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Creative, Innovative and Computational Thinking in STEM Through Technology



ATCM 2023, December 10-13

Conference Venue Nongnooch Pattaya Garden & Resort, Pattaya, Thailand

1.     Abstracts for Invited Papers

2.     Abstracts for Contributed Papers

3.      Abstracts for Presentations with Abstract Only

4.      Abstracts for Hands-on workshops

5.      Abstracts for Poster Sessions


Abstracts for Invited Papers

Abstract for 22002

22002  Rethink our math curriculum now before we are replaced by A.I.

Wei-Chi Yang

Radford University     USA   


Abstract. While Ph.D. math degree programs are being eliminated, don’t we have to think about why students need to choose math to be a major? We will reason why we need to incorporate technologies into STEAM areas, and we shall see how dynamic geometric approaches can provide critical intuition and motivation to learners and make challenging problems more accessible to more students. Integration of the computer algebra system with the dynamic geometry system will not only allow us to make conjectures and discover more mathematics but also provide us with an excellent methodology to deal with many real-life problems. The paper ID 22003 will be a subset of this general talk.

Abstract for 22003

22003  Graphs of Uniform Convergence on Iteration of Loci generated by Special Convex Combinations of Curves and Surfaces          

Wei-Chi Yang

Radford University     USA   


Abstract. We extend the convergence of locus discussed in the paper [5], which originated from a practice problem for the Chinese college entrance exam. In this paper, we are interested in the limit of a recursive sequence of loci built on a special convex combination of vectors involving curves or surfaces. We shall see many interesting graphs of uniform convergence of sequences generated by parametric curves and surfaces, which will inspire many applications in computer graphics, and other related disciplines.


Abstract for 22022

22022  Analysis of Progressive Casino Game Betting Systems      

Cole Payne - Rick Klima - Neil Sigmon       

Appalachian State University; Radford University    USA


Abstract. This work is primarily the product of the first author (who is also the presenting author), a student who completed the work under the direction of the secondary authors. We analyze three progressive betting strategies, each applied to three casino games, aimed at identifying optimal strategies after a given number of bets. The strategies analyzed are Martingale, Paroli, and Fibonacci, each of which is applied to the casino games blackjack, roulette, and craps, with bets placed that pay 1:1. The purpose of this work is not to try to discover methods for beating the house, which are known to not exist, but rather to search for methods for advancing gameplay through a maximum number of bets while retaining the possibility of earning a profit. Programming in the computer algebra system Maple will be used for the calculations.


Abstract for 22046

22046  Linear Algebra Computational Tool for LaTeX      

Ajit Kumar - Chetan Shirore 

Department of Mathematics; Institute of Chemical Technology; Nathalal Parekh Road; Matunga (E); Mumbai 400 019 (INDIA); Department of Mathematics; Institute of Chemical Technology; Mumbai, India  


Abstract. Linear algebra is used in different branches of science, engineering, and data science. There are many tools for doing computations on vectors and matrices. LaTeX is one of the most widely used typesetting systems for scientific publications, and there is often a need to type vectors and matrices inside LaTeX documents and perform different operations on them. We have developed a computational tool for linear algebra to deal with standard operations on vectors and matrices inside LaTeX. The standard practice of LaTeX users is to export computational results from other software and compile them inside LaTeX. This may be cumbersome when there are vast computations. The exported output from other software may need some editing before importing it into LaTeX as it may not be in LaTeX-compatible format or in the format that the user expects. The main aim of this paper is to give a brief introduction to the computational tool of linear algebra developed by us. This paper extends the series of basic computational tools that we developed. It will reduce the dependence of LaTeX users on external software and can also be deployed for pedagogical uses.


Abstract for 22052

22052  Construction of six heptahedra each line-symmetric to its dual      

Jen-chung Chuan       

National Tsing Hua University           Taiwan


Abstract. It is known that there are 34 topologically distinct convex heptahedra. Among them only six are self-dual. With the technology furnished by Cabri 3D and WolframAlpha, this paper presents a concrete construction of each of the 6 self-dual pairs together with the associated midsphere and the line of symmetry. The six self-dual heptahedron are given by the following symbols: (6,3,3,3,3,3,3)-(6,3,3,3,3,3,3) (one hexagonal and six triangular faces) (5,4,3,3,3,3,3)-(5,4,3,3,3,3,3), (one pentagonal, one quadrilateral and five triangular faces) (4,4,4,3,3,3,3)[1]-(4,4,4,3,3,3,3)[1], having three mutually adjacent triangular faces (4,4,4,3,3,3,3)[2]-(4,4,4,3,3,3,3)[2], having two pairs of adjacent triangular faces (4,4,4,3,3,3,3)[3]-(4,4,4,3,3,3,3)[3], having exactly one triangular face adjacent to two triangular faces (4,4,4,3,3,3,3)[4]-(4,4,4,3,3,3,3)[4], all four triangular faces share one common vertex In designing/constructing the models, we have consulted these ancient geometric wisdom: The Arbelos (Shoemaker s knife), in Leon Bankoff, A Mere Coincidence, Mathematics Newsletter, Los Angeles City College, November 1954. Apollonius construction (to construct all the circles that are tangent to three given circles). See Special cases of Apollonius problem in Wikipedia. Sangaku problems Inversion. We are unable to construct (5,4,3,3,3,3,3)-(5,4,3,3,3,3,3) nor (4,4,4,3,3,3,3)[3]-(4,4,4,3,3,3,3)[3] using ruler-and-compass along. Our construction of these two heptahedra depends on high-precision numerical approximations with WolframAlpha queries: solve (1+(x^2-1)^ (3/2)+(x^2-1))( ^2-1)=1 for (5,4,3,3,3,3,3)-(5,4,3,3,3,3,3) solve(1+x^4=x^2+x^3) for (4,4,4,3,3,3,3)[3]-(4,4,4,3,3,3,3)[3] The paper is of interest in 3D Visual Art Design, in Math Competition and in Science Fair Project. The extended abstract together with the associated *.cg3, *.mov, *.gif files are located at: Link to the extended abstract.


Abstract for 22057

22057  A Classification of Tritangent Conics: The Power of Geometric Macros in Dynamic Geometry       

Jean-Jacques Dahan   

IRES of Toulouse       France


Abstract. Based on our knowledge of conics and my previous work, I will detail the algorithms for constructing conics tangent to the three sides of a triangle, internally and externally. These constructions developed in a dynamic geometry environment (here the new Cabri) largely using the Macro Construction tool (which is none other than a program of this environment) will make it possible to visualize all these conics in motion and to highlight evidence of some surprising properties of these families of conics: in particular, we will be led to conjecture a classification of conics tangent to the three sides of a triangle according to the position of one of their foci. This work requires for each type of conic introduction concerning the construction algorithms of their characteristic elements as well as of their tangent lines within a dynamic geometry environment.


Abstract for 22061

22061  Bridging the Mathematics Gap Through the Use of Mathematical Apps     Ma. Louise Antonette De Las Penas - Debbie Marie Verzosa - Maria Alva Aberin - et al.        

Ateneo de Manila University; Department of Mathematics and Statistics University of Southern Mindanao; Philippines; Department of Mathematics, Ateneo de Manila University; Philippines.    


Abstract. During the COVID-19 pandemic, school campuses worldwide were forced to close, and students had to learn primarily from home. This sudden disruption is estimated to have caused significant learning loss among learners. This paper reports the use of mathematical applications (apps) to bridge the mathematical learning gaps in Grades 1 to 11 in the Philippines after the pandemic, as part of a project funded by a national government agency. The apps include those that strengthen foundational concepts in number and fraction sense in grade school mathematics, develop proving skills in geometry, promote mastery in algebraic and trigonometry through drill and practice, and facilitate statistical understanding and reasoning. The description of the apps, their design, and their pedagogical basis are discussed. Challenges encountered in the implementation of the project are also presented.


Abstract for 22079

22079  A Particle Swarm Optimisation approach to the Generalised Fermat Point Problem: Rethinking how a problem is solved  Weng Kin Ho - Chu Wei Lim          

Nanyang Technological University; AO Studies, Singapore


Abstract. This position paper claims that the way a mathematical problem is solved depends on the technology available to the problem-solver. Drawing on the authors mathematical experience of finding a new solution to an old problem the Generalised Fermat Point Problem, salient observations are drawn to illustrate how a problem solver s experience can be shaped by technological affordances.


Abstract for 22081

22081  Mathematics teacher training from the perspective of STEM -- a particular case   

Roman Hasek 

University of South Bohemia Czech Republic         


Abstract. The ability to respond creatively and effectively to new challenges, whether it is acquiring new knowledge, solving problems, or the teaching process, is a key factor in determining the success of today's teachers. An important task of teacher training schools is therefore to create a suitable environment for the provision of education, as well as impulses for the development of the necessary knowledge and skills. This paper presents a specific project and corresponding activities for students implemented within mathematics teaching courses at the University of South Bohemia. Historical sources, both classical and local, from the area of present-day Czechia, are used. Emphasis is placed on the use of computers, especially dynamic geometry software, to model problems and their effective solution.


Abstract for 22083

22083  Understanding Geometric Pattern and its Geometry Part 10 Geometry lesson from Paigah Tombs

Miroslaw Majewski   

New York Institute of Technology; Abu Dhabi Campus       United Arab Emirates


Abstract. Symmetry groups are a recent development in modern geometry. Their origins can be traced from a paper by M. J. Buerger and J. S. Lukesh (see [1] ). A very solid mathematical foundation of them can be found in Conway''s 'Symmetries of Things.' We can also find there his Magic Theorem for plane symmetry groups, the so-called wallpaper groups, with complete proof. Some mathematicians believe this theorem can be used to create any plane geometric pattern. Unfortunately, the Magic Theorem is not enough. It can help to determine the overall geometric structure of the pattern, but it does not handle what is happening inside the fundamental region of it. Thus, we may have an infinity of geometric patterns within the same symmetry group. However, in many cases, symmetry groups can help us reconstruct an existing geometric design or create a new design. This paper discusses a selection of patterns found in Paigah Tombs, or the Maqhbara Shams al-Umara, in Hyderabad, India. We will limit our discussion to a selection of hexagonal designs. Following this discussion, we will show how to analyze and reconstruct these patterns.


