regular tetradecagon (14 edges) and regular heptagon (7 edges). These patterns are found in several locations, ranging from Damascus to the Maghreb.

This paper aims to investigate how existing tetradecagonal patterns were created, construct tessellations used to develop these patterns and explore how traditional methods for octagonal and decagonal patterns can be extended to tetradecagonal designs

Abstract for 22146

Understanding Geometric Pattern and its Geometry Part 12 – Octagonal investigations

Authors: Miroslaw Majewski

Affiliations: New York Institute of Technology, Abu Dhabi Campus

This paper aims to show some basic examples of octagonal tessellations and patterns made with them. We will limit our investigations to a group of patterns with 90-degree intersections of lines. We will discuss the ‘square side and diagonal’ ratio and its use in architectural adornments.

Abstract for 22244

Developing Continuous Families of Monohedral Spherical Tilings with GeoGebra: Mathematical Theory and Educational Practice

Authors: Ana Maria Breda, José Manuel Dos Santos

Affiliations: Department of Mathematics, Faculty of Sciences and Technologies, University of Coimbra;, Centre for Research and Innovation in Education (inED), Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal Center for Research and Development in Mathematics and Applications (CIDMA), Aveiro, Portugal

This article examines the generation of continuous families of monohedral spherical tilings and shows how dynamic geometry and computer-algebra tools support both the mathematical analysis and pedagogical use of these constructions. Three continuous families are derived from a seed in GeoGebra and verified algebraic methods. Real-time orbit generation under SO(3) isometries. Symbolic expressions for arc lengths, vertex valences, and rotation matrices, provides formal proof of congruence for each parameter value. The families interpolate between established discrete tilings, extend current catalogues and offer candidate spherical designs, suggesting unresolved questions when seeds of lower symmetry or reflections are considered. Pedagogically, the same workflow enables learners and prospective teachers to vary a single parameter and observe systematic changes in polygon shape, symmetry and convexity. Stereographic projection links spherical constructions to planar graphs, furnishing tasks suitable for non-Euclidean geometry modules and technology-rich teacher education. Reported studies indicate improvements in spatial reasoning, deductive argument, and learner engagement when dynamic tools support such content. The investigation, therefore, contributes new material to tiling theory and a reproducible protocol for classroom practice. Future research examines spectral and combinatorial invariants, and undertake longitudinal classroom trials to evaluate curricular impact.

Abstract for 22248

Pedal curves of conics:a tale of cubics, sextics, octics and more

Authors: Noah (Thierry) Dana-Picard

Affiliations: Jerusalem College of Technology

Constructions and exploration of plane algebraic curves have received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. This push revived the study of classical plane curves, together with the discovery of new interesting curves. Here, we use automated methods to explore pedal curves of conics. This exploration provides constructions of interesting geometric loci, given at first by parametric representations. Implicitization is then an important process which uses strong algebraic machinery. Its output is the discovery that the pedal curves under study are sextics, octics and other curves of higher degree. We explore their irreducibility and their singular points (crunodes, cusps, etc.).

Abstract for 22258

Mathematics Education in the Age of AI: Challenges and Prospects for Secondary Teachers in Japan

Authors: Hideyo MAKISHITA, Tadashi SHIBATSUJI, Mahiko TAKAMURA

Affiliations: Yamato University, Shibaura Institute of Technology, Kashiwa Junior & Senior High School, Tokyo Polytechnic University

The rapid evolution of generative artificial intelligence (AI) technologies—such as ChatGPT, Claude, and Gemini—has begun to reshape how mathematics is taught and learned. In Japan, the secondary mathematics curriculum and teaching practices face growing pressure to shift from transmission-based instruction to inquiry-oriented, technology-integrated learning environments. This paper explores how Japanese middle and high school mathematics teachers can prepare for this transformation. Key areas of focus include lesson redesign, the development of AI literacy, the integration of AI into inquiry-based learning, and the redefinition of assessment practices. By positioning AI as a partner in mathematical thinking rather than solely as a computational tool, we argue that mathematics education can become more meaningful and creative in the age of AI.

Abstract for 22263

New Results About Semi-Regular Polygons Circumscribed Around A Given Ellipse

Authors: Jean-Jacques Dahan

Affiliations: IRES of Toulouse

In this article, we focus on the class of polygons we previously referred to as semi-regular, which are more commonly known as equiangular polygons circumscribed about a given ellipse. In our earlier work, we formulated a large number of conjectures concerning the variations in the areas of these polygons for all values of n (where n denotes the number of sides), in connection with the behavior of certain relatively complex functions. This article presents the current state of my research aimed at establishing those conjectures in the general case. I provide complete proofs for the conjectured results when n=3, 4 and 6 while the case n=5 has so far resisted various lines of attack. The investigation, still largely conducted through experimental exploration using dynamic geometry software, has also led to the discovery of several surprising additional results, some of which have been proven, while others remain conjectural and await proof. This research is far from complete, as it explores a domain that appears not to have been previously studied. This article highlights, among other things, the crucial role of technology-mediated experimentation in the process of discovery.

Abstract for 22266

Mathematics Teachers’ Perceptions and Practice of Computational Thinking

Authors: Keng Cheng Ang, Marc Yi Fei Yeo

Affiliations: Nanyang Technological University, 1 Nanyang Walk, Singapore 637616

Assessing mathematics teachers’ readiness for CT instruction requires an understanding of their CT beliefs, which is inadequately addressed in the literature. The current study fills this gap by examining (i) Singapore mathematics teachers’ CT beliefs and conception of CT within mathematics pedagogy, (ii) ways which this conception impacts their teaching practices, and (iii) challenges they encounter in incorporating CT in mathematics instruction. The analysis of survey and interview data collected from in-service Singapore mathematics teachers revealed three main findings: firstly, pedagogy-related beliefs that (i) CT is beneficial for pedagogy, (ii) CT constitutes teachers’ existing teaching practices, and (iii) CT is necessary/important for pedagogy; secondly, teachers generally have a limited conception of CT practices and their pedagogical implementation in mathematics lessons; lastly, teachers affirm that CT competence, designing CT lessons, and employing CT pedagogies are challenges in CT integration while also identifying other obstacles and possible solutions for these. This study therefore is an attempt to form an assessment of CT instruction among Singapore mathematics teachers, identifying gaps in CT expertise and obstacles that can be addressed as well as existing practices and beliefs that can be harnessed to facilitate CT pedagogy within a mathematics classroom.

Abstract for 22282

Using Technology to Develop Inquiry-Based Mathematics Teaching Models

Authors: YUAN YUAN

Affiliations: National Taichung University of Education

This paper explores two models of applying technology to mathematical inquiry. The first model is teacher-guided, aiming to assist students in discovering and understanding mathematics through model-based learning. The second model adopts a student-centered perspective, where learners actively construct problem situations to explore mathematical concepts. Both models have been shown to enhance students’ mathematical learning effectively. Moreover, using digital tools, students can deepen their understanding of mathematical problems. In traditional mathematics classrooms, instructional approaches often present solutions too quickly, leaving students disengaged from the problem context and missing the joy of mathematical exploration. Integrating technological tools into mathematical inquiry can help students apply mathematical concepts, develop computational thinking, and utilize powerful technological functions to explore and solve complex and unfamiliar mathematical problems.

