Abstract for 22122

Cracking the Enigma Code: Beyond the Bombe

Authors: Adam Downs, Neil Sigmon, Rick Klima

Affiliations: Appalachian State University, Radford University

The work of Allied codebreakers in the cryptanalysis of the Enigma cipher machine during World War II has been well-documented, and rightfully recognized as one of the supreme achievements of the human intellect. One of the trickiest parts of this analysis related to the plugboard, which contributed by far the largest factor to the total number of configurations of the entire machine. To determine the daily plugboard connections, codebreakers used electromechanical devices called the bombe and checking machine. After they found the plugboard connections though, they still needed to discover some additional machine settings. The difficulty in discovering these additional settings varied depending on which branch of the German military had created the messages under attack, since each branch used slightly different procedures. The process was in fact significantly more difficult for messages created by the German Navy, as opposed to those created by either the German Army or Air Force. In this paper, we will describe and demonstrate some of the procedures involved in recovering this additional information that was needed to fully cryptanalyze the Enigma machine. To assist in demonstrating these procedures, technology involving Maplets will be used.

Abstract for 22144

Heptahedra each having a pair of parallel faces and their applications in Sangaku constructions

Author: Jen-chung Chuan

Affiliations: National Tsing Hua University

Introduction
Nathan Altshiller Court first studied a tetrahedron with all edges tangent to one single sphere, and coined the term “circumscriptible tetrahedron”. Borrowing the idea, a polyhedron having all edges tangent to a midsphere is said to be circumscriptible. For a circumscriptible polyhedron, the circle formed by taking the intersection of a face with the midsphere is thus tangent to each edge of the face. Hence each face admits an incircle. A circumscriptible heptahedron is therefore associated with a family of 7 circles on the midsphere, with each circle tangent to 3 or more other circles of the family and the edges of the heptahedron are precisely the common tangents of the incircles.

Main Result
There are two parts to this paper:
Part One: (3D) Construction of a circumscriptible heptahedron satisfying:
1) topological condition: the heptahedron belongs to one of the 34 topological distinct types;
2) parallel faces: the heptahedron has a pair of parallel faces [r,s] formed by r-gon and s-gon;
3) equal inradius: the radii of the incircles of polygons [r,s] are equal.
Part Two: (2D) Construction of a planar pattern of two families of circles (blue and red) satisfying:
1) number of blue circles: 7
2) concentric pair: of the 7 blue circles there exist exactly 2 sharing the same center;
3) tangency and orthogonality: (a) circles of the same color have zero or one point of contact; (b) blue-blue contact point coincides with the corresponding red-red contact point; (c) at the point of contact the two common tangents are perpendicular.

Concrete Results

There are 81 non-congruent circumscriptible heptahedra each have a pair of parallel faces of the same radius of the incircle. To each such heptahedron, the associated 2D “Concentric Sangaku” construction problem is abbreviated as CS. The visual display of the 81 heptahedra together with the associated CS are linked in the Extended Abstract.

6 heptahedra each having only one single pair of parallel faces: (5,4,4,4,4,4,3)[3,3], (4,4,4,3,3,3,3;1)[3,3], (4,4,4,3,3,3,3;4)[4,3], (4,4,4,3,3,3,3;5)[4,3], (4,3,3,3,3,3,3;1)[3,3], (4,3,3,3,3,3,3;2)[3,3].

24 heptahedra each having two pairs of parallel faces: (6,5,5,5,3,3,3)[5,3], (6,5,5,5,3,3,3)[3,3], (6,4,4,4,4,3,3)[4,3,], (6,4,4,4,4,3,3)[3,3], (6,4,4,3,3,3,3;2)[3,3;1], (6,4,4,3,3,3,3;2)[3,3;2], (6,4,4,3,3,3,3;1)[3,3;1], (6,4,4,3,3,3,3;1)[3,3;2], (5,5,5,4,4,4,3)[5,4], (5,5,5,4,4,4,3)[4,3], (5,5,5,4,3,3,3;2)[4,3], (5,5,5,4,3,3,3;2)[3,3], (5,5,4,4,4,4,4)[5,5], (5,5,4,4,4,4,4)[4,4], (5,4,4,4,3,3,3;4)[5,3], (5,4,4,4,3,3,3;4)[4,3], (5,4,4,4,3,3,3;1)[4,3], (5,4,4,4,3,3,3;1)[3,3], (5,4,3,3,3,3,3;2)[3,3;1], (5,4,3,3,3,3,3;2)[3,3;2], (4,4,4,4,4,3,3;2)[4,4], (4,4,4,4,4,3,3;2)[4,3], (4,4,4,3,3,3,3;2)[3,3;1], (4,4,4,3,3,3,3;2)[3,3;2].

27 heptahedra each having three pairs of parallel faces: (6,6,4,4,4,3,3)[5,3]
(6,6,4,4,4,3,3)[3,3], (6,6,4,4,4,3,3)[4,3], (6,5,4,4,3,3,3;1)[4,3], (6,5,4,4,3,3,3;1)[3,3;1], (6,5,4,4,3,3,3;1)[3,3;2], (5,5,5,4,3,3,3;1)[5,3], (5,5,5,4,3,3,3;1)[4,3], (5,5,5,4,3,3,3;1)[3,3], (5,5,4,4,4,3,3;1)[4,4], (5,5,4,4,4,3,3;1)[4,3;1], (5,5,4,4,4,3,3;1)[4,3;2], (5,5,4,3,3,3,3;1)[3,3;1], (5,5,4,3,3,3,3;1)[3,3;2], (5,5,4,3,3,3,3;1)[3,3;3], (5,4,4,4,4,4,3) [5,4], (5,4,4,4,4,4,3)[4,4], (5,4,4,4,4,4,3)[4,3], (5,4,4,4,3,3,3;2)[5,3], (5,4,4,4,3,3,3;2)[4,3], (5,4,4,4,3,3,3;2)[3,3], (4,4,4,4,4,3,3;1)[4,4], (4,4,4,4,4,3,3;1)[4,3], (4,4,4,4,4,3,3;1)[3,3], (4,4,4,3,3,3,3;3)[4,3], (4,4,4,3,3,3,3;3)[3,3;1], (4,4,4,3,3,3,3;3)[3,3;2].

24 heptahedra each having four pairs of parallel faces: (6,5,5,4,4,3,3)[5,4], (6,5,5,4,4,3,3)[5,3], (6,5,5,4,4,3,3)[4,3], (6,5,5,4,4,3,3)[3,3], (6,5,4,4,3,3,3;2)[4,3;1], (6,5,4,4,3,3,3;2)[4,3;2], (6,5,4,4,3,3,3;2)[3,3;1], (6,5,4,4,3,3,3;2)[3,3;2], (5,5,4,4,4,3,3;2)[4,4],
(5,5,4,4,4,3,3;2)[4,3;1], (5,5,4,4,4,3,3;2)[4,3;2], (5,5,4,4,4,3,3;2)[3,3], (5,5,4,3,3,3,3;2)[4,3], (5,5,4,3,3,3,3;2)[3,3;1], (5,5,4,3,3,3,3;2)[3,3;2], (5,5,4,3,3,3,3;2)[3,3;3], (5,4,4,4,3,3,3;5)[4,3;1],
(5,4,4,4,3,3,3;5)[4,3;2], (5,4,4,4,3,3,3;5)[4,3;3], (5,4,4,4,3,3,3;5)[3,3], (5,4,4,4,3,3,3;3)[4,3;1], (5,4,4,4,3,3,3;3)[4,3;2], (5,4,4,4,3,3,3;3)[3,3;1], (5,4,4,4,3,3,3;3)[3,3;2]. Link to expanded abstract.