Abstract for 22090

22090  Education for the Future: Crafting 3D Geometric Models and Building Mathematics Knowledge with 3D Printing 

Petra Surynkov            

Department of Mathematics Education; Faculty of Mathematics and Physics; Charles University       Czech Republic         


Abstract. This paper addresses the creation of 3D geometric models using 3D printers and introduces a newly designed and 3D-printed construction set of polygons for educational purposes. The process of creating these geometric models encompasses steps such as design, 3D computer modeling with Constructive Solid Geometry (CSG), 3D computer modeling of parametric surfaces using principles of differential geometry, 3D scanning of real objects, and the process of manufacturing itself. Students can be involved in the entire process of crafting models for 3D printers, and these resulting printed models can be utilized in geometry education at all levels (university and secondary school in our scenario) as instructional aids. We explore the potential methods to design geometric objects using 3D computer modeling software; this covers both commercial options and open-source software like Tinkercad, a free web application for 3D design, electronics, and coding. We present the fabrication of a new construction set of polygons which consists of different shapes of regular and irregular polygons and it is intended for use in mathematics teaching to study polygon properties and create diverse types of tessellations at the secondary school level. The effects of using these instructional aids were tested with several groups of students. All steps of the model design for 3D printing, in combination with the physical 3D printed models, shed new light on mathematics education and more broadly, to education as a whole. This process engages students in solving real-world problems and enhances their understanding of geometry while familiarizing them with 3D computer modeling and 3D printing technologies. Both 3D virtual models and 3D printed models can act as manipulative instructional aids.


Abstract for 22092

22092  Exploring Creativity and Innovation in STEM Education: With and Without Technology    

Vanda Santos 

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, Portugal           

Abstract. In this work, we present a collection of geometric problems described in wooden tablets known as Sangaku. These original problems developed in Japan during the Edo period. Quadrilaterals, a subject of immense geometric richness, have been widely researched in literature. They offer opportunities to explore constructions with rulers and compasses, various representation techniques, proofs, and theorems, with and without technology. The main objective of this study is to demonstrate how Sangaku geometric problems can serve as valuable pedagogical resources, integrating different disciplines and enriching students learning experiences. In addition to deepening the mathematical aspects of these problems, special attention was also given to the artistic elements present in the wooden tablets, stimulating students to the creative expression inherent to Geometry. Adopting an interdisciplinary approach, the activity seeks to stimulate students'' creativity, encouraging them to create visual representations of problems and explore various artistic materials, while developing their visual communication and mathematical skills. This approach placed a strong emphasis on promoting transversal skills and attitudes, promoting the development of interdisciplinary skills. Consequently, it contributed to a broader and more integrated education in several fundamental disciplines.


Abstract for 22098

22098  Locus of viewpoints from which a conic appears circular   

Yoichi Maeda - Makoto Kishine       

Tokai University; St. Viator Rakusei Junior and Senior High School, Japan           


Abstract. We know that circular shapes we encounter in daily life may appear to be elliptical from some viewing points. It is reasonable to expect that an ellipse may appear to be circular from certain viewpoints. We investigate the locus of viewpoints from which an ellipse appears circular. It will be shown that the locus of viewpoints is a hyperbola passing through the two foci of the ellipse. Conversely, the locus of viewpoints from which a hyperbola looks circular is an ellipse passing through the two foci of the hyperbola. Further, the locus of viewpoints from which a parabola looks circular is itself a parabola, passing through the focus of the original parabola. There is a simple duality between the object to be observed and the observer.


Abstract for 22099

22099  Arts and Maths: A STEAM introduction to envelopes with automated methods    

Noah (Thierry) Dana-Picard  

Jerusalem College of Technology      Israel  


Abstract. Starting from a piece of string art, we propose a STEAM approach to motivate activities about envelopes of parametric families of surfaces. The examples are provided by 1-parameter families of planes and yield ruled surfaces with cuspidal edges. The topology of the surface obtained by geometric and algebraic work can be compared to the shape of well-known monuments (whence an incitement to outdoor mathematics). Later, we discuss the transition from 2D to 3D: regarding the automated methods, it is nontrivial as commands available in a 2D setting may not be available for working in 3D. Nevertheless, the algebraic manipulations are similar in 2D and 3D, based on the same packages. Here, the main example is offered by an astroid in the plane, and its 3D generalization as an astroidal surface. Finally, we discuss the examples according to the STEAM approach, and to Balacheff s computer transition.


Abstract for 22100

22100  Inversion Transformation Studies with Software     


Holon Institute of Technology           Israel  


Abstract. The circle Inversion transformation was invented by L.I. Magnus in 1831 as a plane transformation defined as follows: For a given fixed circle, that is with center O and radius b, the inverse of any point P (distinct from O) is such point P'' on the ray OP that |OP|*|OP |=b . In the base case of a circle centered at the origin and unit radius, the inversion is an R plane transformation f:(x, y) -> (x/(x +y ), y/(x +y )) or a complex mapping f: z -> 1/z*. The popular educational software limits the transformation mechanism with only explicitly defined objects images. On the one hand, this leads to incorrect models, but on the other hand, it facilitates the representation of the geometric properties of the inversion. The report provides a different approach to the representation of transformations, including the inversion, implemented in the author's program VisuMatica, in which any of the forms of defining the transformation of the plane (f: R -> R or f: C -> C) automatically shows the transformation image of the entire plane with all the objects on it. This approach also has its drawbacks, for example, in general, the image of a segment is not a segment, although geometric segments often just serve as an illustration of the distance between points. The report demonstrates ways to resolve such conflicts and the possibility of an in-depth study of geometric and complex mapping features of inversion transformation.


Abstract for 22101

22101  Sangaku Mathematics Puzzles: A Catalyst for Cultivating Creative Thinking and Problem-Solving Abilities using The Geometer s Sketchpad           

Krongthong Khairiree

International College; Suan Sunandha Rajabhat University Bangkok Thailand.


Abstract. The purpose of this study was to examine how Sangaku Mathematics Puzzle serves as a catalyst for cultivating students' creative thinking and problem-solving abilities, aided by the dynamic software: The Geometer's Sketchpad. Action research was conducted in the College of Hospitality Industry Management, Suan Sunandha Rajabhat University, Bangkok, Thailand, in the year 2022. A total of 19 students studying in the second year of their bachelor s degree in education, majoring in mathematics, participated in this study. The duration of the action research project was about two months. A flipped classroom model incorporating cooperative learning and the Geometer's Sketchpad was employed in this study. These methods were used in line with the policy of the Ministry of Education in Thailand during the COVID-19 pandemic situation in the years 2021 and 2022. The research findings showed that with the combination of Sangaku puzzles and The Geometer's Sketchpad, students are encouraged to think outside the box and approach mathematical problems from different perspectives. In addition, the flipped classroom and cooperative learning model encourages teamwork and communication among students, promoting a deeper understanding of mathematical principles.


Abstract for 22104

22104  Interactive visualization of curvature flows 

Sage Binder - Matthias Kawski         

Arizona State University; University of Iowa            USA   


Abstract. After a short motivation, we introduce several different curvature flows: A naive flow on the curvature under the heat equation, the curve-shortening flow, the mean curvature flow for imbedded surfaces, and the Ricci flow on surfaces of revolution and for abstract 2-manifolds. The main focus is on interactive visualizations using animations of curves, and surfaces, and in the case of the Ricci using flow on a metric field similar to Tissot s indicatrix. We refer to and briefly demonstrate an existing applet for the curve-shortening flow, and present our own code written in SageMath / Python for other flows, including for the Ricci flow on surfaces of revolution, thus recreating animations first presented by Rubinstein and Sinclair. Our code is publicly available on GitHub and invites for further experimentation, especially with different initial shapes.


Abstract for 22105

22105  Developing mathematical and computational thinking through spreadsheets.

Jonaki Ghosh 

Lady Shri Ram College; Delhi University     India   


Abstract. Computational thinking has been gaining plenty of attention in education in recent times and has been identified as an important skill to be developed in children right from the school years. Papert s pioneering work in the 1980s led to concretizing the term computational thinking (CT). While CT encompasses a broad skill set applicable across contexts and subject domains, it is also intimately connected with mathematical thinking (MT). The ability to deal with challenging problems, represent ideas in computationally meaningful ways, create abstractions for the problem at hand, break down problems into simpler ones, and engage in multiple paths of inquiry are some of the skills common to both CT and MT. Mathematics, as a core school subject, is therefore a natural choice for integrating CT. Some topics in the school mathematics curriculum, such as probability, lend themselves more easily to the integration of CT. The study of probability and randomness is intriguing to most students and forms an integral part of mathematics curricula at the high school level. Most of the problems in textbooks, however, tend to focus on tossing coins, rolling dice, or selecting cards from a standard deck of cards. These seem a bit contrived and hence do not provide sufficient motivation for students to learn. The teaching of probability can be enlivened through many interesting problems and simulation can be an effective tool for modeling such problems. Simulation enables the student to generate and explore data meaningfully and, as a result, grasp important probability concepts. Spreadsheets, such as MS Excel, equipped with random number generators and graphing capabilities provide opportunities to explore problems through the inquiry-based approach. Technological and pedagogical affordances offered by spreadsheets, in exploring mathematical concepts are very conducive for developing inquiry-based exploratory tasks. The talk will focus on some interesting problems, which highlight important concepts related to probability as taught in the school curriculum. Explorations based on the Birthday Paradox, Monty Hall Problem; and other such problems will be used to highlight the underlying ideas as well as their pedagogical affordances. Elements of probabilistic thinking such as empirical probability, classical probability, and conditional probability will be discussed. The suggested explorations, both mathematically and computationally rich, were integrated into a foundational mathematics course in an undergraduate pre-service teacher education program. Students, from diverse backgrounds in terms of their mathematical ability and interest, attended the course. The talk will highlight the potential of such exploratory tasks in engaging students in the processes of visualization, identifying and generalizing patterns, analyzing data and algorithms, and preparing meaningful representations on a spreadsheet. Such processes are important from both computational as well as mathematical perspectives. Evidence of progression in students' thinking as they engaged with these exploratory tasks and their positive feedback led to a convincing argument for integrating such tasks into the mathematics courses of the program. The supporting role of spreadsheets in mediating computational and mathematical thinking was an important learning from the study.