Abstract for 22303

Geometric Proofs in Education: Integrating Digital Tools for Innovative Teaching Practices

Authors: Vanda Santos

Affiliations: Research Centre on Didactics and Technology in the Education of Trainers, University of Aveiro, Portugal, Centre for Informatics and Systems of the University of Coimbra

Mathematical proof constitutes a fundamental logical structure for validating propositions and holds a central place in mathematics education. In the field of geometry, it takes on particular importance by fostering the development of deductive reasoning, argumentation, and conceptual understanding. Recognized as a key area of the curriculum, geometry significantly contributes to the development of logical-spatial thinking and the ability to solve real-world problems.

Within this framework, dynamic geometry systems enable the exploration of geometric properties in a visual and interactive way, facilitating the formulation and validation of conjectures by students. As an example, an activity is proposed in which students use digital tools to construct figures, identify patterns, formulate conjectures, and apply inference rules with the aim of demonstrating geometric properties - thus promoting an active, meaningful approach to learning geometric proof, in line with mathematical reasoning

principles.

Abstract for 22318

Geometrical reasoning through open-ended tasks in a Dynamic Geometry Environment: An analysis through the lens of Variation Theory

Authors: Jonaki Ghosh

Affiliations: Lady Shri Ram College, Delhi University

In this article, we present the Buried Treasure Problem as a carefully designed exploratory task in dynamic geometry, aimed at supporting students’ transition from geometric exploration to formal proof. Framed within the principles of the Theory of Variation, the task invites grade 9 learners to investigate a geometric marvel using the Dynamic Geometry Environment (DGE), GeoGebra. Marton’s Variation theory is used as an epistemic lens to highlight how the four patterns of variation - contrast, separation, generalisation, and fusion are used to interpret dragging activities and to guide learners to notice invariants amidst variation. By systematically varying elements of the buried treasure problem such as landmark positions, turn directions, and step lengths, students were guided to discern critical mathematical features, such as, midpoint constancy, congruency and properties of quadrilaterals, that remain invariant despite changes in the configuration. The design of the task employs key variation patterns to draw learners’ attention to underlying structures essential for deductive reasoning. The article illustrates how such variation-informed design can support students in recognizing invariant properties, making conjectures and eventually formulating proofs, thereby bridging intuitive exploration with formal geometric argumentation in DGE. The findings of the study provide insight into the nature of tasks that are appropriate for a DGE environment, which can be “triggers” for proof and extends the notion of variation-invariant duality as a theoretical basis for DGE task design.

Abstract for 22333

Decreasing nature of a certain function related to the Steiner’s inellipse

Authors: Kia Keng Giam, Weng Kin Ho, Jean-Jacques Dahan

Affiliations: National Institute of Education, Temasek Junior College, Singapore, IRES of Toulouse, Paul Sabatier University, Toulouse, France

This paper answers an open problem proposed by Jean-Jacques Dahan in his ATCM 2024 paper, asking for a formal proof that the function $f(x)=\sum_{k=0}^2 \sqrt{1-c^2 \sin^2 \left(x+\frac{2k\pi}{3}\right)}$, where $c$ is a constant in $[0,1]$, is decreasing on the interval $\left[0, \frac{\pi}{6}\right]$. Crucially, we employ a CAS (Computer Algebra System) and some basic inequalities to yield the proof. In passing, we take note of some salient pedagogical lessons gleaned from this cross-generational collaborative research.

Abstract for 22335

Arbitrary precision numerical methods with online computation

Authors: Alasdair McAndrew

Affiliations: Victoria University, Melbourne, Australia

Texts on numerical methods usually present the same sets of methods: for solving equations there are a few bracketing methods, then the secant and Newton’s method; for integration we have the Newton-Cotes rules, maybe Romberg integration, possibly Gaussian integration, and a couple of others. There are, however, many more methods than these, often just as simple, but with faster convergence. It is hard, however, to demonstrate to students--- particularly pre-service teachers---the power of these methods when using only limited precision arithmetic, which is all that is available on their standard tools. Experiments with the software Pari/GP and high precision provided powerful evidence of the speed of convergence, in a way that theoretical discussions could never manage. The students thus experienced some profound mathematics from an experimental and experiential perspective. This article explores some of those methods, as well as several others, in an invitation to experimental mathematics.

Abstract for 22347

Using Block Frequencies to Break Hill Ciphers

Authors: Brian Douville, Rick Klima, Neil Sigmon

Affiliations: Appalachian State University, Radford University

This paper focuses on the breaking of Hill ciphers, a classical encryption method rooted in linear algebra, without knowledge of the key. We will explore the challenges associated with breaking Hill ciphers, and introduce a pragmatic method employing frequency analysis of letter combinations. The initial phase provides a theoretical foundation for breaking ciphers, emphasizing challenges and mathematical complexity specific to Hill ciphers. We introduce a Maplet that uses frequency analysis of letter combinations, and demonstrate its effectiveness in decrypting messages without a known key. The results highlight the method’s effectiveness and unveil vulnerabilities within Hill ciphers. The work also adds a creative perspective to the exploration of cryptanalysis without explicit key knowledge, offering practical insights into breaking classical encryption techniques. This project represents progress in decrypting classical ciphers and creates different methods for imaginative approaches to encryption challenges. The findings provide a basis for further exploration into keyless decryption techniques, fostering creativity in the field of cryptanalysis.

Abstract for 22348

A Fundamental Examination of the Determinants of Inquiry-based Learning Attitudes Across Subject Differences between Mathematics and Other Subjects

Authors: Masanori Fukui, Atsushi Tamura, Tadashi Takahashi, Yudai Sano, Yoon Fah Lay, Eng Tek Ong

Affiliations: Department of Information Engineering, Graduate School of Engineering, Mie University, Iwate Prefectural University, Japam, Hagoromo University of International Studies, Japan, Tokushima University, Japan, Universiti Malaysia Sabah, Malaysia, UCSI University, Malaysia

Inquiry-based learning (IBL) is widely regarded as a key pedagogical approach for fostering 21st-century skills. However, the extent to which subject specialization and ICT competencies shape teachers’ attitudes and implementation of IBL remain unclear. This study surveyed 611 elementary, middle, and high school teachers in Japan, categorized into mathematics and non-mathematics groups. We examined three dimensions of IBL attitudes (perceptions, instructional confidence, and perceived importance), four ICT skill factors (lesson preparation, in-class use, student guidance, and ICT ethics), years of IBL instruction, and overall teaching experience. Welch’s t-tests revealed no significant differences between the two groups in IBL attitudes or ICT competencies. Multiple regression analysis showed that classroom-oriented ICT skills (in-class use, student guidance) and prior experience in IBL were significant positive predictors of IBL attitudes. In contrast, lesson preparation skills were negatively associated with confidence and perceived importance. These findings suggest that real-time, student-centered ICT integration and hands-on IBL experience play a more critical role than subject expertise in shaping teachers’ readiness and receptiveness to implement IBL. Implications for professional development are discussed.

Abstract for 22355

AI helps solve educational problems

Authors: VLADIMIR NODELMAN

Affiliations: Holon Institute of Technology

In the author’s previous works, an optimal (minimal and sufficient) system of types of tasks and teaching methods was proposed, based on the analysis of the logical structure of the concepts being studied. This made it possible, with the help of software, to organize a controlled process of materialized mental actions aimed at mastering concepts.