Abstract for 22146

Understanding Geometric Pattern and its Geometry Part 12 – Octagonal investigations

Authors: Miroslaw Majewski

Affiliations: New York Institute of Technology, Abu Dhabi Campus

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

Abstract for 22150

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

Authors: Jonaki Ghosh

Affiliations: Lady Shri Ram College, University of Delhi

Dynamic Geometry Environments have lent a new dimension to the teaching of proof in mathematics. Curricula across various countries have acknowledged the importance of the role of proof in school mathematics. The NCTM Principles and Standards (2000) states that students should be able to “make and investigate mathematical conjectures” and “develop and evaluate mathematical arguments”. In a similar vein, the Position Paper on Teaching of Mathematics (NCF 2005) emphasizes the need for “systematic reasoning in mathematics” and articulates that the aim of teaching proof should be to enable students to “make and investigate conjectures and understand that there are various methods of reasoning”.DGE affords the possibility to perform geometric constructions to a high degree of accuracy leading to empirical investigation of problems through experimentation and discovery. This has significant implications for enabling students to engage in conjecture making, systematic argumentation and to the teaching of proof. As Hanna (2002) points out, a DGE enables students to “easily test conjectures by exploring given properties of the constructions they have produced, or even ‘discover’ new properties.”

The primary feature of a DGE which distinguishes it from experiencing Euclidean Geometry

in a paper-pencil environment is the ability to drag parts of a geometrical figure thus making it

dynamic. The dragging feature is now recognized as a tool in itself and researchers have

identified different dragging modalities using which a learner can engage in geometrical

investigations. Leung (2008, 2012) distinguishes between different types of dragging – for

exploration, for contrast and for confirmation. Referring to the theory of variation in learning,

he maintains that “variation is the epistemic essence of the drag mode in DGE”. The ability to

make conjectures and discover properties of geometrical figures is made possible by the

simultaneous interplay between the varying and the invariant in a dragging episode. According

to him, one of the key purposes “in DGE dragging strategies is to discover invariant properties

in the midst of varying components of a geometrical configuration.” The impact of the

variational theory, in particular of the four functions of variation, namely – contrast, separation,

generalization and fusion, in DGE exploration and task design has attracted the attention of

many researchers in the last few decades.

In this talk we shall describe a study in which pre-service teachers with varied mathematical

ability and limited exposure to DGE, attempted non-routine open ended geometrical tasks in a

DGE environment. Their responses to the tasks in terms of empirical investigations, conjecture

making, systematic argumentation and transitioning towards proof will be analyzed through

the lens of the theory of variation. The findings of the study provide insight into the nature of

tasks that are appropriate for a DGE environment, which can be “triggers” for proof and extends

the notion of variation-invariant duality as a theoretical basis for DGE task design. Further, this

approach also makes non-routine geometrical problems, usually not addressed in school

mathematics, accessible to students. The study is merely a beginning attempt to extend the

work done in the area of DGE task design via variational theory approach.

Abstract for 22154

Illustrating the Pre-Conjecture Phases of Experimental Research mediated by Dynamic Geometry: How Generalization Can Generate a Multitude of Highly Plausible Conjectures About Semi-Regular Polygons

Authors: Jean-Jacques Dahan

Affiliations: IRES of Toulouse

The origin of this work lies in the result concerning the area of the Steiner ellipse of a triangle: it asserts that the Steiner ellipse is the largest-area ellipse inscribed in a triangle. The first comprehensive proof of this result was provided by Minda and Phelps in 2008 ([5]). Finding their proof, which used complex numbers, not very geometric, I began an investigation using dynamic geometry. This led me to present an original proof, which, unfortunately, contained a part justified only experimentally ([6], [1’]). Unable to find a formal proof for this part, I passed the task to my colleague Michel Carral, who found a purely geometric solution and asked me to present it in Prague ([8], [3’]). Today, I decided to revisit the search for the missing proof from my 2019 attempt. This is the story of that work (see [3]). I show how my inability to prove the decrease of a complicated function on the interval [0, π/6] led me to reexamine the problem in various ways, generating, to my great surprise, unexpected results. This erratic search subsequently led me to explore a problem that generalizes the one that had been obstructing me. These new investigations proceeded methodically and systematically, producing both geometric and functional conjectures, will be detailed below. Although the proofs remain elusive, I discovered results that will be the focus of future research. This research journey perfectly illustrates the pre-conjecture phases of experimental research, as described in my 2005 thesis ([4]). It is worth noting that I have already demonstrated the crucial role of the generalization process in my article on tritangent conics ([9], [4’]).

Abstract for 22161

Creating Planar k-isogonal Tilings

Authors: Ma. Louise Antonette De Las Penas, Mark Tomenes, Agatha Kristel Abila

Affiliations: Ateneo de Manila University, Ateneo de Manila University Southern Luzon State University

This paper addresses the research problem of the characterization of a class of tilings or tessellations called k-isogonal tilings in the Euclidean and hyperbolic plane. Tilings that satisfy the property of having k transitivity classes or orbits of vertices under the action of their respective symmetry groups are called k-isogonal tilings. We contribute to answering the research problem by giving various constructions of k-isogonal tilings carried out with the aid of the dynamic geometry software GeoGebra.

Abstract for 22168

Development of a Question Distribution and Answer Collection System for Mathematics Classes Using Only One Line of Text

Authors: Setsuo Takato, Hideyo Makishita

Affiliations: KeTCindy Center, Shibaura Institute of Technology, Shibaura Institute of Technology, Japan

KeTCindy and KetCindyJS are macro packages we developed for Cinderella, a dynamic geometry system. They allow the interactive creation of files of TeX figures and HTML.

Since the pandemic began, we have been developing an LMS, KeTLMS, that can be used in online or blended classes. In mathematics classes, a major issue is how to communicate mathematical expressions. For teachers, it is easy to write them in TeX, but not so easy for students. They often take screenshots of their notebooks and submit them, which makes it difficult for teachers to grade them. In KeTLMS, questions and answers including mathematical formulas are exchanged as follows:

1. We have defined KeTMath rules, which make TeX math expressions easier. For example, fr(sin(x)+cos(x),x) means $\dfrac{\sin x+\cos x}{x}$ in TeX.

2. These formulas are instantly displayed on the HTML screen as two-dimensional formulas.

3. KeTMath keyboard is placed on the HTML screen.

4. Teachers create a text file of questions using KeTMath rules, and generate HTML of the questions using the Cinderella file named

`toolketmathE.cdy''. They distribute it via a platform such as Google Classroom.

