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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:
https://drive.google.com/drive/folders/1O4tlGHw7Z5JsSkgRXcziaD6Z0dXH2KDo?usp=sharing.
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
VLADIMIR NODELMAN
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.
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
22063
STUDENTS COGNITIVE DEVELOPMENT IN LEARNING BASIC DIFFERENTIATION RULES
USING DESMOS CLASSROOM ACTIVITY BASED ON THE THREE WORLDS OF MATHEMATICS
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 (https://www.netpad.net.cn/), 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.
References:
1. Sagemath
Official Website: www.sagemath.org
2. Mathematical Computation with Sage
by Paul Zimmermann et al.
3. NPTEL Online Course on
Computational Mathematics with SageMath by Ajit
Kumar (https://archive.nptel.ac.in/courses/111/106/111106149/)
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
www.youtube.com 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
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