The specific tasks of these types—which are linked to the particular content of the concepts—were previously proposed to be formulated by teachers themselves. Currently, it has become possible to entrust the formulation and presentation of these specific tasks to AI. The report presents the mechanism of an autonomous application that achieves this goal through internal interaction with AI, with corresponding examples. In addition, the possibilities of using AI to realize fundamental pedagogical ideas—which until now could not be implemented—are discussed.

Abstract for 22361

ChatGPT and AI Enhancing Undergrad Math

Authors: Matthias Kawski

Affiliations: Arizona State University

Generative Artificial Intelligence (AI) systems such as ChatGPT, built on large language models (LLMs), present both challenges and opportunities for teaching and learning mathematics. Although not originally designed for logical reasoning or formal proof-writing, these models are increasingly capable of generating plausible drafts of mathematical arguments.

We briefly discuss the surprising successes of generative AI at the International Mathematical Olympiad, as well as more well-established systems that can validate and certify formal proofs. Our primary focus is on mid-level undergraduate courses, particularly those introducing students to formal proof writing and introductory analysis of functions of a real variable.

Within this context, we examine the capabilities and notable limitations of LLMs. Far from being a hindrance, the logical missteps frequently made by these models, ranging from minor inaccuracies to fundamentally flawed strategies, can be powerful tools in an inquiry-based classroom. Students are often more engaged when critiquing imperfect AI-generated arguments than when critiquing drafts written by their peers, making these tools uniquely effective for fostering critical thinking and proof literacy.

Abstract for 22369

Generative AI in teaching mathematics: Implications, affordances and challenges

Authors: Greg Oates

Affiliations: The University of Tasmania

With the advent of OpenAI, Generative AI (GenAI) has certainly taken the world by storm. To date, much of the debate around its use is reminiscent of the debates around calculators, in the arguments for and against, and how it might best be used. This paper serves as a provocation in posing questions we should be asking about the future impact of AI, with a principal focus on what mathematical content and skills we believe our students should be learning in a world where AI is going to continue to develop. Indeed, what might our role as teachers be in such a world? Given how rapidly GenAI is developing, it is impossible to draw a line in the sand; nevertheless, this argues we should be thinking about the future, and how agile we must be in our own professional learning and curriculum development, in meeting constantly changing imperatives for learning.

Abstract for 22370

Fostering Creativity in Mathematics Education through Technology-Enhanced STEAM Innovations

Authors: Zsolt Lavicza

Affiliations: Johannes Kepler University, University of Cambridge, International GeoGebra Institute, Budapest Metropolitan University

This presentation examines recent technological and pedagogical advancements in STEAM education, with a particular focus on how innovative tools can enhance mathematics teaching and foster creative thinking. I will highlight new directions in STEAM-related research that integrate mathematics with other subject domains through technology-driven and AI-supported approaches. Key collaborative initiatives include partnerships with the JKU STEAM Education Research Lab and GeoGebra, which showcase emerging technologies such as Augmented and Virtual Reality applications, 3D Printing, Machine Learning, and Mobile-based experiments. These tools—particularly 3D technologies—play a transformative role in deepening mathematical understanding, strengthening spatial reasoning, and bridging the gap between digital and physical learning environments. Furthermore, Artificial Intelligence is now at the forefront of this transformation, offering unprecedented possibilities for personalised, engaging, and data-informed mathematics education. Our Research Lab at JKU explores how AI-powered systems can analyse learner interactions in real time, providing adaptive assessment, automated feedback, and dynamically tailored learning pathways. Such capabilities allow educators to respond to individual learning needs, identify misconceptions early, and foster problem-solving and creative thinking skills more effectively. AI can also support teachers by automating routine tasks, generating customised practice materials, and recommending targeted interventions based on Big Data analytics. In addition to these topics, we will explore how large-scale data from AI-enhanced platforms related to our teacher education projects can be harnessed to identify and cultivate creative thinking processes in mathematics teachers and students, enabling researchers to better understand how creativity develops in technology-rich learning contexts. By combining creativity, AI, and various technologies within sound pedagogical frameworks, these approaches provide powerful opportunities for innovation, collaboration, and transformative impact in mathematics education and the broader STEAM landscape.

Abstract for 22372

Competence-based problems in Mathematics: How to design (and grade) them?

Authors: Jose A Vallejo

Affiliations: Universidad Nacional de Educación a Distancia

Competency-based mathematics is an educational approach that focuses on ensuring students master specific mathematical skills and concepts before moving on to more advanced material. As the focus is not just on memorization, but on understanding how mathematical concepts are used to solve real-life problems, an important part in any course is the set of problems offered to students to work with. In this talk, I will comment on the design of such problems, and the difficulties typically found in grading student’s responses.

Abstract for 22388

Math Meets Play: The Design of a Serious Game in Calculus in the Philippines

Authors: Ma. Louise Antonette De Las Penas, Debbie Marie Verzosa, Maria Alva Aberin, Mark Anthony Tolentino, Mark Loyola, Juan Carlo Mallari

Affiliations: Ateneo de Manila University, University of Southern Mindanao

The creation of serious games for teaching and learning tertiary level mathematics is a creative technological innovation that supports active learning among students, intended to develop their skills associated with content knowledge and to make them more capable and relevant as 21st century professionals. This talk presents a serious game focusing on important concepts in Calculus. Sound, research-based pedagogical frameworks in mathematics and gamification design elements incorporated into the game will be discussed, which will enable students to grasp the essential concepts in calculus that facilitate perseverance, higher retention of the subject matter, and improved grading marks. The storyline, set-in modern-day Philippines, and the various characters that will be bring the game to life will be introduced to the audience. Initial results of the testing of the game, conducted for faculty and students, will be presented.

Abstract for 31001

Insights for Creating Effective Mathematical Figures

Author: Douglas Meade

Affiliation: University of South Carolina, USA

While it is true that "a picture is worth a thousand words", which thousand words? Is the picture mathematically correct? Does it provide insight? Does it motivate additional thoughts? Does the picture make a statement, or does it start a discussion? These are some of the questions that will be addressed and discussed in this presentation. Examples of both good and bad mathematical figures. Attention will also be spent discussing how to help our students become better mathematical artists.