5. Students answer the questions using KeTMath rules and submit them as a one-line text generated with the button `Rec''.

6. Teachers collect students'' answers, grade them, and communicate the results to students.

The text files are small in size and easy to process. For example, teachers can also easily create CSV files for table formats. KeTLMS can handle questions of various types, including not only standard questions that ask students to answer mathematical expressions, but also questions to prove an equation and post-class surveys.

Abstract for 22172

The Development of Fraction Virtual Manipulatives and Their Applications to Low-achieving Elementary School Students

Authors: YUAN YUAN

Affiliations: National Taichung University of Education

The concept 0of fractions is fundamental, but students have consistently needed help to learn it. This study aims to develop a virtual fraction teaching aid (fraction virtual manipulatives) that can be used on tablets to assist students with difficulty learning fractions. This report will discuss low-achieving math students'' challenges in using graphical representations to explain the meaning of fraction calculations. Then, the features of the developed digital tool will be discussed based on these challenges and applied in teaching low-achieving math students to explore its effectiveness. Finally, suggestions for teaching fractions will be provided.

Abstract for 22173

Learning Experiences: Connecting A-Level Mathematics with Mathematics Used in The Real World via Machine Learning

Authors: Weng Kin Ho, Zhu Hui Joel Quek

Affiliations: Nanyang Technological University, National University of Singapore

One of the aims of the current Advanced Level H2 Mathematics Syllabus in Singapore is for students to connect ideas within mathematics and apply mathematics in the contexts of sciences, engineering and other related disciplines. A practising classroom teacher will find this very hard to achieve. On one hand, the mathematics that supports real scientific and engineering applications is often too sophisticated and lies beyond the reach of classroom mathematics -- at least as perceived by the teachers. On the other hand, textbook examples that bear some semblance of a real-life application often appear contrived. The teacher''s challenge is to find middle ground that caters for both accessibility and authenticity. This paper situates Gradient Descent, an elementary concept/technique commonly featured in Machine Learning, to create meaningful learning experiences with the aim of connecting topics within mathematics, and with the actual mathematics used to solve real world problems.

Abstract for 22174

Topological Structures Between Two Closed Surfaces Inspired by An Entrance Exam Problem

Authors: Wei-Chi Yang, Weng Kin Ho, Guillermo Dávila

Affiliations: Radford University, National Institute of Education Nanyang Technological University 637616 Singapore, Departamento de Matemáticas Universidad de Sonora Hermosillo (Son) CP 83000 México

We shall explore with technological tools a problem we posed in [8], which originated

from a college practice entrance question (see [3]). In this paper, we are investigating

whether a certain closed surface-inspired by the aforementioned college exam problem

and an a¢ ne transformation-is topologically equivalent to a sphere, utilizing the three-

dimensional visualization capabilities of computer technology to aid our initial analysis.

This technological affordance not only makes our investigation accessible to readers with

just an undergraduate mathematics background but also allows us to study this surface

in detail, finally leading us to a rigorous solution to the problem. Our work highlights

the essential role that technology plays in advancing and communicating mathematical

research.

Abstract for 22180

Polynomials associated with bicentric polygons

Authors: Alasdair McAndrew

Affiliations: Victoria University, Melbourne Australia

A "bicentric polygon" is one all of whose vertices lie on a circle (this makes it a cyclic polygon), and all of whose edges are tangential to another circle (this makes it a {tangential polygon). All triangles are bicentric---every triangle has a circumcircle and an incircle---but not all quadrilaterals are bicentric. Non-square rectangles, for example, are cyclic but not tangential, and any non-square rhombus is tangential without being cyclic. Bicentric polygons are also important to a result called "Poncelet''s Porism", or "Poncelet''s Closure Theorem", which says in effect that the circles corresponding to any bicentric polygon also correspond to an infinite number of other polyygons: indeed every point on the outer circle will be a vertex of some such polygon. Much work has gone into determining formulas connecting the radii of the two circles and the distance between their centres; this goes back to Euler and is still being actively investigated. As the number of sides of the polygon increases, the corresponding formulas grow in complexity. In this article we explore these formulas as polynomials in one variable, using computer algebra as our means of exploration.

Abstract for 22196

The Tangram: A Timeless Puzzle in Modern Education

Authors: Vanda Santos

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

The Tangram, a traditional seven-piece puzzle originating from China, has long captivated educators with its simplicity and complexity. Beyond its historical roots as a form of entertainment, the Tangram has found a significant place in modern education, leveraging its potential to enhance cognitive and spatial reasoning skills. This paper explores the integration of Tangrams in educational settings, highlighting their application in teaching mathematics, geometry, and fostering creativity. Additionally, it examines innovative approaches such as digital Tangram applications with Scratch.

These advancements have redefined how Tangrams are utilized, making them more accessible and versatile for learners. The discussion underscores the Tangram''s enduring relevance as a tool that bridges traditional learning methods with contemporary technological innovations, ultimately promoting a more engaging and effective educational experience.

Abstract for 22204

Professional Development in Coding and Computational Thinking for Mathematics Teachers

Authors: Keng Cheng Ang, Marc Yi Fei Yeo

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

Since 2006, computational thinking (CT) has been popularised as a critical interdisciplinary skill and linked to mathematical thinking, solidifying its applicability in mathematics education. Singapore has actively introduced CT in its mathematics curriculum and provided professional development (PD) opportunities for mathematics teachers to develop their competencies in incorporating CT in mathematics classrooms. However, research examining how and whether such PD prepares educators to teach mathematics using CT is scarce. The study fills this gap by examining how a PD course that introduces the VBA coding language in Microsoft Excel for computational problem solving develops mathematics educators’ coding skills and CT, and how participating in-service teachers perceive the course with regards to learning coding. Qualitative analysis of the course design revealed that the course materials are capable of helping learners develop CT through instilling in them certain coding habits, while qualitative and quantitative analysis of Likertscale and open-ended responses in the course feedback highlighted many strengths and suggested areas for improvement in various aspects of the course, like course structure, course materials, level of course difficulty, and perceived usefulness and applicability of the course. These findings reveal the benefits of computational approaches adopted in this study for developing CT and coding skills, the relevance of such approaches in mathematics education, areas that can potentially be improved for more effective PD, as well as how rich insights generated by feedback and course design analysis can contribute to assessing the impact of PD and tailoring PD courses to specific teacher needs and concerns.

Abstract for 22213

Calculus Is Everywhere: A Proof by Example

Authors: Douglas Meade

Affiliations: Department of Mathematics, University of South Carolina

A common statement made by many calculus instructors is that calculus is useful in many real-world settings. Many of these same instructors then struggle to come up with examples other than area, volume, surface area, projectile motion, exponential growth, and logistic growth.

Twenty-six (26) new applications of calculus are included in “Calculus and Analytic Reasoning”, a new calculus book by Sherman K. Stein and the presenter. Most Calculus Is Everywhere (CIE) sections are no more than three pages. Sixteen (16) of the book’s 18 chapters have one or two CIEs, one has four CIEs, and one does not have a CIE.