Abstract for 30101

30101 The mathematics of the solera system

Alasdair McAndrew

College of Sport, Health and Engineering

Victoria University, Australia


Abstract. Fractional blending, also known as the solera system, is a technique dating from the mid-19th century, for the aging of liquids such as fortified wines, spirits, and balsamic vinegar. Such products require careful aging before they can be sold, and careful mixing of liquids. from different ages is thus required. At each stage, every six months for example, each year, a new un-aged liquid is added to the system, and a sequence of mixings is used to filter, as it were, this new material through the system. The result at the end is a liquid carefully blended from different ages, with the oldest predominating. When properly done, this ensures a constant supply of an appropriately aged product. The mathematics can be described as a sequence of difference equations, or recurrence relations, which leads into some

matrix algebra, and it turns out that this mathematics is more interesting than the simple explanation of the system might lead one to believe. This article explores this mathematics, using a computer algebra package for all the heavy lifting.


Abstract for 30103

30103 Automated checking for mathematical exams on large language models

Hongguang Fu, Xiuqin Zhong, Changyu Chen

University of Electronic Science and Technology-Chengdu (UESTC), China


Abstract. Large Language Models (LLM) have achieved historical breakthroughs in natural language understanding, especially ChatGPT4, which has also made significant progress in automatically solving mathematical problems. This paper innovatively proposed an automated checking method for mathematical exams based on standard answers and LLM.

Based on the knowledge integration and semantic comparison capabilities emerging from LLM, this paper explored the use of prompt engineering with LLM, to automatically assess the similarity between students' answers and standard answers in mathematical exams. Furthermore, the paper addressed checking challenges when one question has multiple answers. Finally, the paper conducted automated checking step-by-step.

The paper experimented with a series of large language model prompt generation methods, and comparative analysis found that prompts based on the Json format can effectively guide LLM to understand comparison marking tasks and output structured marking results as required. The results showed that in most cases, LLM can effectively distinguish the differences between student answers and standard answers.

However, in some complex problems or those with multiple solutions, the method may make incorrect checking. To address this, this paper introduced a large number of various mathematical problem instances, utilized LLM to perform comparison checking tasks, and summarized the possible reasons for checking failures in these tasks. Furthermore, by incorporating methods such as chain of thought prompts, in-context learning prompts, knowledge injection prompts, external tool selection prompts, and sub-task decomposition prompts, this paper optimized the checking workflow and prompt generation methods based on LLM.

Finally, this paper solved the issues encountered in comparison checking and formed a systematic automated checking method based on LLM.


Abstract for 30104

30104. Making Geometry Dynamic: Design Considerations in Mathematical Interactivity

Nicholas Jackiw

Vancouver, Canada


Abstract. This paper surveys situations in the early development of Dynamic Geometry Software in which designers had to invent plausible mathematical behaviors for specific dynamic configurations. It offers both a case study in the design of mathematical software and a reflection on the potential contribution dynamism makes to the history of mathematical representation.


Abstract for 30105

30105  GeoGebra as a Tool for Creating Content for e-Textbooks: Interactive Figures and Adaptive Homework Problems

Douglas B. Meade, Department of Mathematics, University of South Carolina, Columbia, SC 29208 USA

Paul Seeburger, Department of Mathematics, Monroe Community College, Rochester, NY 14623 USA


Abstract. GeoGebra, as its name suggests, is thought of as a tool for geometric and algebraic explorations. E-textbooks, as its name suggests, are electronic versions of printed textbooks. But does that all either of these names mean? Our answer is a resounding NO! An e-textbook for calculus, differential equations, or any content that involves themes that involve change or dynamics, should allow the student to experience these essential characteristics of the ideas they are learning. In this presentation, we will demonstrate a sampling of interactive figures that illustrate and explore topics including multiple representations of area functions, the motion of a spring, bifurcation, phase portraits for a system of differential equations, and difference equations. And, to reinforce the educational impact of these figures, we will share some of the assignable resources we have created that require the use of the interactive figures from their book. We will also explain, and show, a little about how these resources are implemented in GeoGebra.


Abstract for 30106

30106 Math in STEM

Edward M. REEVE, Utah State University, Logan, Utah USA


Abstract. Mathematics (Math) is the foundation for STEM.  It is generally used in STEM to find patterns in data.  These patterns can be used to test relationships, draw general conclusions about data, and model the real-world.  This presentation will review STEM, STEM Education, and look at the role of math in STEM. 


Abstracts for Contributed Papers

Abstract for 22018

22018  How Many are Factorable?  

Marshall Lassak         

Eastern Illinois University, USA


Abstract. In this paper, an investigation in quadratic factoring is shared that begins with a straightforward problem that technology enables to evolve into other avenues of investigation of varying complexity and accessibility.


Abstract for 22019

22019  Applications of Lua for LaTeX Documents 

Chetan Shirore - Ajit Kumar 

Department of Mathematics; Institute of Chemical Technology; Mumbai; Department of Mathematics; Institute of Chemical Technology; Mumbai; India


Abstract          This article discusses various applications of Lua for LaTeX documents. It mainly focuses on enhancing the graphical aspect of LaTeX using Lua and creating Android applications from LaTeX documents. This is an extension of our work of creating computational packages for LaTeX using Lua. The computational packages we developed are available for LaTeX users on the CTAN repository and bundled with standard TeX distributions. In continuation of this work, the development and deployment of the luaplot package is discussed in this article. It also describes the outline for creating Android applications from LaTeX files using Lua and other resources. The Android applications created from LaTeX files do not need the internet, are static, and do not support calculations. The one purpose is to reduce the dependence of LaTeX users on external software for computations and graphing. Some of the packages we developed can also be deployed for pedagogical purposes. The other purpose is to provide techniques and methods to make mathematical content in LaTeX documents available to Android users.


Abstract for 22024

22024  Teaching high school students the intimate relation between definite integrals piecewise quadrature and areas         

Rattanasak Hama - Mircea Sabau - Sorin Sabau        Thailand         

Faculty of Science and Industrial Technology; Surat Thani Campus; Prince of Songkla University; Surat Thani 84000; Thailand; Tokai University; Faculty of Science; Department of Mathematics 1117; Kitakaname; Hiratsuka; Kanagawa; 259-1292; Japan; Graduate School of Science and Technology Physical and Mathematical Sciences Tokai University; Sapporo 005-8600; Japan


Abstract          Numerical integration is an important topic for modern analysis and differential equations. From an educational point of view, in the high school mathematical curriculum, the definite integral is often understood as an application of indefinite integrals, and area computation is a further application. High school students enjoy calculating definite integral sound areas by using the Fundamental Theorem of Calculus without understanding the essence of definite integrals as limits of Riemann sums, a natural idea leading to the more advanced notions of piecewise quadrature and measure. We propose a unified teaching approach of definite integrals for high school students which allow not only a mathematical understanding of the notions of definite integrals and area computations through the notion of piecewise quadrature but also the relation with the area of the different figure known already and prepare the ground for the notions of numerical integration and theory of measure to be learned at undergraduate level. Another important application is the calculus of limit of the sum of terms of an infinite sequence that can be represented as a finite area through piecewise quadrature. To facilitate authentic comprehension, the concepts are accompanied by GeoGebra scripts to visually depict their application in mathematical education, thus highlighting the direct integration of Information Technology within this domain.


Abstract for 22027

22027  Enhancing Mathematics Instruction for Students with Visual Impairment: A Teacher Training Program on Accessible Online Math          

Pongrapee Kaewsaiha - Chaweewan Kaewsaiha - Luechai Tiprungsri - et al.         

Digital International Business Program; SSRU; Suan Sunandha Rajabhat University


Abstract          This research article presents a comprehensive training program designed to enhance the knowledge and skills of lower secondary math teachers in Thailand regarding producing online mathematics materials that cater to visually impaired students. The training program encompassed various topics, including utilizing LaTeX for writing math expressions and equations to facilitate screen readers and adopting vector graphics to ensure scalability for students with low vision. Additionally, the program trained math teachers to create accessible documents, illustrations, videos, web pages, and online tests. A total of 94 lower-secondary math teachers participated in a one-day training session conducted online via Zoom. Pre- and post-training evaluations were conducted to measure participants knowledge of teaching mathematics to visually impaired students and their attitudes toward accessible mathematics. The evaluations also assessed participants'' satisfaction levels and skills acquired from the training program. Statistical analysis revealed a significant improvement in participants'' knowledge and attitudes toward accessible math (p < 0.001, paired-sample t-test). Furthermore, the findings indicated a high level of participant satisfaction, with an average rating of 4.66 out of 5.00, demonstrating the effectiveness of the training program. Participants strongly agreed that they obtained valuable skills in creating accessible math lessons, as indicated by an average rating of 4.47 out of 5.00. The results highlight the positive impact of taking accessibility factors into account in teaching mathematics online, ultimately fostering an inclusive learning environment for all students.


Abstract for 22044

22044  Application of Machine Learning to Slow Tourism Market Segmentation: A Case Study at Nanzhuang   

Ming-Gong Lee - Che-Chia Nien       Taiwan           

Ph.D. Program in Engineering Science; Chung Hua University; Department of Tourism and Leisure; Chung Hua University; Graduate Student; Department of Computer Science and Information Engineering; Chung Hua University


Abstract          Truly little is known about the characteristics of tourists to Nanzhuang township, one of four Cittaslow townships in Taiwan. This study gives implications about the distinctive styles of tourists to Nanzhuang. Today, Nanzhuang township is famous for its role as a slow city in Taiwan. It is reasonable to assume this characteristic would have an influence on its tourism market. In order to understand the types of tourism to Nanzhuang and to apply a beneficial advertising strategy in terms of the principles of the Cittaslow organization, we need to know the features of tourists to this township. A survey drafted according to the Cittaslow principles was performed, and a total of 222 responses were collected. Machine learning (ML) tools for data science, such as k-means clustering, Principal Component Analysis (PCA), and one-way ANOVA were applied to do proper clustering and analysis of the data. The results have shown that the tourists can be suitably categorized into three distinct groups: Advocates of Slow Tourism (AST); Conscious of Slow Tourism (CST), and Unconscious of Slow Tourism (UST). Interestingly, the descriptive statistics between these three groups do not show any difference in their background, for instance, regarding age and education. A precise marketing strategy for slow tourism should be carefully considered accordingly.