Abstract for 31002

My Dream of a Geometric Museum

Author: Jen-Chung Chuan, video produced by Ming-Yuan Chuan

Affiliation: National Tsing Hua University, Taiwan

Part 1: Kaleidocycles

Seg 1 Oral Introduction

Seg 2 Minimal Kaleidocycle formed by 6 tetrahedra

Seg 3 Minimal Kaleidocycle formed by 8 tetrahedra

Seg 4 Minimal Kaleidocycle formed by 12 tetrahedra

Seg 5 Kaleidocycle formed by 8 regular tetrahedra

Seg 6 Kaleidocycle formed by 8 truncated tetrahedra

Seg 7 Kaleidocycle formed by 8 Elongated gyrobifastigum

Seg 8 Kaleidocycle formed by by 12 tetrahedra

Seg 9  Kaleidocycle formed by 6 tetrahedra and 6 Triakis tetrahedra

Seg 10 Kaleidocycle formed by 8 Gyrobifastigum

Seg 11 Kaleidocycle formed by 10 tetrahedra, the most well-known

Seg 12 Kaleidocycle formed by 10 Schmidt-Conway Biprism

Seg 13 Elongated Gyrobifastifigium

Seg 14  16 non-regular Dodecahedrons

Seg 15  Kaleidocycle formed by 32 disks

Part 2: Villarceau Circles

Seg 1 Euler’s Disk

Seg 2 Display of Christmas Lighting (1) 12 Villarceau Circles

Seg 3 Display of Christmas Lighting (2) 12 Villarceau Circles

Seg 4 Hoola Hoop

Seg 5 Villarceau Circles sweeping 180 degrees w.r.t. the axis of the torus forming one-sided surface

Seg: 6 Same as above with 180 Villarreal circles

Seg 7 Same as above

Seg 8 Three Moebius Bands each enclosing the other two

Seg 9 Three Torus formed by 180 tubes, each enclosing the other two

Seg 10 Three Moebius Bands each enclosing the other two

Seg 11 Three Kaleicycles each formed by 16 tetrahedra, each rotating by itself and yet mutually disjoint  and enclosing the other two.

Abstract for 31003

"AI in Mathematics Education: Tool, Teacher, or Troublemaker?"

Authors: Russel Carlson, Matthias Kawski, Greg Oates

Affiliations: BYU-Hawaii, Arizona State University, University of Tasmania, Tasmania

Panel Abstract

As generative AI continues to reshape the educational landscape, mathematics educators face many challenges, including the following: distinguishing between AI as a tool for doing mathematics and AI as a partner in teaching and learning mathematics. This panel brings together three perspectives that explore the evolving role of AI in mathematics education—from its potential to generate mathematical arguments and proofs, to its limitations and ethical implications for curriculum design. Panelists will examine how AI can provoke deeper student engagement, support critical thinking, and simultaneously disrupt traditional learning pathways. The session will also consider the professional agility required of educators as AI capabilities expand, and how understanding its limitations can inform more effective teaching strategies.

Audience Question:

In a world where AI can increasingly “do” mathematics, what do you believe is the enduring value of learning to think mathematically—and how should that shape our teaching?

Abstract for 22285

Pedagogical Approaches to Visualizing Complex Roots of Polynomial Equations

Authors: Jun YAMADA

Affiliations: Aichi Prefectural Tsushima High School

In this paper, we discuss how, with the realization of the GIGA School Initiative, ICT environments are being developed, and tablet devices are becoming more widespread in high schools, leading to a steady increase in arithmetic and mathematics classes that utilize these technologies. Here, we consider the visualization of the solution to the Bombelli equation, x^3-3px-2q=0 (p and q are real numbers), as a visualization teaching material that uses ICT. We confirmed that by using ICT (GeoGebra, Python), it is possible to visualize the complex solution to a cubic equation in three dimensions. By visualizing complex numbers, which must be considered in four dimensions, in three-dimensional space, it becomes possible to view complex numbers from a different perspective, and we believe this will be an effective teaching method for presenting teaching materials and developing lessons.

Abstract for 22230

Fair Generator Allocation via Equitable Coloring of the Cartesian Product of Pan and Path Graphs

Authors: Merliza Libao, Royce Grecie Acaso

Affiliations: Caraga State University

In many parts of the Philippines, intermittent power supply forces office managers to switch to portable generators during brownouts. We model an office floor as m contiguous segments (vertices of a path P_m), each segment hosting n lamps arranged in an n-pan (a cycle C_n with a pendant). The Cartesian product n-pan □ P_m then represents every lamp on the floor. We seek an equitable k-coloring of this graph so that: No two adjacent lamps draw power from the same generator, and each generator serves almost the same number of lamps. After establishing that X_= (n-pan)={■(2, n even,@3, n odd,)┤we prove constructively that for every m≥2

X_= (n-pan □P_m )=X_= (n-pan)

Our layer-shift method “lifts” any equitable coloring of the n-pan into one of the products by cyclically incrementing color indices along each path layer. A detailed parity-case analysis (for n (mod  3)) ensures the size-balance condition holds in every layer. We supplement the theory with static diagrams and classroom-ready animations generated via open-source Python to help educators demonstrate how equitable graph coloring can inform fair generator scheduling under fluctuating power conditions.

Abstract for 22234

Senior Mathematics Delivered Online

Authors: Narelle Morris

Affiliations: FisherONE

This session will be devoted to discussing the success of delivering Senior Mathematics online to students in Queensland, Australia through FisherONE.

FisherONE evolved with global trends to create an innovative solution to provide high-quality, accessible education for Senior students across Queensland, with subjects unavailable at their current school. A unique offering made possible by dedicated staff, FisherONE is a community with values such as building an inclusive future, ensuring all students have access to equitable learning opportunities.

In 2024, my first cohort of Year 12 students achieved results well above the state average.

Why is it successful?

Why do the students engage with it?

How do we use technology in our delivery?

What technology do we use?

Brisbane Catholic Education is the first to embrace Microsoft CoPilot in any school system across the world.

How do we embrace and utilise AI?

The future of schooling in Australia will also be addressed.

Abstract for 22235

“SkillForge”: An Integrative, AI-Driven Game-Based Learning System for IT Beginners

Authors: Ovinda Teran Withanage

Affiliations: sliit university

SkillForge is an intelligent, game-based learning platform designed to accelerate IT skill development for beginners through AI-powered adaptive learning, real-time feedback, and community-driven support. The system integrates multiple advanced components, including Transformer-based logical error detection, NLP-based explanation generation, and reinforcement learning for dynamic question adaptation. It features modules for interactive code debugging, intelligent interview preparation, and machine learning-based peer matching using clustering and Graph Neural Networks. With its personalized and scalable learning approach, SkillForge addresses challenges in traditional IT education by providing engaging, tailored experiences suitable for self-learners, academic environments, and corporate training. The platform’s preliminary evaluations demonstrate improved learner engagement, error correction accuracy, and skill acquisition, highlighting its potential to revolutionize digital IT education for novices.

Abstract for 22254

On Determining Integer or Rational Points on Cubic Curves and Surfaces Using Some Form of Infinite Continued Radicals

Authors: Ric Jr Tura, Orville Buelban

Affiliations: Ateneo de Davao University, N/A

A plane algebraic curve (surface) is a set of points in a plane (3-space) that satisfy a polynomial equation in two variables (three variables) of the form $\displaystyle f(x,y)=0$ ($\displaystyle f(x,y,z)=0$). If the polynomial $f(x,y)$ or $f(x,y,z)$ is degree three, then the polynomial equation $f(x,y)=0$ defines a cubic curve and $f(x,y,z)=0$ defines a cubic surface. This paper aims to introduce some form of infinite continued radicals such as $\displaystyle \sqrt{p \pm \frac{q}{\sqrt{p \pm \frac{q}{\sqrt{p \pm ._{._.}}}}}}$ and to establish convergence in $\R$ or in $\C$. In addition, the paper aims to establish properties of these infinite continued radicals that can be used as as tools for investigating rational or integral points on certain cubic curves such as the Mordell curve $\displaystyle y^2=x^3-k$, elliptic curve $\displaystyle y^2=x^3+px+q$, cubic surfaces of the form $\displaystyle ax^2+by^2=z^2$ and $\displaystyle y^3=x^3+px-qz^2$, etc. In particular, one of the results in this paper shows that the given Mordell curve $\displaystyle y^2=x^3-k$ has an integral point whenever the infinite continue radical $\displaystyle I=\sqrt{3 \pm \frac{k-2}{\sqrt{3 \pm \frac{k-2}{\sqrt{3 \pm ._{._.}}}}}}$ converges to an integer.