Most of this presentation will focus on three CIEs, one from each semester of the traditional three-semester calculus sequence:

• Reflections on Reflections: Ellipses, Parabolas, and a Solar Cooker

(Chapter 4: The Derivative)

• Average Speed and Class Size

Chapter 8: Computing Antiderivatives)

• Newton’s Law Implies Kepler’s Three Laws

(Chapter 15: Derivatives and Integrals of Vector-Valued Functions)

The full list of CIEs in the textbook will be presented and shared.

I will be happy to talk about other CIEs as time permits in this talk, or in additional conversations at your convenience. I am also interested in suggestions for additional CIEs, particularly one for the chapter that does not presently have a CIE.

Abstract for 22214

Automated generation of solved problems for self-study

Author: José A VALLEJO

Affiliations: Universitat Nacional d'Educació a Distància, Spain

We study the possibility of generating step-by-step solutions to a certain class of

problems, and its practical implementation with a CAS.

Abstract for 22116

Bayesian Sequential D-Optimal Sampling Designs for Fractional Partial Differential Equations

Authors: Edward Boone, Ryad Ghanam

Affiliations: Virginia Commonwealth University, Virginia Commonwealth University School of the Arts Qatar

Researchers are becoming increasingly interested in using Fractional Partial Differential Equation (FPDE) models for physical systems such as gas flows through porous materials. These models rely on the fraction of the differentiation $\alpha$, which needs to be estimated from empirical data. Experimentation is needed to obtain empirical data where pressures need to be measured at various times, $t$, from the initial pressure and distances $x$ from the pressure source which produces an output pressure $p(x,t)$. While sampling times are easy to choose when a sensor is in place. Typically, the location of sensors from the pressure source are arbitrarily chosen. This work shows how to design experiments using a sequential design with a base design and sequentially adding sampling design points by finding the optimal sensor locations along $x$ by minimizing D-optimality criteria which is essentially minimizing the of the volume of the variance-covariance matrix of all the parameters. For parameter estimation a Bayesian framework is utilized a sequential design is used to search through the possible locations for the next sensor in the follow up design. Two simple FPDE parameterisations are used to illustrate the method with a base design of six sensor locations and with five additional sensors locations determined sequentially. The simple examples suggest that the parameter values influence the location of the next best sensor location.

Abstract for 22117

Engaging Future Secondary Teachers in Technology Experiences

Authors: Marshall Lassak

Affiliations: Eastern Illinois University

Work with future secondary teachers should engage them in technology experiences for both teaching and learning mathematics. These tasks should address both content and pedagogical issues. Building on this foundation, this paper shares sample tasks that provide an intellectual need for someone to use technology to solve varying mathematical problems

Abstract for 22136

Learning guidance based on analysis of symbolic comprehension

Authors: Washino Tomohiro, Tadashi Takahashi

Affiliations: Department of Liberal Studies, National Institute of Technology, Nara College, Faculty of Social Sciences HAGOROMO University of International Studies

When two concepts contain a common concept, overgeneralization (the phenomenon of overgeneralizing specific rules or semantic features) may occur in the process of learners gaining an understanding of the two concepts in relation to each other. We use a neural network to analyze the overlap singularity phenomenon and the elimination singularity phenomenon in singular regions and perform simulations on the loss surface in previous research [4], [5]. In this study, the analysis technique “semantic comprehension" is applied to “symbolic comprehension". We defined four learning stages in the process of understanding of “permutations"and “combinations" and considered the simulation results regarding the change in training loss and the dynamics on the loss surface. Findings from this analysis are used to formulate learning guidance for teachers of mathematics.

[4] T. Washino and S. Ohashi: Learning guidance based on the overlap singularity phenomenon, Sci. Math. Japonicae, e-2023, No. 12, pp. 1-20 (2023)

[5] T. Washino and T. Takahashi: Learning guidance based on the elimination singularity phenomenon, Proceedings of 28th Asian Technology Conference in Mathematics(ATCM 2023), pp. 352-361 (2023)

Abstract for 22141

Classroom Practices with RLA to Promote Inquiry-Based Learning

Authors: Norie AOKI, Hideyo MAKISHITA

Affiliations: Functional Control Systems, Graduate School, Shibaura Institute of Technology, College of Engineering, Shibaura Institute of Technology

In this paper, the author will discuss RLA (Researcher-Like Activity) as a practice that promotes inquiry-based learning, present its characteristics and examples of class practice, and describe its educational effects. The author found that this practice leads to independent, interactive, and deep learning by students. The interactive nature of RLA not only engages students but also involves educators in the learning process. The effective use of ICT in this practice will also be discussed, encouraging educators to participate actively in their students'' learning.

Abstract for 22153

Connecting Trigonometry to Its Geometric Roots: An Introduction to Trigonometric Values

Authors: Niroj Dahal, Binod Prasad Pant, Bal Chandra Luitel, Basanta Raj Lamichhane, Tara Paudel

Affiliations: Kathmandu University School of Education, Lalitpur, Nepal, Kathmandu University School of Education, Hattiban, Lalitpur, NEPAL, Saptagandaki Multiple Campus, Bharatpur, Chitwan, NEPAL, Tribhuvan University, Mahendra Ratna Campus, Tahachal, NEPAL

This research explores two methods through which ten preservice math teachers develop an understanding of trigonometric values. Using the unit circle, preservice math teachers engage in knowledge-building activities such as paper folding and GeoGebra application. Grounded in Altman and Kidron’s 2016 didactical design research, this study examines the cognitive processes ten preservice math teachers undergo during knowledge acquisition procedure. Employing the dynamically nested epistemic action model for abstraction, we analyze how different tasks facilitate ten preservice math teachers’ comprehension of unit circle representations for trigonometric expressions and their associated values. Furthermore, we apply the abstraction in context framework to observe how ten preservice math teachers’ knowledge progresses from traditional ‘triangle’ trigonometry to ‘circle’ trigonometry, aiding in determining trigonometric values.

Abstract for 22157

The Role of Educational Robotics in Integrated STEM Learning Towards the Formation of 21st Century Skills

Authors: Muhammad Husein Arafat, Cucuk Wawan Budiyanto, Rosihan Ari Yuana, Kristof Fenyvesi

Affiliations: Universitas Sebelas Maret, University of Jyväskylä

As a crucial element in Integrated STEM Learning, Robotics plays a vital role in developing 21st-century skills such as communication, collaboration, critical thinking, and creativity. This research aims to (1) analyze how 21st-century skills emerge in integrated STEM learning and (2) analyze how Educational Robotics supports the formation of 21st-century skills in Integrated STEM Learning. The study was conducted at Sekolah Alam Solo Raya, involving primary and junior students. The research method used is qualitative, with learning conducted through Educational Robotics by creating a door security alarm using an Ultrasonic sensor on a Lego Mindstorm EV3 robot. Data were collected through interviews and questionnaires to evaluate the role of robots in learning. Data analysis was performed using Qualitative Content Analysis. The results showed that (1) 21st-century skills emerge in integrated STEM learning by encouraging students to communicate, collaborate, think critically, and create, and (2) Educational Robotics supports the development of 21st-century skills by providing challenges that require cooperation, collaboration, and communication to solve problems. However, students still need to further hone their skills, especially in communication and critical thinking, to achieve a higher level of 21st-century skill development.