Abstract for 22055

22055  Learnings from the Use of Screencast Videography in Mathematics Education Research on Item-Writing     

Mark Lester Garcia - Lester Hao        Philippines     

Ateneo de Manila University


Abstract          This paper presents the viability of screencast videography (SCV) as a methodology in mathematics education research, particularly in the area of item writing. Through the lead author s implementation of SCV in the pilot study of his dissertation project, the authors reflect on the affordances and challenges of utilizing SCV in mathematical item-writing research and its implications in mathematics education. With screencast display as its primary source of data, SCV may also utilize other sources of data, such as webcam footage and audio recording. The authors elaborate on the strengths and weaknesses of these data sources which collectively complement one another. They then share their introspections on the opportunities and limitations of SCV, and how these could be potentially addressed. In sum, SCV as a research methodology promotes corroboration and triangulation of data sources; when applied in mathematical item-writing research, it sheds light on the item-writing process and experience of mathematics teachers. This, in turn, may potentially inform the necessary support mathematics teachers need in designing assessment items that will ideally promote student learning and achievement.


Abstract for 22056

22056  Morphing Tilings of the Plane into Tilings of Surfaces       

Mark Loyola - Ma Louise Antonette De Las Penas   Philippines     

Department of Mathematics; Ateneo de Manila University


Abstract          This work discusses a procedure to generate a tiling $\mathcal{T}_{S_f}$ of a 2-dimensional surface $S_f$ embedded in the Euclidean 3-space $\mathbb{R}^3$ from a tiling $\mathcal{T}$ of the Euclidean plane $\mathbb{R}^2$. We employ the computer algebra system Mathematica to generate 3D graphical images of $\mathcal{T}$ and $\mathcal{T}_{S_f}$ and render animations that create the effect of $\mathcal{T}$ morphing into $\mathcal{T}_{S_f}$.


Abstract for 22060

22060  Leveraging Technology for Effective Teaching and Learning        

Wang Cui - Sisi Wang            China 

High School Affiliated to Renmin University of China


Abstract          During the COVID-19 pandemic, online teaching has become a major teaching method, which must involve the application of various technologies. From initial passive usage to ongoing exploration, our teaching and research team has found that teaching integrated with technology can help students better master and apply mathematical concepts to solve problems compared with traditional teaching, and technology has revolutionized mathematics education by offering innovative tools and resources that can promote active learning and enhance a motivating practice of math. In the realm of integration, technology can play a vital role in helping students visualize and comprehend fundamental concepts and applications. Firstly, the essay introduces powerful technological tools to dynamically enhance the teaching approach of complex mathematical concepts in the classroom through the utilization of TI-Nspire Software. Subsequently, it explores how technology can be integrated into curriculum design.


Abstract for 22063


Desyarti Safarini TLS - Dadang Juandi - Darhim Darhim     Indonesia       

Universitas Pendidikan Indonesia; Sampoerna University


Abstract          Investigating how undergraduate students learn the derivatives is crucial to supporting them in successfully continuing their studies in integral calculus. This case study investigates students cognitive development as they learn the basic differentiation rules using Desmos Classroom (DC) based on the Three Worlds of Mathematics (TWM). This research includes 25 students who enrolled in Calculus 1 at Sampoerna University during the fall semester of the 2022 2023 academic year. DC is used as a generic organizer to facilitate an embodied operation on a function's graph. DC enables students to drag the tangent line and tangency point along the graph of a function, and it allows them to magnify the screen, which helps them make sense of the tangent line and derivative concepts. Students prove the basic differentiation rules on the DC through graphical exploration, numerical computations for practices, and symbolic manipulations. DC-based on the TWM can contribute to the student's cognitive development by helping them learn the basic differentiation rules. All students performed well in the axiomatic formal world by proving the derivative of a trigonometric function. Most students (92%) also succeeded in solving the tangent line problem, which required them to perform proceptual thinking. Many students (64%) also have no limitations on graphical representation. According to this result, students success in formal axiomatic thinking does not imply their success in proceptual thinking. Similarly, success in performing proceptual thinking does not imply success in graphical representation.


Abstract for 22065

22065  Debugging on GeoGebra-based Computational Thinking+Mathematics lessons.  

Wahid Yunianto - Theodosia Prodromou - Zsolt Lavicza     Indonesia       

Johannes Kepler University Linz; University of New England; Australia.  


Abstract          Computational thinking (CT) has become a buzzword recently and gained more attention from countries and researchers. Researchers realize the importance of CT and integrate it into school subjects such as mathematics, science, language, and others. Our research tries to contribute to the plugged CT activities under mathematics subjects. Collaborating with mathematics teachers, principals, and a teacher trainer, we developed a sequence of lessons in GeoGebra. Our lessons integrate CT s facets in the topic of the area of a circle. The development of the GeoGebra-based Mathematics-CT lessons incorporated educational design research methodology. We improved our lessons and implemented them for a few students. In this paper, we focused only on the debugging skill being supported by GeoGebra. Our findings show that fixing commands can be challenging as students have been through several debugging, and it can be complicated if the errors are many. This paper shows the power of GeoGebra to learn integrated CT in mathematics lessons through creating objects and debugging the program.


Abstract for 22067

22067  Development of an online training program for mathematics teachers using GeoGebra            Sasiwan Maluangnont           Thailand         

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand  


Abstract          For years, the Institute for the Promotion of Teaching Science and Technology (IPST), serving as the GeoGebra Center of Thailand, has been providing onsite training to teachers on using GeoGebra for mathematics instruction. However, due to the COVID-19 pandemic, the traditional onsite training has been replaced with an online alternative. The main objectives of this research were: (1) to develop an online training program for teachers focused on using GeoGebra for mathematics teaching and (2) to explore the satisfaction level of teachers who participated in the developed online training program. The study included 108 mathematics teachers as subjects, all of whom took part in the developed online training. The findings indicate that, overall, the participating teachers expressed a high level of satisfaction with the online training in using GeoGebra for mathematics instruction.


Abstract for 22070

22070  Incorporating digital interactive figures: Facilitating student exploration into properties of eigenvalues and eigenvectors        

Ryan Peffer - Judi McDonald - Sepideh Stewart       USA   

Washington State University; University of Oklahoma        


Abstract          Linear algebra is a key topic in mathematics and many other disciplines. In this paper, we consider a set of digital interactive figures (I-figs) using Mathematica created for linear algebra students in introductory and advanced courses, which prioritize pattern-seeking and examples over arithmetic processes. The figures discussed here are a part of digital worksheets designed to facilitate students' ability to visualize and work with eigenvalues and eigenvectors. Minimizing student computation for the benefit of conceptual focus while looking at an unlimited number of examples is an overarching theme. Different design intentions are explored for each of the four example figures. The worksheets provide a foundation for motivating students to participate in a system of observation, conjecture, proof, and theorem. Students were further supported through classroom lessons and additional homework activities.


Abstract for 22071

22071  Learning guidance based on the elimination singularity phenomenon        

Tadashi Takahashi - Tomohiro Washino       Japan  

Konan University      


Abstract          In the study of mathematics, when two items have concepts in common, understanding the relationship between them can be subject to overgeneralization. The technique that applies a simulation using a neural network on the loss surface used to analyze the overlap singularity phenomenon in previous research [4] is extended to the elimination singularity. In elimination singularity, students who answered correctly immediately after learning combinations understand superficially, and students who answered semi-correctly after learning combinations, time passes are affected by overgeneralization. Findings from this analysis are used to formulate learning guidance for teachers of mathematics.


Abstract for 22074

22074  Problem Research and Use of ICT in Mathematics Education        

Norie Aoki - Hideyo MAKISHITA   Japan  

Functional Control Systems; Graduate School; Shibaura Institute of Technology; Civil Engineering; Shibaura Institute of Technology        


Abstract          In Japan, standards have been established for curriculum organization. In this paper, we describe the standards and the transition of the use of ICT. We also discuss the SSH project (Super Science High School), a national project to promote science and mathematics education, and present a case study of the use of ICT in one of the educational activities in the project, based on the author s experience, and describes its educational effects. Furthermore, based on the discussion of the case study, the direction of the use of ICT in statistics and mathematics education in the future will be proposed.


Abstract for 22076

22076  Some Geometric Relationships and Properties of the Cylinder Catenoid; and Helicoid            Porpach Phumsuwan - Napatchol Somnakit - Supanee Hnooheed - et al.    Thailand           

Faculty of Science and Industrial Technology; Prince of Songkla University; Surat Thani Campus; PSU. Wittayanusorn Surat Thani School THAILAND      


Abstract          In this study, we explore the cylinder, catenoid, and helicoid distinct mathematical and geometric objects with unique characteristics and relationships. Our focus is on investigating their geodesics, and we observe a connection between the catenoid and helicoid, both derived from cutting or twisting their respective shapes. While the cylinder has its own properties, the catenoid and helicoid are minimal surfaces with intriguing geometric traits. The catenoid forms by rotating a catenary curve around an axis, while the helicoid results from rotating and translating a straight line. Although these shapes lack a direct relationship, we designate the cylinder as the model surface for comparative analysis. Through this approach, we establish connections between the cylinder and helicoid, as well as the cylinder and catenoid, revealing insights into their relationships and geometric properties.


Abstract for 22077

22077  The Study of Geodesic Computations on Sphere and Spheroid with Optimized Numerical Methods   

Jaruwan Burintharakot - Nathaphon Boonnam          Thailand         

Faculty of Science and Industrial Technology; Prince of Songkla University; Surat Thani Campus; Faculty of Science and Industrial Technology Prince of Songkla University; Surat Thani Campus Thailand        


Abstract          This article explores the problem of determining the shortest distance on spheres and spheroids, which is fundamental for calculating geodesic paths and establishing the computational relationship for all possible routes on a surface. Geodesic paths hold significant importance across a wide range of geometric applications. The study classifies geodesic paths on surfaces into two categories: analytical and numerical and compares the Runge-Kutta and Euler methods as computational techniques. These methods are employed to solve nonlinear ordinary differential equations governing geodesic paths. Based on the comparative analysis, the Runge-Kutta method is identified as the preferred approach for accurate calculations in this study. To ensure efficient computation and swift determination of values, the proposed calculations are implemented using the Google Colab platform, leveraging its capabilities for efficient numerical computations. The results obtained through this study contribute to enhancing our understanding of geodesic paths on spheres and spheroids and provide valuable insights for geometric computations in various fields.