Abstract for 22257

Mathematical Method for Estimating Earthquake Epicenters from Intensity Observations

Authors: Ric Jr Tura

Affiliations: Ateneo de Davao University, N/A

Historical earthquakes, occurring before the use of modern seismometers, are essential to understanding long-term seismic risk. However, estimating their epicenters remains challenging due to the lack of measured instrumental data. In contrast to methods (e.g., Bautista & Oike, 2000) that rely on tectonic structures and generalized isoseismal maps, this project presents a mathematical approach that uses intensity reports alone, which can be interpreted from historical data.

The method estimates epicenters by fitting best-fit circles to locations reporting the same intensity and applying statistical techniques to locate the most probable epicenter. It also quantifies uncertainty, providing an interval within which the epicenter likely lies. A Python-based program was developed to facilitate this, allowing users to input intensity data and visualize the estimated epicenter on a map. The method was tested using intensity data from recent Philippine earthquakes published in PHIVOLCS primers to evaluate accuracy. Results showed promising alignment with known epicenter locations, suggesting the method’s reliability.

This tool offers potential for reinterpreting historical earthquakes, supporting the development of improved hazard maps, and aiding historical seismology research. Ongoing work includes applying the method to historical events, especially in the Philippine context, and refining the algorithm for use.

Abstract for 22260

Data-Driven Reconstruction of Dynamical Systems with the Spectral Exterior Calculus

Authors: Joanna Slawinska, Dimitrios Giannakis

Affiliations: Department of Mathematics, Dartmouth College

In this talk, a data-driven framework will be introduced for the reconstruction and forecasting of dynamical systems on Riemannian manifolds, utilizing spectral exterior calculus to represent vector fields. In this approach, eigenvalues and eigenfunctions of the Laplace operator on smooth functions—approximated via the diffusion maps algorithm—are employed to build overcomplete bases, which act as generators for dynamical systems on the manifold. Through this method, vector fields are approximated as linear combinations of frame elements in L2 and Sobolev spaces, allowing data-driven vector field representations. Monte Carlo sampling is used to estimate vector fields from data points sampled on low-dimensional manifolds, such as the circle and 2-torus, providing flexibility for complex geometries. Initial-value predictions are then performed using these learned vector fields, and forecasted trajectories are compared to those of the true system, with accuracy and stability examined. Insights into the advantages and limitations of this data-driven approach for forecasting in dynamical systems will also be discussed.

Abstract for 22261

Optimal Control and Mathematical Modeling of Ebola Virus Transmission in Bat-Human Interactions

Authors: FAROUK SAAD

Affiliations: Northwest University, Kano

Extended Abstract

Ebola Virus Disease (EVD) is a highly virulent zoonotic infection, primarily maintained in bat populations and transmissible to humans through complex ecological pathways. This work presents a comprehensive mathematical model that captures the transmission dynamics of EVD involving bat and human populations, incorporating both direct contact and environmental contamination routes. The model comprises a system of nonlinear ordinary differential equations with eight compartments: susceptible, exposed, infected, and recovered classes for both bats and humans, alongside an environmental contamination compartment.

We analytically establish key model properties such as positivity, boundedness, and the existence and stability of equilibria. The basic reproduction number R_0 is computed using the next-generation matrix approach, and threshold conditions for disease eradication are derived. The local stability of the disease-free equilibrium is proven under the condition R_0<1.

To evaluate mitigation strategies, we incorporate five control functions representing culling of infected bats, environmental sanitation, human vaccination, quarantine of exposed humans, and treatment of infected individuals. Applying Pontryagin’s Maximum Principle, we derive necessary conditions for optimal control and characterize the corresponding adjoint system. The objective functional aims to minimize the total disease burden and associated intervention costs over a fixed period.

Numerical simulations demonstrate that implementing a combination of these control measures significantly reduces infection prevalence in both populations. Optimal strategies illustrate the effectiveness of targeted intervention timing and intensity, particularly when controls are applied simultaneously rather than in isolation. These results underscore the importance of coordinated efforts between animal and human health systems to curb zoonotic spillover and transmission.

This study contributes actionable insights for public health planning and disease control policy, particularly in regions with high bat–human interface and advances the mathematical understanding of zoonotic EVD dynamics.

Abstract for 22264

Generalized Entry Formula for Computing a Polynomial Resultant Matrix

Authors: Surajo Sulaiman

Affiliations: Northwest University Kano

In an elimination theory particularly using a matrix method to compute multivariate resultant. The goal is to derive or construct techniques thatare considerablee size. In this paper, the entry for computing n by n Dixon matrix was found and is free from any extraneous factor. The result of complexity analysis reveals a significant decrease in terms of the degree ofcomplexityy.

Abstract for 22265

Strong Proper Connection Number of Join of Graphs and Graphs containing Hamiltonian Path

Authors: LJ Twinkle Cagas, Analen Malnegro-Vidal

Affiliations: Ateneo de Davao Mathematics Society, Department of Mathematics, Ateneo de Davao University

A strongly proper path is any sub-path with at most three edges that are colored differently. An edge-colored graph is strongly proper connected if any two vertices are connected by at least one strongly proper path. The smallest number of colors needed for such a coloring of a graph G is called strong proper connection number spc(G) of G. In this paper, the authors presented the strong proper connection number of some special graphs, join of two graphs, and graphs containing Hamiltonian path. Moreover, some examples are provided to support the conjecture stating that every 3-connected graph satisfies spc(G) ≤ 3.

Abstract for 22268

Computational explorations in modern number theory: the Green–Tao theorem and the abc conjecture

Authors: Hiroyuki Chihara

Affiliations: University of the Ryukyus

We present a hands-on example of computational thinking at the intersection of mathematics and programming. Using the Julia programming language and its Pluto.jl notebook environment, we visualize exploratory computations inspired by two central themes in modern number theory: the Green–Tao theorem and the abc conjecture. By combining built-in primality tests with compact code written in Julia, Python, MATLAB, and Mathematica, we generate long arithmetic sequences of primes and enumerate abc-triplets with unusually small radical values. Our educational objective is to allow students to experience the scale and subtlety of modern number-theoretic phenomena through interactive and reproducible computation.