Abstract for 22158

Some Poncelet invariants for bicentric hexagons

Authors: Grant Keady, Alasdair McAndrew

Affiliations: Curtin University, Victoria University

Tangential polygons are (convex) polygons for which every side is tangent to an inscribed circle.

Cyclic polygons are those for which every vertex lies on a circle, the circumcircle.

Bicentric n-gons are those which are both tangential and cyclic.

Every triangle is bicentric.

Bicentric quadrilaterals are those for which the sum of the lengths of opposite sides is the semiperimeter and for which opposite angles sum to pi.

Here we give some results pertaining to invariants of (convex) bicentric hexagons.

A remarkable result of Poncelet is that if one has a pair of circles admitting a bicentric n-gon, then for every point on the circumcircle can be a vertex for a bicentric n-gon.

This is illustrated in the animation at

https://mathworld.wolfram.com/PonceletsPorism.html

The animation indicates that, along with the incentre and circumcentre, the point of intersection of the principal diagonals of a 2m-gon is invariant under the motion.

Such invariants -- here called Poncelet invariants -- have been studied for two centuries, in particular for triangles and bicentric quadrilaterals.

We present results, for bicentric hexagons, that various combinations of distances between vertices - lengths of diagonals and of sides - are invariant.

CAS supplements are available for checking the results.

Abstract for 22162

Exploring Conic Sections through Desmos Artworks: Where Math, Art, and Technology Combine

Authors: Maria Digi Anna Mance-Avila, Maria Alva Aberin

Affiliations: Ateneo de Manila University

This study explores the use of Desmos in creating artworks out of the four conic sections discussed in Pre-calculus, namely: circle, parabola, ellipse, and hyperbola. This performance task was designed to give senior high school students an opportunity to integrate their creativity in arts and their knowledge of conic sections to produce their own artworks using a graphing calculator. Description of the performance task, concepts underlying its design, and examples of Desmos artworks produced by Grade 11 students are presented in this paper. Moving forward, mathematics educators could use this information as a springboard for designing performance tasks that integrate mathematics, art, and technology.

Abstract for 22164

Impact on Student Learning Outcomes in Mathematics using GeoGebra

Authors: Werachai Pattanapiboon, Hitoshi Nishizawa

Affiliations: KOSEN-KMITL, KMITL

In recent years, dynamic geometry software tools for teaching and learning in mathematics have been an integral part of a technology-based learning environment and become ubiquitous in educational institutions. The learning strategy assisted by these mathematics software tools allows students to better understand abstract contents with symbolic expressions through computer visualization with interactive and dynamic graphical representation. This paper presents the study of the effect of using dynamic geometry software, GeoGebra, on student performance and learning skills of geometrical concepts in mathematics teaching. The study was conducted for two groups with the same learning contents but different teaching styles for lectures with and without using GeoGebra software. The collected data from the students’ learning records, including post-test scores, were analyzed, focusing on two categories of symbolic calculations: graphs and inequalities. The performance of two teaching styles was evaluated based on the student achievements on paper-based quizzes, considering the number of retrials and the success rates. This study also investigates the impact of using GeoGebra on student learning skills by comparing score distributions for symbolic calculations and graphs and inequalities categories among three different academic years. The results show that integrating mathematics visualization software in teaching algebra can significantly improve student learning outcomes, providing higher post-test average scores when compared with the conventional teaching style. The results also reveal that using GeoGebra as a teaching tool considerably enhances students’ graphing skills and understanding of geometrical concepts in mathematics, particularly in graphing functions and solving inequalities. In addition, the effectiveness of using GeoGebra for improving mathematics learning outcomes for low-performing students has been confirmed with a higher success rate and lower number of retrials for paper-based quizzes. Thus, early intervention in using GeoGebra to enhance students’ visualization and graphing skills might be helpful, particularly for graphing functions and solving inequalities.

Abstract for 22165

Technology Integration Frameworks in Geometry Education: A Synthesis of Recent Research

Authors: FNU Pujiyanto

Affiliations: Western Michigan University

This synthesis examines technology integration frameworks from empirical research published from 2016-2022 on integration of computer technology (CT) into geometry education across grade levels. We conducted article searches through article database, i.e., Google Scholar and ERIC with relevant keywords. Inclusion criteria focused on peer-reviewed empirical studies combining geometry education, computer technology integration, as well as the availability of technology integration framework. Out of 338 initial search results, 14 articles met the criteria. The results show that there are 10 frameworks, and the predominant technological frameworks used in these time periods is Technological Pedagogical Content Knowledge (TPACK). The technology integration frameworks from selected articles were categorized based on framework categorizations: how students learn with technology, design and evaluation of tools/tasks, how teachers use technology, and how teachers learn to use technology. The majority of frameworks addressed how teachers learn to integrate technology, with nine out of fourteen selected articles. Most studies focused on in-service or pre-service teachers rather than K-12 students. This synthesis reveals framework usage mostly focused on in-service and preservice teachers and highlights gaps in research on frameworks for student learning with technology in geometry.

Abstract for 22177

On a Study of Improvements of the Quadratic Curves Addition Method: Consideration of Theorem 8

Authors: Hideyo MAKISHITA

Affiliations: Shibaura Institute of Technology

In a quest to find the centers of circles inscribed or circumscribed by multiple circles, the author has developed a practical and applicable solution- the quadratic curves addition method. This method, which involves the addition of ellipses, hyperbolas, and parabolas to a drawing made with a ruler and compass, is not just a theoretical concept. The author has constructed the quadratic curves addition method with eight theorems, with Theorem 8 being the focus of this study. Its relation to other theorems is discussed, and we will demonstrate its practicality by using Cinderella and Ketcindy to draw mathematically correct figures for Wasan and Sangaku.

Abstract for 22178

Mathematical Modelling in a 3D Printing Project

Authors: Leyre Gilardi, Lucía Rotger-Garcia, Álvaro Nolla, Juan M. Ribera-Puchades, Angélica Benito

Affiliations: Universidad Autónoma de Madrid, Universitat de les Illes Balears

This paper presents an experience in mathematical modeling conducted with master''s degree students in the Innovation in Education program, focusing on a project involving 3D modeling and printing. The project aimed to integrate hands-on mathematical activities into teacher training. The positive feedback from students and the mathematical competencies developed during the project support the inclusion of such activities in teacher education curricula. This study highlights the potential of 3D modeling and printing projects to enhance mathematical understanding and pedagogical skills among future educators.

Abstract for 22179

E-Learning material creation system that utilizes existing teaching materials

Authors: Takuya Kitamoto, Masataka Kaneko, Takeo Noda, Hiroyoshi Kihara

Affiliations: Yamaguchi University, Toho University, Shizuoka Prefectural Arai Senior High School

This paper describes a new framework for creating E-Learning materials.

The new framework is intended for use by school teachers and can transform an existing

teaching material into an E-Learning system utilizing HTML5 technology.