Abstract for 22084

22084  Fractal Formation in Copper Sulphate Aqueous Solution    Janchai Yingprayoon - Isika RODCHAROEN - Montita VICHAIDIT - et al.           Thailand         

STEM Center; PSU Wittayanusorn School; Suratthani; Thailand   


Abstract          The aim of this project is to study the fractals formation of copper in Copper Sulphate aqueous Solutions. The fractal formation can be observed in various phenomena that do not occur at equilibrium, called Euclidean geometry or non-integer dimensions. By studying the shape and form of the self-replicating Nonlinear Phenomenon from laboratory experiments, Electrodeposition, or electrolysis experiments of copper at the cathode of copper sulphate aqueous solution was performed. The branch formation (fractals) of copper metal (Cu2+) in copper sulfate (CuSO4) solution with different concentrations of 0.4, 0.8, and 1.2 mol/L were studied. When a potential difference is applied to the electrodeposition system, copper replicates itself at the cathode as a dendrite, forming a long solid copper with a higher elevation ('hill'' and ''valley'') statistically. The number of branches of fractals is linearly proportional to the time of experiment in all concentrations. The higher concentration will give more branches of fractals. The size or length of the longest branch is inversely proportional to the CuSO4 solution concentration, which in turn produces more hills than valleys. These uncertain structural patterns can be explained using fractal theory.


Abstract for 22091

22091  Virtual realities to study geometrical aspects of architectural heritage        José L. Rodríguez - Alvaro Martinez-Sevilla - Sergio Alonso           Spain  

University of Almer a; University of Granada


Abstract          In this paper we address the construction of virtual reality scenarios for the NeoTrie VR software, to make some 3D models of architectural objects manageable anywhere. Students will be able to see the pieces (muqarnas, vaults, arches, towers) in a 3D model, and manipulate and assemble them, to understand their spatial arrangement. They will also be able to use Neotrie tools to build and thus better assimilate the underlying geometric structures.


Abstract for 22093

22093  Mathematical Problem-Solving with GeoGebra      

Jerryco Jaurigue - MARIA ALVA ABERIN - Angela Fatima Guzon          Philippines     

Ateneo de Manila University; University of the Philippines Rural High School


Abstract          This paper reports the students processes when tasked to solve mathematical problems in Geometry using GeoGebra. Twelve Grade 10 students divided into 6 dyads participated in the study. Each dyad solved 3 problems using a laptop and their verbal conversations, social interactions, and screen activity were recorded and videotaped. The conversations were transcribed word for word and the transcripts were supplemented by the description of their GeoGebra activities. The qualitative analysis focused on mathematical problem-solving with technology (MPST) processes. The results revealed that grasping, analyzing, exploration, planning, creating, verification, and dissemination were the MPST processes that were usually observed. Challenging problems were characterized by a series of explorations and verifications which were made possible by the features of GeoGebra.


Abstract for 22095

22095  Perception of Learners on Virtual Learning Environment in Higher Mathematics in the Context of Nepal       

Prem Kumari Dhakal  Nepal 

Mid-West University; Nepal; Tribhuvan University; Nepal


Abstract          This paper aims to identify the perception of learners on virtual learning environments in Mathematics at the university level in the context of Nepal. Mid-West University was the study site. This is a qualitative case study design. All the students who were studying Mathematics in different semesters of graduate and undergraduate level in the year 2021 faculty of Education were the population of this study. Ten students were selected as participants using purposive sampling to represent the different ten districts of Karnali Province. In-depth interview was used as the tool for data collection. The interview was conducted using guidelines through phone and online calls using mobile. The interview was recorded on my mobile device and the points were noted in my notebook as well. All the collected information was transcribed, translated, and categorized to developed themes and analyzed in a descriptive manner. The result indicates that learners perceive virtual learning in higher level Mathematics as a necessity and an opportunity. Moreover, the participants said that virtual learning is a useful learning process, and it is better than face-to-face mode because it develops knowledge as well as skill, it also develops the habit of searching for resources, increases self-confidence and independence, provides permanent learning, saves expenditure and provides an opportunity to earn. Similarly, virtual classes can be continued during strikes and other difficulties like lockdowns and experienced and busy professors can take classes in their leisure time even with disabilities.


Abstract for 22103

22103  Enhancing Students Achievement and Investigating Students' Satisfaction in Learning Mathematics by Using Flipped Classroom   

Supotch Chaiyasang   Thailand         

Suan Sunandha Rajabhat University; Bangkok; Thailand    


Abstract The objectives of this classroom action research were to enhance students' mathematical achievement and to survey students' satisfaction with learning by using a flipped classroom. The participants were 32 grade 11 students who enrolled in the second semester of the academic year 2019 at a secondary school in Bangkok, Thailand. The topic used in this study was Vectors in Three Dimensions. The instruments were 7 lesson plans using flipped classrooms and a satisfaction survey. Before class, students studied online learning through video clips, handouts, homework, and quizzes. During class, students discussed the contents that they had studied from home, solved harder problems, and got individual help from the teacher. Learning lasted 14 periods with 50 minutes in each period. There were three cycles of action plans. Data was collected from pretest, posttest, and satisfaction surveys. Data were analyzed by using the Effectiveness Index (E.I.), mean, percentage, mode, and standard deviation. The results showed that: 1) the Effectiveness Index (E.I.) of the flipped classroom was 0.80 which revealed that students' achievement increased by 80 percent from the beginning and 2) students' satisfaction in three categories: students' understanding category, learning activities category, and learning atmosphere category by using flipped classroom were at satisfied, satisfied, and very satisfied, respectively.


Abstract for 30100


30100 Secondary Level Mathematics Teachers' Critical Reflections on the Use of GeoGebra for Teaching Trigonometry

Basanta Raj Lamichhane, Niroj Dahal, Bal Chandra Luitel

Saptagandaki Multiple Campus, Bharatpur Chitwan, NEPAL

Kathmandu University School of Education, Lalitpur, NEPAL


Abstract. Technology-integrated pedagogy creates an engaged learning environment that supports conceptual, relational, and procedural understanding. This study explores the roles of the GeoGebra Application (GA) in teaching trigonometry. The data were collected after and before the seven-day online training programs on using GA in teaching trigonometry through reflective experiences. We used critical reflective practice, cognitive theory, and social constructivism to interpret and make meaning. This study revealed that teachers had disempowering and negative images of trigonometry and its teaching before training. They believed trigonometry is an interpretation-free discipline and teaching as preparation for the final examination. Likewise, they lacked conceptual and relation understanding of the trigonometric knowledge and concepts that severely affected their teaching-learning activities. After the training program, the participant teachers

reported that GA is a handy technological tool that helps visualize abstract trigonometrical concepts, supports the development of positive images toward trigonometry, and fosters an engaged learning environment. Finally, this study signified that integrating GA in trigonometric teaching can positively affect respective teachers' thinking, knowing, and doing.

Abstract for 30102


30102 AI Chatbots as Math Algorithm Problem Solvers: A Critical Evaluation of Its Capabilities and Limitations

Niroj Dahal, Basanta Raj Lamichhane, Bal Chandra Luitel, Binod Prasad Pant

Kathmandu University School of Education, Lalitpur, NEPAL, Saptagandaki Multiple Campus, Bharatpur, Chitwan, NEPAL


Abstract. AI-based chatbots are appearing as a powerful tool for solving mathematical algorithm problems. These chatbots, trained on extensive datasets and natural language models of text and/or code, can understand and generate mathematical expressions. They can show step-by-step solutions to math problems and explain the associated concepts. This paper evaluates AI chatbots like Google Bard, ChatGPT, Bing Chat, and Wolfram Alpha as problem solvers for math algorithms for learners, teachers, and teacher educators from school to university. We discuss how AI recognizes mathematical expressions and equations from simple arithmetic, algebra, trigonometry, and statistics examples. We explore how AI-based chatbots solve basic to advanced math problems, their ability to offer personalized solutions, and their potential to improve students math learning. We highlight their capabilities and limitations. Challenges faced by AI chatbots include a limited understanding of natural language models and prompt engineering, an inability to solve complex math problems, and the potential for bias. Future research should focus on improving AI chatbots' accuracy, reliability, and problem-solving capabilities. Despite the advancements in AI chatbots, students should continue interacting with human teachers to develop their cognitive math skills and conceptual understanding.




Abstracts for Presenting with Abstracts Only

Abstract for 22026

22026  Application of TI graphing calculator in innovative learning activities of mathematics in secondary schools  

Li Li   

Experimental School of Beijing Ritan High School, China


Abstract. As a learning tool, TI graphing calculators play a very important role in helping students explore the real world in activities. This paper focuses on the application of TI graphing calculators in mathematics classroom teaching, project-based learning, and problem-solving. By using TI graphing calculators in mathematics teaching, we can combine information technology with teaching materials to stimulate students' ability to innovate.


Abstract for 22028

22028  Cut Locus Analysis on Surfaces of Revolution for Enhanced Space Station Location           

Phattaraphorn Hama - Thunphitcha Koikim - Pinyada Prakobsin    

PSU. Wittayanusorn Surat Thani School; Surat Thani; 84000; Thailand     


Abstract. This research investigates the application of cut locus analysis on surfaces of revolution to improve the method for planning the location of a space station. Surfaces of revolution, obtained by revolving a graph around an axis, have unique shapes that affect how a spaceship can navigate efficiently. By studying the cut locus, which represents the points where the shortest paths touch the surface, we aim to enhance the effectiveness of spaceship path planning in curved environments. To achieve this, we utilize mathematical modeling, computer simulations, and experiments. We develop algorithms to calculate the cut locus on surfaces of revolution and integrate them into existing path-planning methods. Through simulated scenarios, we compare the performance of our approach with traditional methods to evaluate its benefits. The results of this research will contribute to spaceships by providing insights into the cut locus on surfaces of revolution and its impact on path planning. By incorporating cut locus analysis into spaceship navigation algorithms, we can help spaceships find optimal paths, navigate complex surfaces more efficiently, and effectively avoid obstacles. These findings will be valuable for various applications, such as spaceship exploration, industrial automation, and autonomous navigation in curved environments.


Abstract for 22041

22041  Using automatic speech recognition technology and text-to-speech synthesis technology to enhance undergraduate students' construction and validation of mathematical proofs.