GitHub: https://github.com/fiomfd/ATCM2025

Abstract for 22337

When the Past Shapes the Predator: Memory Effects in Food Web Dynamics

Authors: ANUPAM PRIYADARSHI

Affiliations: Banaras Hindu University Varanasi India

Modeling complex species interactions in ecological communities requires frameworks that account not just for present dynamics but also for historical influences. Traditional integer-order differential equations, while widely used, often overlook these memory effects. In this seminar, we introduce a fractional-order intra-guild predation (IGP) model involving a basal prey, an intermediate predator, and a top predator, where Caputo fractional derivatives are used to incorporate long-term ecological memory. The model adopts Leslie-Gower and Holling type-II functional responses to reflect biologically realistic predation mechanisms. Through bifurcation and iso-spike analyses, we reveal that fractional-order systems exhibit a rich spectrum of dynamics—from stable points to chaos—shaped by the strength of memory. Lower fractional orders, representing stronger memory effects, tend to stabilize populations, while higher orders sustain complex oscillations. These findings demonstrate how fractional modeling not only captures ecological realism more effectively but also offers powerful tools for studying ecosystem stability and resilience.

Abstract for 22354

Explain the truth of the Pythagorean theorem in two-dimensional space through visualization tools

Authors: JIAMU XIANG

Affiliations: XICHENG ACADEMY BEIJING CHINA

The Pythagorean Theorem, which originated in ancient Greece, serves as a basic principle in fields such as architecture and computer graphics. It states that, the sum of the squares of the two right-angled sides is equal to the square of hypotenuse in a right triangle (as a² + b² = c²). The theorem also inspired the construction of Pythagoras'' Tree Fractal, a self-similar geometric structure formed by recursively adding squares to the legs of a right triangle. Plenty of research has been done about this theorem but these studies are limited to Euclidean geometry, lacking a visual exploration of fractal structures in hyperbolic geometry, this makes it abstract and over-theoretical for middle school students in China .

This paper, for the first time, using a visualization-based approach with “GeoGebra”, a common mathematical software in middle school, to construct a simplified Pythagoras tree in the Poincaré disk model, observing the difference between curved branches and Euclidean tree straight-line branching. Results clearly show how negative curvature in hyperbolic geometry transforms fractal structures and angular variation. Because of its negative curvature, hyperbolic geometry replaces straight lines with arcs, fundamentally altering the structure and appearance of fractals compared to their Euclidean counterparts. The results indicate that the Pythagorean theorem still holds in surface space, but its geometric representation has significant changes. The visualization method in this paper proposed in this research provides a straightforward viewpoint in high school mathematical instruction and makes students have an intuitive understanding of graphic changes. In addition, this study uses visualization methods to gain in-depth insights into the Pythagorean tree variations in two-dimensional hyperbolic geometry and potentially directs the application in fields such as computer graphics.

Abstract for 22356

Maintaining Assessment Integrity with Time-Limited, Concept-Focused STACK Quizzes in the Age of AI

Authors: Kentaro Yoshitomi

Affiliations: Osaka Metropolitan University

In the emerging era of coexistence with AI, many of the cheating-resistant question items previously developed using STACK are becoming increasingly unsuitable for use as formal assessments. This shift necessitates a more deliberate selection and application of problems according to their specific purposes. In particular, it is now essential to design assessment tasks that remain valid and meaningful in the presence of powerful AI tools.

This presentation introduces an approach that employs STACK-based, feedback-enabled multiple-choice questions within Moodle’s Quiz activity, administered under strict time constraints. The key design principle is to ensure that such questions can be answered more quickly and accurately by individuals with a deep understanding of definitions and concepts than by AI tools such as ChatGPT Pro. This is achieved by carefully crafting distractors, structuring questions to require nuanced conceptual reasoning, and leveraging STACK’s immediate feedback capabilities to guide student learning while preventing undue reliance on AI-generated solutions.

The proposed method serves a dual purpose: as a formative exercise, it provides students with targeted practice that strengthens their conceptual grasp and problem-solving agility; as an evaluative measure, it allows instructors to capture authentic indicators of student understanding under controlled conditions. The time constraint plays a crucial role in discouraging external consultation, while the feedback component enhances metacognitive awareness and facilitates error correction during practice phases.

Through the integration of these elements, the approach aims to increase both the effectiveness of student learning and the reliability of assessment outcomes in AI-pervasive environments. Case examples from actual university mathematics courses will be presented, illustrating the design process, the rationale behind question formats, and preliminary observations regarding student engagement and performance. These findings suggest that carefully structured, time-bound, feedback-rich quizzes can serve as a viable model for maintaining assessment integrity and pedagogical value in the AI era.

Abstract for 22365

AI Obstacles

Authors: Russel Carlson

Affiliations: BYU-Hawaii

Generative AI (like ChatGPT and other models) is improving by leaps and bounds. While it is a powerful tool, it has limitations that may seriously slow its future progress. One future limitation of these models is that they are running out of new material for training and will soon need to start bootstrapping. While bootstrapping as a principle is useful in certain statistical applications, it might cause AI improvement to plateau. This limitation also may hamper generative AI’s ability to generate new mathematical proofs.

On the other hand, understanding AI’s limitations may help teachers. Currently, teachers in all subjects are being challenged to redesign curriculum to avoid students using the power of generative AI to sidestep learning objectives. We will look at the limitations of generative AI, some attempts by programmers to get around them, and discuss what we, as teachers, might expect for AI’s impact on our students in the future.

Abstract for 22366

Numerical Linear Algebra: Innovative MATLAB Approaches for Merging Theory and Practical Computation

Authors: Jon Loftin, Mike Michailidis, Sepideh Stewart

Affiliations: The University of Oklahoma, MathWorks

The integration of MATLAB-based numerical exercises into linear algebra curricula serves as a powerful tool for enhancing students’ understanding. By combining theoretical concepts with hands-on computational techniques, learners can visualize and apply linear algebra principles in real-world scenarios. This approach not only fosters deeper comprehension but also prepares students for fields where practical application of linear algebra is essential, such as engineering, data science, and physics.

MATLAB offers a user-friendly computing environment that facilitates low- or no-code computing, thus allowing students to concentrate on the critical connection between abstract theory and concrete examples. By aligning exercises with pivotal topics—such as the resolution of linear systems, eigenvalues, orthogonality, condition numbers, and singular value decomposition—students acquire invaluable hands-on experience with MATLAB’s inherent functions, thereby deepening their conceptual comprehension. Furthermore, the implementation of scaffolded tasks, visualizations, and reflective inquiries encourages students to interpret numerical results through the lens of linear algebraic theory, cultivating both computational proficiency and theoretical insight.

This presentation will provide an overview of a newly developed course in numerical linear algebra, focusing on the application of computational techniques to reinforce theoretical principles for undergraduate and graduate students. Following the course, a research survey and interviews with students will be conducted. Throughout the course, we will monitor students’ engagement with linear algebra concepts, the integration of MATLAB, their ability to address real-world applications, their programming skills, and their utilization of AI tools. The design of the course, along with the research methodology, will be thoroughly discussed.

Abstract for 22373

Modelling the glucose-insulin regulatory system: A Mathematical Approach

Authors: Kalyan Das

Affiliations: National Institute of Food Technology Entrepreneurship and Management (Institute of National Importance, Govt. of India), Kundli, Sonepat, Haryana -131028, India., Plot No.97, Sector 56, HSIIDC Industrial Estate,

In this study we have constructed a mathematical model which proposes a novel method for controlling diabetes blood glucose levels in human body. In case of Type 1 Diabetes, we applied a novel mathematical model. The homeostasis which is related with endocrinal regulation of glucose and glycogen levels in the human body through insulin hormone and glucagon is incorporated through a therapeutically feasible mathematical model. Also plasma glucose concentrations, insulin hormone, and plasma insulin concentrations are considered in this model. Equilibrium points analysis of the model is discussed. Local stability of the proposed model has been analysed using Routh-Hurwitz criteria. Global steadiness is also investigated. The numerical solution predicts the difficult condition faced by diabetes patients. MATLAB is used to carry out numerical simulations for the analytical results. As diabetics is very sensitive disease which is highly interrelated with various organs of the human body, in this purpose we carried out computer simulations of various elements (attributes) of the human body in the window of sensitivity analysis.