The E-Learning system created is a web application consisting of a single HTML file,

and can be used not only on PCs, but also on tablets and smartphones.

The E-Learning system created with this framework features a two-layered screen

structure: existing teaching materials are placed on the lower layer of the two-layered

structure, and text boxes and buttons are added on the upper layer, allowing existing

teaching materials to be converted to E-Learning systems. In addition, by incorporating

Algebrite ([4]), a JavaScript library for symbolic computation, it is possible to perform

symbolic computation of mathematical expressions and automatically grade students’

answers.

Since this paper is an extension of reference [3], we first briefly describe the contents

of the reference. Then, after explaining the newly added functions, the flow of actually

constructing an E-Learning system using this system will be explained step by step.

Abstract for 22181

Towards a conceptual framework for integrating mathematical digital competencies in digital project-based learning of mathematics

Authors: Marc Helton Sua, Lester Hao

Affiliations: Ateneo de Manila University

In this paper, we will consider the theoretical connections between Project-Based Learning (PBL) and Geraniou’s Mathematics Digital Competency (MDC). PBL is generally defined by its constructivist theoretical grounding, where students are expected to answer a big question by forming groups and answering complex questions using knowledge and skills from multiple subject matter. Studies have shown that PBL contains five distinct features: collaborative learning, disciplinary subject learning, iterative learning, authentic learning, and student engagement. An evolution in PBL is Electronic or Digital Problem Based Learning (E-PBL), which grew out of the COVID-19 pandemic and the need to adapt. The researchers seek to enhance E-PBL and its features through the MDC by mapping their main features to each other in an effort to enhance and improve student innovation, creativity, and empowerment. Findings show that E-PBL and MDC intersect on the basis of motivation, instrumentation, and competency. The paper suggests that integrating MDC into E-PBL would be a robust framework that encourages collaboration, research, and innovation towards strengthening techno-mathematical literacy and fluency among students.

Abstract for 22183

Research on the Use of Dynamic Geometry via Blended Learning

Authors: Šárka Voráčová

Affiliations: Czech Technical University in Prague, Faculty of Transportation

Teaching geometry through a blend of distance learning, IT support, and in-person consultations has proven to be an effective approach. The use of appropriate software allows for personalized learning experiences, replacing traditional knowledge with the development of valuable habits and strategies. Over two years, we conducted statistical evaluations of students'' knowledge and attitudes after utilizing a blended learning method that actively incorporated dynamic geometry software.

Abstract for 22184

An Initial Analysis on the Reliability of Using Chatbots in Solving Word Problems in Probability

Authors: Reggie Nalupa, Lester Hao

Affiliations: Ateneo de Manila University

This study explores the reliability of using chatbots, primarily ChatGPT-4o and Copilot, in solving word problems in probability. The integration of artificial intelligence in education has transformed instructional methods, offering tools for personalized learning and instant feedback, which are critical for developing problem-solving skills. Chatbots leveraging natural language processing (NLP), simulate human conversations to assist in educational settings. This research focuses on evaluating the accuracy of chatbots in solving probability problems. A comparative analysis approach was employed, wherein probability word problem involving conditional probability were posed to the chatbots. The solutions provided by the chatbots were then compared to the correct solution obtained from reference materials using a specific evaluation criterion. The results highlight the potential and limitations of chatbots in educational applications. While chatbots demonstrated the ability to engage in meaningful conversations and provide correct solutions in some instances, issues such as misunderstanding, complex queries and the necessity for continual algorithm updates were also observed. This study’s findings contribute to improving chatbot design and functionality, aiming to enhance educational outcomes and problem-solving skills. By identifying metrics for accuracy, this research provides insights into the potential of AI-powered chatbots as a reliable educational tool.

Abstract for 22185

Online learning incorporating a mathematics online test system and a dynamic geometry system

Authors: Chieko Komoda, Yasuyuki Kubo, Satoshi Yamashita, Masumi Kameda

Affiliations: Department of Liberal Arts, National Institute of Technology, Kurume College, National Institute of Technology, Yuge College , National Institute of Technology, Kisarazu College , Freelance

This research reports on the creation of rich mathematical content for secondary edu-cation in Japan using the open-source e-Learning platform “Moodle”. The study focuses on utilizing the “page” and “quiz” functions to incorporate complex mathematical ex-pressions and dynamic mathematical graphs as teaching materials. Additionally, the “KeTCindyJS” is used for generating dynamic graphs, and the “STACK” system is em-ployed for automatic grading to evaluate learners’ mathematical knowledge. The primary goal is to develop quizzes within Moodle that integrate advanced mathematical graphs.

Abstract for 22188

Development of a Specification Management System for Multidimensional PISA-like Mathematics Items

Authors: Mark Lester Garcia, Aldrich Ellis Asuncion, Catherine Vistro-Yu, Nia Kurniasih

Affiliations: Ateneo de Manila University, Institut Teknologi Bandung

This paper stems from the primary author’s ongoing dissertation, which encountered a technological-logistical issue during the implementation of an item-writing study. The central problem discussed involves discrepancies between the table of specifications (TOS) for multidimensional PISA-like mathematics items created by teachers and the item specifications indicated in their individual item submission forms. These inconsistencies posed challenges in consolidating item specifications, impacting data collection and analysis (e.g., inaccurate alignment ratings due to mismatches between the TOS and item specifications). To resolve this, the authors developed an item specification management system in MS Excel, which automates processes like verifying incorrect entries and identifying unfulfilled constraints. Testing the system with hypothetical item specifications showed its ability to perform data validation, identify input errors, and detect entry conflicts; hence making it a viable and efficient alternative to the workflow used in the original study. These findings are significant for future studies replicating the primary author’s dissertation, as the system mitigates potential issues in the manual input of item specifications, particularly for multidimensional PISA-like items with multiple dimensions such as item format, content category, context category, and process category. Such a specification management system can be very useful on a larger scale, as independent item-writing projects in educational institutions can utilize this without having to endure the use of several TOS’s simultaneously which can inevitably cause confusion among the item-writers which makes the item specifications prone to manual errors; and without having to rely on commercially available item-banking software.

Abstract for 22190

Constructing Multi-layered Acrylic Tiling Models Using Laser Engraving and Cutting

Authors: Mark Loyola, Ma. Louise Antonette De Las Peñas, Mark Tomenes

Affiliations: Department of Mathematics, Ateneo de Manila University, Department of Mathematics Ateneo de Manila University Philippines

This work discusses the creation of tiling or tessellation models that support the teaching of mathematics. The geometric models are first constructed using a computer algebra system and then realized as tangible manipulatives using laser engraving and cutting.