Kyeong Hah Roh - Yong Hah Lee     Arizona State University; Department of Math Education, College of Education Ewha Womans University Seoul; Korea 


Abstract. Automatic speech recognition (ASR) technology automatically enables computers to recognize and transcribe spoken language into written text. This technology has been used in education to provide students with personalized feedback on their spoken language skills or to support students literacy development. On the other hand, text-to-speech (TTS) synthesis technology can allow students to listen to text and help to improve reading comprehension. In this paper, we focus on the potential of these technologies to support students' construction and validation of mathematical proofs. This study aims to examine how ASR and TTS technologies could promote students self-regulated reasoning while constructing and validating mathematical proofs. We report results from task-based interviews with undergraduate students who exhibited logical inconsistencies in their mathematical assertions in the pre-screening survey. The interviews were designed to invite students to use ASR technology to initiate writing their first draft of a mathematical proof, and to use TTS technology repeatedly to refine their written proof. In the presentation, we provide insights into how such technology could be used to assist students in the construction and validation of mathematical proofs. We also discuss the challenges students and instructors might face with these technological aids.


Abstract for 22043

22043  Predicting Boat Movement in Windy Conditions through Vector Field Analysis   

Supanee Hnooheed - Phatcharee Udomsup - Khonkaraponpan Rodpangwan          

31 Moo 6; Makham Tia; Mueang; Surat Thani; Thailand 84000     


Abstract. This research focuses on developing a method to forecast the movement of boats when faced with strong winds. By analyzing the flow of vector fields, we aim to understand how the wind affects the trajectory of boats. This knowledge is essential for safe navigation and improving performance in sailing competitions. To achieve this, we gather wind data from various sources and combine it with specific boat characteristics. By studying the vector field created by the wind, we can calculate the forces acting on the boat and predict its path. We employ computational techniques, such as computational fluid dynamics, to simulate the interaction between the boat and the wind. Machine learning algorithms may also be used to enhance the accuracy of trajectory predictions. The results of this research will have applications in marine navigation, boat design, and performance optimization. The ability to predict boat trajectories accurately in windy conditions will benefit sailors, ensuring their safety and helping them plan better routes.


Abstract for 22048

22048  The use of a DGE to investigate linear constructs.  

Stian Hirth     

University of Bergen 


Abstract. Many university students find the purely arithmetic approach to linear algebra (LA) to be confusing and not easily relatable. Research also suggests that the high level of abstraction in LA is a big hurdle for many students (Dogan, 2018). I hypothesize that using geometrical visualizations as a supplement to the regular lectures in the course may contribute to two things: (i) Help the students to understand the relationship between the arithmetic and the geometric aspects of the linear constructs in the course. (ii) Increase the understanding of certain LA results (for example det(A)=0 if and only if A is not invertible) by giving them the opportunity to discover geometrical arguments while working with visual representations. The focus of this presentation is the intervention that will be used in my PhD to test this hypothesis. A Dynamic Geometry Environment (DGE) can be used to produce visual representations of several of the linear structures included in a typical linear algebra curriculum. Linear concepts and operations that are possible to produce and interact with using DGEs include (but are not limited to): - Systems of linear equations - Linear dependency/independency - Matrix operations - Determinants - Column spaces and null spaces - Eigenvalues and eigenvectors - Projections Mathematical investigation tasks are tasks where the main objective is to investigate some mathematical phenomena. DGEs are well-equipped for investigations because they have built into them tools that allow for guessing, pattern-seeking, making connections, predicting, hypothesizing, and proving (Leung & Baccaglini-Frank, 2016). A couple of typical dynamic tools found in DGEs are: - Dragging tools making it possible to drag figures and coordinate systems to explore how a change in position might affect the studied phenomena. - Sliders making it possible to change the values of variables in the program to see how it affects the studied phenomena. In my PhD project LA students will be working in groups of 3-4 students to solve mathematical investigation tasks related to linear constructs. The DGE GeoGebra will be used to solve the tasks. GeoGebra is well-equipped for producing and working with a variety of linear structures. The task sheets to be used are comprised of general instructions, explanations of the tools in GeoGebra, and discussion tasks relating to the structures produced. The aim of the activity is for the student groups to be able to make a connection between the constructions in GeoGebra and the LA results (definitions, theorems, etc.) relating to the constructions. The emphasis in the presentation will be on the investigation tasks, and what the students might be able to investigate/discover when working with them. Methods for data generation and analysis in the project will also be presented. References: Dogan, H. (2018). Mental Schemes of Linear Algebra Visual Constructs. In (pp. 219-239). Cham: Cham: Springer International Publishing. Leung, A., & Baccaglini-Frank, A. (2016). Designing Assessment Tasks in a Dynamic Geometry Environment. In (Vol. 8, pp. 77-98). Switzerland: Switzerland: Springer International Publishing AG.


Abstract for 22049

22049  A monotone iterative method for solving singular nonlinear diffusion problems.              

Shih-Hsiang Chang     Far East University, Taiwan 


Abstract. A monotone iterative method involving Green's function is presented for solving the singular nonlinear diffusion problems y''''(x)+m/x y''(x) = f(x,y), y''(0)=0, Ay(1)+By''(1) = C, where 0 <= x <=1, m>=0, A>0, B>=0, and C>=0. Further, the nonlinearity f(x,y) is assumed to be continuous in 0<= x <=1, but it is allowed to be singular in y and sign-changing. Existence and uniqueness results for such problems are established using the method of lower and upper solutions with a monotone iterative technique under the restriction that f(x,y) is non-increasing in y in the region formed by the lower and upper solutions. This guarantees the uniform convergence of the proposed iterative algorithm. Different from the previous research works, there is no need at all to introduce an artificial term with an adjustable parameter in the differential equation of the discussed problems. This makes it simpler to calculate the explicit expression of Green s function related to such problems. The approach is illustrated on four singular nonlinear diffusion problems including some real-life applications.


Abstract for 22053

22053  On super domination number of the cross product of paths 

Nuttapusit Keatipimol - Nitithon Budnamphet         

PSU Wittayanusorn Suratthani School


Abstract. The open neighborhood of a vertex v of a graph G is the set N(v) consisting of all vertices adjacent to v in G. A subset D of V(G) is called a super dominating set of G if every vertex u in a set V(G) - D, there exists v in D such that the intersection between N(v) and V(G) - D is the set {u}. The super domination number of G is the minimum cardinality among all super dominating sets in G. The path P_n is a connected graph with vertex set V(P_n) = {0, 1, 2, , n-1} and edge set E(P_n) = {{i, i+1} | i = 0, 1, 2, , n-2}. For any graphs G and H, the cross product of G and H is denoted by GxH is the graph with vertex set V(GxH) = V(G)xV(H) and edge set E(GxH) ={{{u, v}, {x, y} | {u, x} is edge in G and {v, y} is edge in H}. In this article, we obtain some upper bounds for the super domination number of P_n x P_m for some positive integers n and m.


Abstract for 22062

22062  Contribution to the learning of mathematics by ICT

Tsutomu Ishii  Bunkyo University, Japan.   


Abstract. The introduction of ICT in Japanese schools is progressing. The impact of online classes due to COVID-19 is the reason. Remote teaching has become possible. And it is contributing to the improvement of the quality of classes. In this paper, we target classes in Japanese elementary schools. Afterwards, we focus on concrete instruction and the use of ICT, in children's learning situations. To examine the actual class from these three perspectives. As a result, the effect of ICT is clarified.


Abstract for 22082

22082  Astronomical Simulation for Constellation in Celestial Hemisphere          

Hataipat Rakluangsakul - Kavisara Jivarut   

PSU Wittayanusorn Suratthani School


Abstract. Astronomy is gaining popularity in Thailand and simulated domed observatories have emerged to make it more accessible. This research uses non-Euclidean geometries - Hyperbolic and Elliptic - to simulate star clusters as a single celestial dome. The study investigates the resulting appearance of the sky, where all-star clusters converge, revealing various phenomena. The goal is to provide an immersive experience of both the southern and northern celestial hemispheres, offering new insights into constellations in these regions. Parallax angles from telescopic observations and accurate simulations align southern celestial star clusters with the northern hemisphere. Further studies are encouraged to deepen our understanding of non-Euclidean geometries in astronomy and their potential applications. This research fosters interest in astronomy and offers a captivating perspective on celestial phenomena.


Abstract for 22110

22110  The Alhambra was visited by a mathematician.      

José A. Martínez-Aroza        

University of Granada, Spain


Abstract. The Alhambra is a palace and fortress complex located in Granada, Andalusia, Spain. The complex was built in 1238 and continuously modified by the successive Nasrid rulers, until the conclusion of the Christian Reconquest in 1492. The palace complex is designed in the Nasrid style, the last blooming of Islamic art in the Iberian Peninsula, that had a great influence on the Maghreb to the present day, and on contemporary Mudejar art, which is characteristic of Western elements reinterpreted into Islamic forms and widely popular during the Reconquest in Spain. In this presentation we will see some mathematical aspects of the complex, paying special attention to the richness of proportions and the mathematical structure of the surprisingly wide variety and complexity of tile mosaics that can be found in this monument.


Abstract for 22112

22112  Utilizing Puzzles and Games in Regular Classes for Primary Schools: Why What; and How

Chuanbo Zuo - Shuaitao Zuo - Xuanfang Long        

Hawgent Technology Center in Mathematics (Guangzhou); Beijing Normal University - Hong Kong Baptist University United International College; Guangxi Normal University          


Abstract. The After-Class-Schooling policy published by the Chinese Government in 2017, began to be really valued after another policy called Double Reduction (Shuangjian) was issued on July 24, 2021. Under the Double Reduction policy, Off-Campus Institutes are not allowed to teach kids of grade 1 to 9 mathematics, and teachers cannot teach their students mathematics during the After-Class Schooling. Therefore, parents of primary and secondary school students became more anxious about their children s math scores. As we all know, the process of Solving puzzles and challenging brain games can promote, develop, and enhance the abilities of observing, calculating, reasoning, and logical thinking which are the needed bases for learning mathematics. This presentation is going to introduce the background, thinking, and practice of utilizing puzzles and games in regular classes of primary schools to improve kids' mathematical performance.


Abstract for 22113

22113  Robust Optimization Techniques for Disease Prevalence Estimation in Pooled Testing Scenarios       

Md Sarker      

Radford University; Radford; VA 24142, USA


Abstract. Efficient surveillance of infectious diseases is achieved through group testing. The benefits of this approach depend on the pool size used. Existing statistical methods to determine optimal pool sizes often rely on simpler pooling protocols or perfect diagnostic assays. Our work addresses these limitations by introducing a general optimization technique. We evaluate the efficiency of disease prevalence estimation and associated costs using group testing data. The optimal pool size is determined by minimizing efficiency measures. To mitigate reliance on an a priori disease prevalence estimate, we employ a multistage adaptive pooling approach. We demonstrate that our approach significantly enhances estimator efficiency, even in cases of misspecified a priori estimates. Additionally, we provide a user-friendly software application using the R shiny package for straightforward implementation of our optimization techniques.