Abstract for 22374

Integration using the RUBI software

Authors: David Jeffrey

Affiliations: University of Western Ontario

The system RUBI stands for "RUle Based Integration". This system was developed by Albert Rich, one of the authors of the Computer Algebra system "Derive". The RUBI system is in the public domain and can be downloaded freely. Albert worked on RUBI for 15 years, until his recent death. A community of supporters is now maintaining the system. In this talk I shall explain the way RUBI works and demonstrate some of the advantages it offers. I shall also describe work to increase the availability of RUBI on different software platforms.

Abstract for 22375

The Lambert W function turns 30 and continues to find applications

Authors: David Jeffrey

Affiliations: University of Western Ontario

The Lambert W function was named in 1996, and has now found applications in many areas of science. It is a popular subject of Youtube videos and student projects. The function W(z) obeys W*exp(W)=z and it obeys some beautiful equations and its numerical values can be obtained from computer systems such as Maple, Mathematica and other systems. This talk will describe some properties and some of the popular applications.

Abstract for 22379

HEARING FUNCTIONS: Using Sonified Graphs to Improve Students’ Interpretation of Functions

Authors: Samuel John Parreño

Affiliations: University of Mindanao

This study aimed to improve students’ understanding of functions, with emphasis on slope (increasing and decreasing behavior) and concavity. Hearing Functions is a brief classroom intervention that makes graphs audible through two mappings: Value→Pitch, where higher values correspond to higher notes, and Slope→Pitch, where faster change corresponds to higher pitch. The lesson was implemented in senior high school General Mathematics using a pretest, guided listening with think–pair–share prompts, and a posttest. Data sources included paper assessments, observation checklists, student exit slips, and short interviews. Findings indicate clearer discrimination between value and rate, more accurate sound-to-graph matching, and better recognition of concavity. Students reported concrete listening strategies and corrected the common misconception that pitch in the Slope→Pitch mapping represents height rather than rate. Teachers noted strong engagement and feasible delivery with minimal equipment. The approach aligns with multiple-representation pedagogy and offers a reusable routine that supports function interpretation and prepares learners for introductory calculus topics.

Abstract for 22381

The Factorial Prime Hybrid System: A Novel Framework for Number Representation and Computation

Authors: Jose Bernardo Bello

Affiliations: Holy Face of Jesus Lyceum of San Jose, Inc.

This study introduces the Factorial Prime Hybrid System (FPHS), a new numerical framework that merges factorial bases with prime factorization. FPHS encodes integers by integrating factorial growth with prime indexing, producing representations that differ fundamentally from positional or purely prime-based systems. The paper outlines the formal structure of FPHS, demonstrates its use through illustrative examples, and examines its initial algebraic properties. Results indicate that FPHS can reveal hidden patterns in prime distribution, simplify certain decompositions, and provide alternative perspectives on divisibility. Potential applications are identified in computational mathematics and cryptography, where such hybrid structures may offer both efficiency and novel insights. By bridging factorial and prime perspectives, FPHS contributes a distinctive addition to the study of number systems and invites further exploration of its theoretical and practical implications.

Abstract for 22384

Asymmetric Power ARCH Modeling of Nigerian Stock Market Volatility under Different Distributional Assumptions

Authors: ADETUNJI ILORI

Affiliations: NATIONAL MATHEMATICAL CENTRE, ABUJA, NIGERIA

This study investigated the performance of APARCH model for four different innovations (student''s t, normal, skewed student''s t and generalized error innovations) using Nigerian daily stock price series from 30/01/2012 to 03/10/2024, yielding a total of 3139 observations. The aim was to determine the innovation distribution that best captures the asymmetry and kurtosis exhibited by the returns on financial data. The descriptive properties of the series revealed that the distribution of returns for the stock prices was skewed and leptokurtic. The unit root test was carried out using the augmented Dickey-Fuller (ADF) test, and the result revealed that the returns on the series was stationarity. The ARCH LM-test detected the presence of ARCH effects, which justified the use of the GARCH model. The mean equation was estimated, and APARCH (1,1) model was fitted to the data, using different innovations. The findings of the study revealed that APARCH (1,1) model with generalized error distribution gave the overall best fit, with the lowest AIC (-8.4235) and the highest log-likelihood (13223.44). Findings of the study further revealed that the forecast from APARCH (1,1) model with the generalized error distribution has strong numerical accuracy with low MAE (0.002906), indicating that the model''s predictions are close to the actual values. From the findings of this study, it was deduced that the selection of suitable innovations in financial volatility modelling is pertinent for an appropriate forecast of the financial market.

Abstract for 22385

Taylor Wavelet-Based Numerical Framework for Fractional Real-Life Model Problems

Authors: AKANKSHA SINGH, Ankur Kanaujiya, Jugal Mohapatra

Affiliations: Research Scholar, Department of Mathematics, National Institute of Technology Rourkela, Odisha India, Department of Mathematics, National Institute of Technology Rourkela, Odisha India

This study presents a robust Taylor wavelet-based framework for numerically solving fractional real-life model problems in diverse fields such as biology, engineering, finance, and medicine. In this approach, the state and control functions and the fractional derivative operators are approximated using Taylor wavelets and their associated operational matrices. The proposed wavelet method effectively addresses fractional-order systems'' inherent complexity and nonlocal characteristics. The Lagrange multiplier technique further enhances computational tractability, transforming the original fractional optimal control problem into an equivalent system of algebraic equations. A detailed convergence analysis is provided, and error estimates are derived to validate the accuracy of the method theoretically. Numerical experiments confirm the efficiency of the proposed approach, demonstrating its capability to capture the essential dynamics of fractional models with high precision.

Abstract for 22386

B-Spline Galerkin Method for Fifth Order BVP: Error Optimization using Equidistribution Principle

Authors: Heena ., K.N.S. Kasi Viswanadham

Affiliations: Research Scholar, Department of Mathematics, National Institute of Technology Warangal, Professor, Department of Mathematics, National Institute of Technology Warangal

In this article, we have introduced an innovative modification of the quartic B-spline-based Galerkin method for efficiently solving fifth-order two-point boundary value problems with Dirichlet, Neumann and Robin boundary conditions emphasizing particular focus on the equidistributional of error principle. The basis functions have been redefined using the Dirichlet boundary condition, and solution for the non-singular stiffness matrix was obtained by solving the band diagonal matrix. The non-linear BVPs were reduced to a sequence of linear BVPs using the concept of quasilinearization given by Richard Ernest Bellman and Robert E. Kalaba in 1965. The numerical results demonstrate that implementing this principle reduces the maximum absolute error by a factor of 0.01. These findings confirm the accuracy and effectiveness of the proposed method. This method is applicable in solving the equations arising in the modeling of electromagnetic fields in various materials, couple stress fluids, and stress distribution in biological tissues and organs.