Abstract for 22191

THE EFFECT OF USING EDUCATIONAL ROBOTICS IN DELIVERING STUDENT GEOMETRY MATERIALS ON THE DEVELOPMENT OF COMPUTATIONAL THINKING SKILLS

Authors: Cucuk Wawan Budiyanto, Kristof Fenyvesi, Nur Isnaini Hanifah, Aris Budianto

Affiliations: Sebelas Maret University, University of Jyväskylä

This study aims to: (1) Determine how the developed robotics devices can facilitate Computational Thinking abilities in Geometry learning, (2) Determine how the ER Lego Mindstorm module developed can facilitate Geometry learning. The research was conducted using a qualitative method with subjects being 4th to 6th-grade students from a nature-based school. The sample was determined using purposive sampling and then selected according to specified criteria. The instruments used to determine the impact of robotic devices used in geometry instruction, and the achievement of aspects of Computational Thinking during learning were observation and interviews. Observation and interviews were analyzed using descriptive and content analysis. Based on the research results, it can be stated that (1) Computational Thinking in geometry learning using robotic devices can be well facilitated, (2) The utilization of the ER Lego Mindstorm Module developed to facilitate geometry learning can be used. The hands-on practice makes it easier for students to understand geometry learning.

Abstract for 22193

The Effect of Using Educational Robotics in Learning Physics Material on the Relationship Between Work and Energy on The Development of Computational Thinking Skills

Authors: Cucuk Wawan Budiyanto, Kristof Fenyvesi, Alfiyah Aini Hanifah, Aris Budianto

Affiliations: Universitas Sebelas Maret, Sebelas Maret University, University of Jyväskylä

This study aims to examine the effect of robotics devices in facilitating physics learning on the material of Effort and Energy and the ability of Computational Thinking (CT) of students at Sekolah Alam Soloraya. Using a qualitative method with purposive sampling, data were collected through observation and semi-structured interviews, and data validity was tested by triangulation. The results show that robotics is effective as a simulation-based learning media that supports the understanding of physics materials and CT skills. Students demonstrated CT skills in identifying problems, designing, programming, and evaluating robots, although there were differences in the level of achievement of CT skills among them.

Abstract for 22195

AI, Tensors, and Math Homework

Authors: Russel Carlson

Affiliations: BYU-Hawaii

Many of the current advances in artificial intelligence are based on the mathematics of tensor spaces and optimization. However, most math instructors are not well versed in tensors, as it is often taught as an abstract topic in graduate algebra classes. The purpose of this paper is to help describe tensors and their properties, and how they are used in artificial intelligence. Also, this paper will examine how this informs the behavior of artificial intelligence when it is used to answer mathematics questions.

Abstract for 22201

GeoGebra for Visualizing Mathematical Concepts: Teachers'' Narratives on Use of It for Conceptual Learning

Authors: Binod Prasad Pant, Niroj Dahal, Bal Chandra Luitel

Affiliations: Kathmandu University, Kathmandu University School of Education, Hattiban, Lalitpur, NEPAL

Integrating information and communication technology (ICT) in mathematics education has been increasingly recognized as a powerful tool for increasing students’ interest and performance. It is widely discussed that students’ understanding of mathematical ideas is not satisfactory, especially in terms of conceptual understanding. Using narrative inquiry as a research method, we examined the experiences of four secondary mathematics teachers—two men and two women—who successfully integrated GeoGebra while teaching geometry and function, an ICT application, into their regular mathematics classes. These classes typically consist of around 20 students aged 13 to 14 years. Through in-depth interviews and reflective narratives, this study explored the teachers’ insights on how GeoGebra transforms the learning environment in school mathematics. The participants reported that GeoGebra significantly advances concept formation by allowing students to visualize and manipulate mathematical ideas and concepts such as geometric shapes and algebraic functions. This interactive engagement clarifies abstract ideas and accelerates students’ curiosity and motivation, making learning more enjoyable. Further, participants observed that students are more enthusiastic and willing to engage with challenging mathematical problems when using GeoGebra. The study concluded with recommendations for teachers to use GeoGebra effectively in math lessons. It advocates for professional development programs to equip teachers with the necessary skills to integrate ICT tools like GeoGebra effectively and suggests avenues for further research to explore the long-term impact of such technologies on student engagement and learning outcomes.

Abstract for 22206

Preparing Math Teachers for the Future: Analysing the Use of Technology in a Master’s Program

Authors: José Manuel Dos Santos, Jaime Carvalho e Silva, Zsolt Lavicza

Affiliations: Departament of Mathematics, Faculty of Sciences and Technologies, University of Coimbra;, Centre for Research and Innovation in Education (inED), Center for Research and Development in Mathematics and Applications (CIDMA), Departamento de Matemática, Universidade de Coimbra, Linz School of Education, JKU

Current guidelines for the mathematics curriculum from primary to secondary education in Portugal include Computational Thinking as a cross-curricular theme and advocate for the systematic use of technology. Official mathematics program documents pro- vide methodological suggestions for teachers to develop computational thinking through the use of dynamic geometry environments, such as GeoGebra, internet applets, Scratch, and Python. In this context, it is important to understand how future teachers interpret the use of these technological tools in the first year of a Master’s degree in Teaching Mathematics for Basic and Secondary School Teachers in Portugal. This study analyses the work of 12 students during the “Computational Tools for the Teaching of Mathematics” course unit. Supported by the research-based design methodology, the study examines the work carried out over two school years, as well as the adjustments made between the first and second cycles of this intervention, using qualitative data analysis techniques. The results indicate that the integration of content knowledge and technological knowledge among the partici- pants is complex throughout the two intervention cycles. Combining pedagogical content knowledge with technological and content knowledge presents new challenges for the initial training of mathematics teachers. This study offers insights to improve the course unit for future editions and identifies issues to consider for continuous teacher training in Portugal.

Abstract for 22210

Applications of GPT and Copilot in Tourism Courses: A Case Study in Chung Hua University

Authors: Ming-Gong Lee, Che-Yuan Yang

Affiliations: 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

We utilize AI tools, ChatGPT and Copilot, to courses in Tourism college. Their functions allow students to achieve target through simple instructions and creative spells to these tools. Without working on advanced AI programming, students can meet and even reach success of their performance far beyond their imagination. Utilization of these AI tools in the hospitality courses should be encouraged so that engineering types of learning in various programming languages can be minimized to encourage hospitality students to participate in AI applications.

Abstract for 22220

Integrating 3D Modelling into STEAM Education

Authors: Jozef Hvorecký, Vera Ferdiánová, Angelika Schmid, Lilla Korenova

Affiliations: University of Ostrava, Ostrava, Czech Republic

3D printers appear more and more frequently in all types of schools. To exploit them effectively, their educators have to become familiar with their appropriate application in their classes. The authors participate in an ERASMUS+ project which intends to assist future (pre-service) teachers to plan and carry out their future teaching activities with 3D modelling through a STEAM-based transdisciplinary approach.

The main aim of our project is to design, to develop and to implement teaching approaches with 3D modelling. In order to follow contemporary trends in education, we promote the learning-to-learn approach by “learning to do” tasks enhancing creativity and production of 3D models. We are working on a MOOC to support both teacher training and school-based STEAM learning and to facilitate equal access to STEAM learning. In particular, we pay attention to specifics of partner countries’ curricula and teacher training.

The tasks and activities will address both in-class and online courses for future teachers, As our primary aim is to concentrate on transdisciplinary education, we will develop not only the activities. We will create a repository of high-quality teaching and learning resources as well as their evaluation criteria. In the future, the dissemination of project results is premeditated.