Abstract for 32001

32001 Reform and Exploration of Mathematics Teaching Methods Based on the Concept of Core Literacy and Creative Adoption of Interactive Web-based Platform

WU Guannan Tongxiang Puyuan Tongxing School, Tongxiang City, Zhejiang, China


Abstract. Tongxing School in Puyuan, Tongxiang City, is actively exploring "Internet + Education", striving to achieve the construction of a digital campus environment, continuously improving the level of campus informatization, and leading the education with the support of informatization. Our school takes "digital empowerment for teachers and students" as its theme, with the help of Netpad (, a Chinese online mathematics tool, steadily promotes the construction of the mathematics laboratory. With such an exploratory environment, students can visually and graphically comprehend many abstract mathematical concepts and complex geometric figures on the screen through operation, observation, communication, and other activities, making difficult problems easier to understand and boring graphics more interesting and vivid. In the mathematics laboratory, students create mathematical graphics, apply mathematical knowledge, solve mathematical problems, compare mathematical skills with other students, and improve their mathematical literacy. The reform of classroom teaching methods has been steadily promoted, and with the help of the massive online resources in the Netpad, our teachers have simplified the process of preparing for classes, increased the opportunities for teacher-student interactions with its convenient operability, and optimized the effectiveness of teaching and learning implementation by means of its powerful visualization functions, thus, an efficient mathematics classroom has been created smoothly. The enhancement of students' digital literacy has been implemented continuously, and through a long period of cultivation, students in our school have already formed the habit of actively searching for and acquiring resources related to the classroom content before class, and they are able to make effective use of the teaching resources collected by themselves or provided by the teachers and share with their classmate's different insights into the content they have learned. Some of them who have better learning abilities can even make precise and creative use of the teaching resources and truly achieve independent learning.

Focusing on the future, Tongxing School needs to continue to explore the role of digitalization in education and teaching and build a rural digital teaching system with Tongxing characteristics.



Abstracts for Hands-on workshops

Abstract for 22030

22030  Using GeoGebra to Visualize 3-Dimensional and 2-Dimensional Figures 

Pathamaporn Awachai - Sasiwan Maluangnont - Sutharot Nilrod - et al.    

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand


Abstract. Several research studies indicate that students have difficulties in learning dimensional relationships of the geometric figure. Students usually struggle with visualizing images of the front, sides, and top of the given 3-dimensional figures. The use of technology, such as GeoGebra, is one of the tools to demonstrate 3-dimensional and 2-dimensional figures. This workshop will start with introducing how to use basic geometry tools in GeoGebra. Then, the participants will use the basic geometry tools to create 3-dimensional figures from cubes and vectors. The participants will be able to show images of viewing the front, sides, and top of the created 3-dimensional figures. Also, pedagogical examples and discussion of implementing the created instructional media in classroom instruction will be included in this workshop.


Abstract for 22033

22033  The Usability of GSP 5.06 in Designing and Creating Mathematics Instructional Materials        

Siriwan Jantrkool - Pilaluck Thongtip - Alongkot Maiduang - et al.

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand; The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand


Abstract. Currently, computers and various technologies are being used more extensively to assist in classroom learning. The Geometer's Sketchpad 5.06 (GSP 5.06) is a software that helps teachers incorporate technology in teaching mathematics to make it more meaningful for students. It fosters a positive attitude towards mathematics and enhances mathematical skills and processes. In this workshop, participants will learn how to use GSP 5.06 to create custom tools for producing instructional materials that teach front, side, and top views of three-dimensional geometric figures composed of cubes. These tools can help develop students spatial sense and visualization.


Abstract for 22035

22035  A grid paper as a technological tool for creativity in the Too Pretty to Eat STEM Activity           Alongkot Maiduang - Alongkorn Tangsanguantham          

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand  


Abstract. This is a workshop, where participants will enjoy a creative STEM activity Too Pretty to Eat. This activity will challenge the participants to use a grid paper to design the cuttings of a square slice of bread into two and four congruent parts, as many ways as possible, to design attractive fanciful sandwiches. This activity aims to stimulate the inherent creativity of the participants by asking them to design new sandwiches that they have never seen before. The workshop is also intended to analyze the role of a grid paper as a technological tool in this visualization task. Using a grid paper to design the cutting of a square into two and four congruent parts Suitable for STEM Teachers from K-Grade 9.


Abstract for 22036

22036  Using Mathigon Application to Transform Mathematics Classrooms         

Ronnachai Panapoi - Phattharawadee Hadkaew - Jannapa Uttama - et al.   

The Institute for the Promotion of Teaching Science and Technology (IPST) ; Ministry of Education; Thailand  


Abstract. Due to the spread of COVID-19, mathematics classes have recently moved from face-to-face settings to online ones. Many mathematics teachers have struggled with locating suitable digital tools to support their innovative teaching strategies. Most mathematics teachers use Google Classroom, ZOOM, and Microsoft Team applications. However, within these platforms, teachers still need to create digital instructional materials to be employed during their lessons. Therefore, free and friendly-to-user digital platforms with mathematically provided digital instructional materials need the teachers. This workshop will (1) introduce you to a free application called Mathigon that can make a traditional mathematics classroom more interactive and individualized; (2) show you examples of lessons/courses using this application, (3) assist you in utilizing the application, and (4) discuss challenges of using the application.


Abstract for 22038

22038  Using board games to organize learning about intellectual property           

Sayamchai Suksai - Dr.Nusavadee Pojananukij,

the Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand; The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand      


Abstracts. Today's society pays more attention to Intellectual Property (IP) knowledge than in the past, as inventions or product designs that infringe upon the intellectual property of others result in the loss of many benefits for creators, such as product patents, copyrights, or enormous expenses. Despite the abundant information on IP, the various categories and their details might cause problems in teaching and learning. Therefore, this activity uses an educational board game to organize learning about intellectual property. The objective is to enable learners to gain knowledge on important parts of the IP, invention patents, and product design patents. Secondly, it guides the learners on how to improve a product whose patent belongs to others. Finally, it enhances learners' awareness of infringement and the ability to protect their own products. Additionally, the use of board games also attracts learners' attention and help them develop important skills and competencies, such as analytical thinking, effective communication, and problem-solving skill.


Abstract for 22045

22045  Enhancing Computational Thinking in Primary Education through Unplugged Learning Activities     PHORNPHIMON TANGCHAISIN - JINDAPORN MUAKMAUNWAI - NIRAMIS PAINPRASERT - et al.   

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand.


Abstract. The successful concept of teaching computing science without using a computer, known as Computer Science Unplugged, successfully enhances computational thinking skills in primary school students. This workshop showcases Unplugged activities and instructional materials developed by the Institute for the Promotion of Teaching Science and Technology (IPST) to foster computational thinking (i.e., Decomposition, Pattern Recognition, Abstraction, and Algorithm). The four Unplugged activities that are highlighted in this workshop are Buzz Builders Puzzle, Fancy Ferris Wheel, The Cube Town, and Adventure in Wonderland. These activities create a positive learning environment, where students develop problem-solving skills and deepen their understanding of computational thinking concepts. Additionally, Unplugged activities play a significant role in fostering meaningful learning experiences, enabling pupils to apply their knowledge in diverse contexts. Regarding the utilization of IPST''s instructional materials, participants decode the presented Unplugged activities to create engaging learning experiences that enhance primary school students'' logical thinking and problem-solving skills. These activities empower pupils with essential skills to navigate real-world problems and challenges while thriving in a technology-driven society.


Abstract for 22085

22085  Creative Math STEM

Janchai Yingprayoon 

STEM Center; PSU Wittayanusorn School; Suratthani; Thailand   


Abstract. Many children find mathematics difficult and boring. But they are curious, and they love to have fun with exciting things around them. Appropriate activities can be found to stimulate them to have fun and love learning mathematics. The workshop showed ways of developing creativity in mathematics and technology education to increase intellectual curiosity, develop problem-solving and thinking skills, promote discovery, and unleash creativity. There were five activities in the workshop.


Abstract for 22086

22086  Mathematics Origami           

Pongsakorn Kaewcholkram - Janchai Yingprayoon,

STEM Center; PSU Wittayanusorn School; Suratthani; Thailand; STEM Center; PSU Wittayanusorn School; Suratthani; Thailand            

Abstract. This workshop presents how to teach mathematics with paper folding activities or Origami. Introducing active learning activities, and creative mathematics activities outside the classroom, which makes the classroom meaningful with fun learning activities.


Abstract for 22087

22087  Fun with Coding Robots       

Janchai Yingprayoon,

STEM Center; PSU Wittayanusorn School; Suratthani; Thailand   


Abstract. This workshop shows how to teach coding and robotics in everyday life applications. A basic idea of how to write simple computer programs by using robots will be introduced. Creative thinking and decision-making activities are also presented.

Abstract for 22088

22088    Using Desmos Graphing Calculator and FFT App for teaching High school Mathematics and Physics             

Pongsakorn Kaewcholkram - Janchai Yingprayoon,

STEM Center; PSU Wittayanusorn School; Suratthani; Thailand; STEM Center; PSU Wittayanusorn School; Suratthani; Thailand.


Abstract. Learn how to use the Desmos graphing calculator tools to explore ways that students can develop their own power as mathematical problem solvers. Explore points, tables, functions, inequalities, sliders, and lists. Leave excited to learn more and with the resources to continue practicing. Fast Fourier Transform App will also be introduced.


Abstract for 22107

22107  Hands-on Training on SageMath     

Ajir Kumar    

Department of Mathematics; Institute of Chemical Technology; Nathalal Parekh Road; Matunga (E); Mumbai 400 019 (INDIA)


Abstract. SageMath is a free and open-source computer algebra system (CAS) based on Python programming language and it offers immense computing power. One can use Sage Math for a wide variety of applications from basic computations and visualization to linear and abstract algebra, number theory, graph theory differential geometry, etc. It can also be used as a pedagogical tool in mathematics teaching. This Hands-on workshop on SageMath aims to introduce the basics and advanced features of SageMath. We plan to explore concepts in Calculus, linear algebra, and number theory along with visualization during the workshop.