Abstract for 22390

Exploring Geometry Creatively: Islamic Art in the Math Classroom

Authors: Warabhorn Preechaporn

Affiliations: SEAMEO RECSAM

Geometry has been embedded in architectural structures and design forms for centuries. The earliest documented connections between geometry, astronomy, human proportions, and music can be traced to the ancient Greeks, especially the works of Pythagoras and Plato. Before the Greeks, earlier civilizations had already demonstrated their understanding of sacred geometry through its application in their constructions. This article aims to highlight the integration of geometry in Islamic art as a resource for secondary mathematics activities. The patterns are constructed from fundamental geometric shapes—such as circles, triangles, squares, and hexagons—and enriched through mathematical transformations like symmetry and tessellation, which enhance their intricacy and visual appeal. This paper emphasizes geometric concepts and engaging classroom activities, such as the hands-on construction of Islamic geometric patterns with a compass and ruler. In addition, digital tools like GeoGebra are employed to design tessellations and intricate patterns. These activities foster a positive learning environment in which students enhance their problem-solving abilities, strengthen spatial reasoning and visualization skills, actively engage in enjoyable tasks, and deepen their understanding of geometric concepts.

Abstract for 22391

Technology-Based Teaching Integration in Tertiary Mathematics: An Inductive Quantitative Approach Theory Development Using Structural Equation Modeling

Authors: Genaro Ardina, Guillermo Jr. Bautista, Edsel Inocian, Sylvester Cortes, Mona Emara

Affiliations: University of Cebu Lapu-Lapu and Mandaue, University of the Philippines - Diliman, Cebu Normal University, Cebu Technological University, Johannes Kepler University 

This study aimed to construct and validate a theoretical model of technology-based teaching integration in tertiary-level mathematics, addressing a gap in understanding how digital tools influence students’ cognitive and non-cognitive outcomes. Grounded in the Technology Acceptance Model (TAM) and Self-Determination Theory (SDT), the research responds to the increasing need for empirical validation of technology’s impact in mathematics education. Using an inductive quantitative approach, the study employed Structural Equation Modeling (SEM) to analyze data from 390 tertiary STEM students across public and private Higher Education Institutions (HEI’s). Constructs measured included perceived ease of use, perceived usefulness, mathematics motivation, engagement, and academic performance. Validated instruments ensured high reliability and validity across all dimensions. The study contributes to educational theory by offering a validated framework that explains the dynamic interplay between technology and learning. Findings revealed that perceived ease of use and usefulness of technology significantly and positively influenced students’ motivation in mathematics. Motivation, in turn, emerged as a crucial mediator, significantly predicting both engagement and academic performance. However, perceived ease of use and usefulness did not directly influence engagement, nor did engagement significantly impact academic performance. These results led to the formulation of the Technology-Motivation Teaching and Learning Theory (TMTLT), which posits motivation as the central mechanism linking technology integration with improved academic performance. For practitioners, the findings emphasize the importance of integrating user-friendly and pedagogically beneficial technologies to enhance student motivation. For researchers, the model presents a foundation for further empirical testing across different educational contexts. The study advocates for more inclusive and effective digital integration in STEM education, promoting higher motivation, engagement and performance among students. Future research should explore the applicability of TMTLT across disciplines, learning environments, and cultural contexts to strengthen its generalizability.

Abstract for 22392

Requirements for teacher training to advance the use of ICT in mathematics classes

Author: Tsutomu Ishii

Affiliations: Bunkyo univ.

The use of ICT in mathematics classes is progressing in many countries. The reason for this is based on the view of work that many Japanese people have. In Japan, where lifelong employment is the premise, emphasis is placed on human resource development after employment, rather than skill improvement through job changes. This human resource development also applies to teachers, and training is an obligation for all teachers. Considering this situation, in order to advance the use of ICT in mathematics classes in Japan, it is essential to develop teaching materials for teacher training.

Abstract for 32001

Integrating a Hybrid Statistical Downscaling-based HMM-RF Model for Enhanced Rainfall Prediction in Selangor

Authors: Noor Hamizah Mohamad Sani[1], Shazlyn Milleana Shaharudin [1,4], Muhammad Safwan Ibrahim [2], Upmanu Lall [3,4], Mou Leong Tan [5,6]

Affiliations: [1] Universiti Pendidikan Sultan Idris, 35900

Tangjong Malim, Perak, Malaysia, [2] Universiti Sains Islam Malaysia, [3] Columbia Water Center, Columbia University, New York, USA, [4] Water Institute, School of Complex Adaptive Systems, Arizona State University, Tempe, AZ, USA, [5] GeoInformatic Unit, Geography Section, School of Humanities, Universiti Sains Malaysia, [6] Al-Ayen University, Iraq

Accurate rainfall prediction is crucial for effective weather forecasting and climate modeling. This study aims to assess the effectiveness of a hybrid Statistical Downscaling-based Hidden Markov Model-Random Forest Model (SD-based HMM-RF) for rainfall prediction in Selangor, Malaysia. It also examines the best imputation methods for handling missing data, selects predictors for statistical downscaling by reducing dimensionality, and addresses uncertainties in zero-bounded rainfall data. The study utilized observed data (predictand) from 33 rainfall stations and atmospheric data (predictor), covering the period from 2008 to 2018. Seven imputation methods were tested: Mean Imputation (MeI), Median Imputation (MI), Expectation-Maximization (EM) Algorithm, Markov Chain Monte Carlo (MCMC), k-Nearest Neighbor (kNN), Non-iterative Partial Least Square (NIPALS), and Random Forest (RF). Principal Component Analysis (PCA) was used to manage high-dimensional data and select predictors, while HMM was applied to address uncertainties in zero-bounded rainfall data. Five hybrid models: Random Forest (SD-based HMM-RF), Support Vector Machine (SD-based HMM SVM), Decision Tree (SD-based HMM-DT), k-Nearest Neighbors (SD-based HMM-KNN), and Artificial Neural Networks (SD-based HMM-ANN) were evaluated. Performance metrics, including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Forecast Error (MFE), Nash Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency (KGE), and Rank Correlation Coefficient (ρ) were used to identify the most accurate rainfall prediction model. MI emerged as the best-performing method, achieving the lowest RMSE (0.146) and MAE (0.021), along with the highest NSE (1.000) and Pearson correlation coefficient, r (1.000) for all stations. PCA identified five principal components (PC1 – PC5) with a cumulative variance cut-off until 93.254%. HMM analysis determined that three hidden state layers (K=3) at iteration 2000 were optimal, with the lowest Bayesian Information Criterion (BIC) of 260,018.30. Among the models, statistical downscaling-based HMM-RF consistently outperformed others, showing superior accuracy and reliability in rainfall prediction, as indicated by its RMSE (2.298), NSE (0.752), MAE (1.900), near-zero MFE (-0.049), KGE (0.526) and ρ (0.898). By improving rainfall prediction accuracy, the hybrid model can enhance early warning systems, inform infrastructure planning, and reduce the economic impact of future flooding events, thereby contributing to more resilient urban development in the region.