Abstract for 22118

Enhancing Computational Thinking Skills: Unplugged Activities and Coding for Mathematics Classroom

Authors: Warabhorn Preechaporn

Affiliations: SEAMEO RECSAM

Computational Thinking (CT) skills has been stated by Jeanette Wing (2006) as an essential skill for all and 21st Century way of solving problems. This article aimed to illustrate unplugged activities and coding to foster computational thinking basic skills. The activities will be applied for problem solving and better understanding of mathematics concepts. In this paper focused on the unplugged activities which conducted in the workshop such as Decomposition, Pattern Recognition, Abstraction, and Algorithm that can be applied for problem solving. Nevertheless, Scratch programming can be used for coding in teaching primary mathematics. The study was collaborated with primary mathematics teachers and to survey their perception of CT skills in mathematics classroom. The result provided that the CT skills can be used for problem solving in mathematics classrooms, which is essential to prepare future teachers and students on CT skills. It is necessary for students in the future because the students can apply CT skills for solving problems in daily life as well.

Abstract for 22207

Challenges and Perceptions of Mathematics Teachers Towards Digital Textbook Adoption

Authors: Tommy Tanu Wijaya, Yiming Cao, Xinxin Li

Affiliations: Beijing Normal University, Beijing Normal University, Beijing, China

The advancement of technology in mathematics education has been found to have a positive impact. This technological progression has also influenced the transition from printed to digital mathematics textbooks. Digital mathematics textbooks are electronic books that incorporate interactive content, multimedia integration, and adaptive learning technologies designed to enhance the educational experience. Unlike traditional textbooks, digital versions offer dynamic content that can be updated in real time, providing the most current information and methodologies. They also facilitate personalized learning paths, allowing for differentiated instruction that can cater to the unique needs of each student. These textbooks often include tools for assessment, instant feedback, and analytics, enabling teachers to track student progress and adapt instruction accordingly. Some experts believe that this shift aligns with 21st-century developments and will provide numerous benefits and opportunities for future educators. However, the adoption of digital mathematics textbooks presents distinct challenges for mathematics teachers. Despite full support for the use of digital resources, the implementation of digital mathematics textbooks remains suboptimal. This study aims to identify the usage of digital mathematics textbooks by teachers, their perceptions of these resources, and the challenges they face during instructional activities. We employed a quantitative approach to assess the utilization of digital textbooks by teachers, followed by a qualitative approach using interviews to explore the perceptions and challenges associated with their use in teaching mathematics. The participants of this study included 289 mathematics teachers in China who have previously used digital mathematics textbooks in their teaching practices. Five teachers were purposively selected based on age, gender, and teaching experience to participate in follow-up interviews. Our findings reveal that the respondents possess basic knowledge about utilizing digital mathematics textbooks for teaching. However, 65.08% of the teachers reported using digital textbooks only 1-2 times per semester, typically for special occasions such as competitions or open classroom sessions. Many teachers infrequently use digital textbooks due to a belief that these resources do not significantly impact learning outcomes and require more effort compared to traditional teaching methods. The reluctance to adopt digital textbooks more broadly suggests a gap in teachers'' understanding or trust in the efficacy of digital tools in enhancing mathematical learning. It is recommended that educational leaders integrate comprehensive training programs focusing not only on the operational use of digital textbooks but also on pedagogical strategies that leverage digital resources to improve learning outcomes. Additionally, developing a feedback loop where teachers can share their experiences and challenges could foster a more supportive community of practice. This engagement could be facilitated through regular workshops, peer-to-peer sessions, and integration of user-friendly analytics in digital textbooks to track and reflect on student performance in real time. Furthermore, policymakers should consider incentivizing schools that demonstrate innovative uses of digital technologies in their curriculum, encouraging a broader shift towards digital resources. These initiatives could significantly reduce the reluctance observed among mathematics teachers and help realize the potential benefits of digital mathematics textbooks in enhancing student learning and engagement.

Abstract for 22217

Understanding the Graphical Representation of the Derivative through the Dynamic Digital Technology GeoGebra

Authors: Gily M. Aguilos^1,2, Maria Alva Q. Aberin¹

Affiliations: ¹Department of Mathematics, School of Science and Engineering,

Ateneo de Manila University, Quezon City, Philippines; ²Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, Laguna, Philippines.

To learn the concept of derivative, one needs to understand its different representations. One of which is its graphical representation. The graphical representation of the derivative is associated with finding the gradient of the curve or the slope of the tangent line to the graph of the function at a point. Guided by Duval’s Theory of Registers of Semiotic Representations together with Bartolini Bussi and Mariotti’s Theory of Semiotic Mediation, this study aims to examine how students learn the graphical representation of the derivative using the dynamic digital technology GeoGebra. Specifically, this study wants to answer the following questions: (1) What are the cognitive factors causing students’ difficulties in understanding the graphical representation of the derivative? and

(2) How does GeoGebra support students in understanding the graphical representation of the derivative?

This study followed the grounded theory design. Data were gathered through observations, secondary data collections, interviews, and study sessions with undergraduate calculus students at a university in the Philippines. Data were analyzed using constant comparative analysis involving initial, intermediate, and advanced coding. The results of this study revealed that students’ difficulties in understanding the graphical representation of the derivative were related to their ability to evolve artifact signs into mathematical signs. It involves performing treatments and conversions in the different registers. These are then affected by their background knowledge, critical thinking skills, and visualization. Results also revealed that GeoGebra has features that help students alleviate these difficulties. These features are its capacity to do mathematical computations, display and format objects, and allow users to choose, manipulate, and simulate processes. These features of GeoGebra support students in visualization, sensation, coordination, interaction, pattern recognition, segmentation, and integration.

Abstract for 22149

Challenge facing mathematical experiments since 1995

Author: Jen-chung Chuan

Affiliations: National Tsing Hua University

The First ATCM was held in 1995. Throughout the years the tools for mathematics experiments has undergone a great deal of changes due to the evolution of the technological environment. In this workshop, we attempt to re-experience the moments that made Mathematic Experiment exciting. We are facing the new environment offered by AI PC. Upon the first publication of Lotus 1-2-3, do we expect the excitement be lasting? Or, can AI PC last longer than Lotus 1-2-3?

Abstract for 22189

KeTCindyJS and KeTLMS --Various Applications in Mathematics Classes--

Authors: Yasuyuki Kubo, Masaki Suzuki

Affiliations: Yuge KOSEN, Numazu KOSEN

We have created some examples of effective teaching materials for mathematics classes using KeTCindyJS and KeTLMS. KeTCindyJS allows anyone to easily create HTML containing interactive figures by linking the dynamic geometry software Cinderella and CindyJS. KeTLMS is an HTML app that enables students who are not familiar with TeX to easily exchange questions and answers, including mathematical formulas. By embedding the elements necessary for questions and answers, communication between teachers and students in remote and hybrid classes can be improved. This communication is designed to be user-friendly so that even students who are not familiar with TeX syntax can handle mathematical formulas. As examples, we will show how to make the following HTML:
(1) Gaussian elimination method
(2) Displaying the n-th root of a complex number
(3) SIR model of infectious diseases