1. Sagemath Official Website:

2. Mathematical Computation with Sage by Paul Zimmermann et al.

3. NPTEL Online Course on Computational Mathematics with SageMath by Ajit Kumar (


Abstracts for Poster Sessions

Abstract for 22034

22034  Battleship via Conic Section in GeoGebra   

Pinyada Damdoung - Sasiwan Maluangnont

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand  


Abstract. Conic section is the abstract concept, which students learn in high school. Students usually remember standard forms of equations of conic sections, convert given equations to standard form, and write graphs of conic sections. The abstraction of this concept makes students bored with the lesson. Using games is one of the ways to interest and motivate students. Students will enjoy it when they apply their understanding of the conic section to solve the given problem. This poster presentation will present instructional material named Conic Section Circle (CSC) . The CsC is a game created by GeoGebra software. To play the game, students have to apply their understanding of the standard form of the equation of a circle to solve a problem about destroying a battleship army. The CsC game also comes with an activity worksheet which includes game instructions and guiding questions.


Abstract for 22037

22037  Enhancing Students Mathematical Attitude by Using Cartoon Animation about Mathematicians Historical Stories     

Woranart Yoosook - Jinnadit Laorpaksin - Ratinan Boonklurb        

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand; Faculty of Education; Chulalongkorn University; Thailand; Faculty of Science; Chulalongkorn University; Thailand


Abstract. Since the beginning of the modern era, several students have been disrupted from learning because of social media, while knowledge has still been a significant basis for well-being in their future. Although several research shows that attitude has direct effects on students learning, in Thailand, there is a small number of learning materials that are accessible via social media and enhance attitude toward mathematics. Therefore, IPST developed mathematical learning media in the form of a cartoon animation series called The Great Mathematicians. The cartoon animation series presents an autobiography of 20 crucial mathematicians with the purpose of enhancing students' attitudes toward mathematics. The Great Mathematicians are broadcast via on the Math IPST channel. After implementing it in classrooms, results indicate that the Great Mathematicians Series can promote students' attitudes toward mathematics and increase students' interest in learning Mathematics.


Abstract for 22039

22039  Using Augmented Reality to Enhance Mathematical Learning       

Ronnachai Panapoi - Jannapa Uttama           

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand  


Abstract. With the rapid growth of technology, students now have easier access to smartphones and other devices. Due to this accessibility, augmented reality (AR), a technology that creates interactive experiences by fusing computer-generated information with the real world, can now be used in the field of education. With AR, teachers can demonstrate topics virtually in a variety of subjects. These illustrations aid students in better understanding the ideas. For instance, the science AR application is designed to help students determine atomic weight, chemical elements, and chemical reactions. Naturally, this setting can enthrall students and help them remember the topics. In mathematics, some augmented reality (AR) is implemented to help students master challenging concepts like geometry. This study aims to comprehend how teachers employ augmented reality (AR) objects in Thai mathematics textbooks and which of the objects can improve students'' mathematical learning. To help achieve these objectives, questionnaires will be given to teachers about how they incorporate each AR object into their courses and how their students engage with them. Along with classroom observation, individual interviews will be undertaken to glean some insights. Findings will help us better understand the types of AR objects that can address students problems with learning mathematics and how to employ them in mathematical lessons.


Abstract for 22040

22040  Using GeoGebra to Study the Relation between Degree and Radian          

SUTHAROT NILROD - Pinyada Damdoung           

Institute for the Promotion of Teaching Science and Technology (IPST); Institute for the Promotion of Teaching Science and Technology (IPST), Thailand 


Abstract. Degree and radian are used to measure angles in Trigonometry. Students usually remember that 360 degrees equal to 2Pi radians. Then, they apply the remembered statement to convert the given angle size from degrees to radians and vice versa. However, the students do not understand indeed definition of the radian. As a result, their understanding of the relation between degree and radian may not be retentive. The use of instructional material, that allows students to explore and discover the important concepts about degree and radian, is one of the ways to solve this problem. This poster presentation will present an instructional material named The Relation between Length and Radius of the Circle (RLRC) . The RLRC material is created by GeoGebra software. It allows students to investigate, make a conjecture, and make a conclusion about the relation between degree and radian. The RLRC material also comes with an activity worksheet. The worksheet consists of exploration steps and questions, which guide students along their learning processes.


Abstract for 22042

22042  Deep learning-based three-dimensional computational image reconstruction         Mansik Jeon - Daewoon Seong - Youngae Gu - et al.          

School of Electronic and Electrical Engineering; College of IT Engineering; Kyungpook National University; School of Electronic and Electrical Engineering; Kyungpook National University; 80 Daehak-ro; Buk-gu; Daegu 41566; Republic of Korea; Department of Nuclear Medicine; Chonnam National University Medical School & Hwasun Hospital; Department of robotics engineering; DGIST Korea (South)


Abstract. Photoacoustic microscopy (PAM) is a non-invasive, label-free functional imaging technique that provides high absorption contrast with high spatial resolution. Spatial sampling density and data size are important determinants of the imaging speed of PAM. Therefore, sparse-sampling methods that reduce the number of scanning points are typically adopted to enhance the imaging speed of PAM by increasing the scanning step size. For the reason that sparse-sampling methods sacrifice spatial sampling density, deep learning-based reconstruction methods have been considered as an alternative; however, these methods have been applied to reconstruct the two-dimensional PAM images, which is related to the spatial sampling density. Therefore, by considering the number of data points, data size, and the characteristics of PAM that provide three-dimensional (3D) volume data, in this study, we newly reported deep learning-based fully reconstructing the under-sampled 3D PAM data, which is obtained at the actual experiment (i.e., not manually generated). To achieve reconstruction without limitations on the under-sampling ratio along all three axes, the super-resolution ResNet was modified to obtain a flexible upscale ratio for single- and dual-axes. Thus, the sparse 3D PAM dataset was successfully reconstructed in all directions for various under sampling ratios. The performance of the proposed model was quantitatively evaluated using five different factors and compared with that of the interpolation methods. The results of quantitative analyses demonstrate that the proposed method exhibits robustness and outperforms interpolation-based reconstruction methods at various under-sampling ratios, enhancing the PAM system performance with 80 times faster-imaging speed and 800 times lower data size. Moreover, the applicability of this method is experimentally verified by upscaling the sparsely sampled test dataset. The proposed deep learning-based PAM data reconstructing is demonstrated to be the closest model that can be used under experimental conditions, effectively shortening the imaging time with significantly reduced data size for processing. In addition, Specifically, the proposed method boosts the imaging speed by reducing the effective number of imaging points, which makes it suitable for PAM applications requiring high imaging speeds, such as the monitoring of dynamic response, neural activity, and hemodynamics.


Abstract for 22068

22068  Prediction of Saving Money in GeoGebra   

Sasiwan Maluangnont - Sutharot Nilrod       

The Institute for the Promotion of Teaching Science and Technology (IPST); Ministry of Education; Thailand


Abstract. The application of sequences and series in high school mathematics involves predicting savings, wherein students learn and apply mathematical formulas to determine the amount of money saved in a given scenario. However, students often fail to recognize the interrelations among the principal amount, interest, length of deposit time, and their impact on the total savings. This poster presentation introduces a mathematics activity titled 'Prediction of Saving Money.' The activity is complemented by instructional materials designed using GeoGebra software. Through this activity and the accompanying instructional material, students are provided with opportunities to make conjectures, conduct investigations, and draw conclusions regarding the future total amount of saving money in each situation.


Abstract for 22108

22108  Practice and Assessment of Creating Mathematics Questions through Interaction with a Computer       

Shigeki KITAJIMA   

Meisei University       Japan  


Abstract. The purpose of this study is to assess the practice of creating mathematical questions through interaction with a computer for second-year university students and to examine the results and challenges of this practice. In this study, performance criteria were introduced to allow students to self-regulate their performance. The analysis of the students' quiz questions showed that the quality and quantity of their efforts in programming exercises in asynchronous learning improved.


Abstract for 22109

22109  Practical Research on Performance in STEM Education: Focusing on Awareness of Auxiliary Lines for Geometric Problems Using an Eye-Tracker     

Yutaka OHARA         

Gakushuin University; Japan            


Abstract. (1) Problem Definitions The STEM education trend is getting more attention than ever before due to technological advancements. In the field of mathematics as well, it is desirable to promote education that integrates technology in terms of both content and method. In this research, I present a qualitative analysis based on data collected by means of an eye-tracker tool, concerning the outcome of mathematical problem-solving at the middle school level. Because, in geometric problems, the act of drawing auxiliary lines is often left to the intuition of the students, and although this is the key to facilitating the solution, it is difficult to support it (Palatnik & Sigler,2019). (2) Objectives The purpose of this research is to make clear the similarities and differences in the visual observation of the question itself between mathematics teachers and students. In addition, by analyzing eye movements in solving geometric problems, we obtain suggestions on how wearable eye-tracking technology can be used for teaching mathematics (Casalvieri & Gambini, 2022). (3) Methods For this purpose, a total of 4 subjects were involved in this experimental research (novice expert approach) with a two-pair design employed. In order to clarify how to see the place where auxiliary lines should be drawn in similarity problems, I analyzed the points that mathematics teachers and junior high school students pay attention to using eye tracks. (4) Results Gaze measurements with an eye-tracker showed clear differences in attention areas between mathematics teachers and students. At the same time, the reasons for this were qualitatively confirmed by protocol analysis of the interviews. Specifically, they had a common awareness of finding similar triangles. However, the middle school students saw vaguely at the partial figure, while the mathematics teachers first looked at the whole, and then focused on parallel lines to identify the corresponding or alternate angles. These findings showed that the wearable eye-tracker gives informative feedback about the visual attention for auxiliary lines. (5) Conclusions By using technologies such as eye-tracker, we could expect learning guidance that compensates for the weaknesses of conventional instruction in geometry from the perspective of STEM education. How this finding could be more standardization in mathematics teacher training courses is open to discussion. (6) References Casalvieri, C., Gambini, A., (2022), Analysis of Solving a Cauchy Problem Using an Eye-Tracker, International Journal for Technology in Mathematics Education, vol.29, no4, pp.189-199. Palatnik, A., Sigler, A. (2019), Focusing Attention on Auxiliary Lines When Introduced into Geometric Problems, International Journal of Mathematical Education in Science and Technology, vol.50, no2 pp.202-215.