Abstracts for Invited and
Plenary Papers
Abstract for 21684
Building the Russian
Nesting Dolls by Dissecting the Five Platonic Solids
Author: Jen-Chung Chuan
Affiliation: Department of Mathematics, National
Tsing Hua University, Hsinchu, TAIWAN 300
Motivated
by the Nesting Russian Dolls, we are to make this follow dissections
1. Staring
with a regular dodecahedron D
2. D is
dissected in to a cube C and 6 mutually congruent "roofs
3. C is
dissected into a regular tetrahedron T and 6 mutually congruent non-regular tetrahedra
4. T is
dissected into a regular Octahedron O and 4 mutually congruent tetrahedra
5. O is
dissected into a regular Icosahedron
I and 6 mutually congruent non-convex hexahedra
We thus
have the nested polyhedra D, C, T,
O, I.
Abstract for 21708
Steiner Ellipse and
Marden’s Theorem
Author: Jean-Jacques Dahan
Affiliation: IRES of Toulouse, FRANCE
In this
paper we will see the richness of both algebraic and dynamic approaches of a
problem related to the three zeroes of a third-degree complex polynomial and
the two zeroes of its derivative. Visualization with DGS in the Argand plane
of these five points with the help of CAS will facilitate the exploration
leading to the discovery of a very special ellipse (the Steiner ellipse).We
will first prove (via a geometric proof) the existence and the uniqueness of
such an ellipse (tangent to the triangle defined by the zeroes of the third
degree polynomial at the midpoints of these zeroes) and then prove (complex
proof) that the foci of this ellipse are the zeroes of the derivative
polynomial (Marden’s theorem). Connecting easily DGS and CAS within the
TI-Nspire environment is a crucial tool of this work as well as the use
of sliders to summarize the different stages of the investigations, the
conjectures and their corroboration (experimental) or their validation
(proof). This paper aims to show ideas of challenging mathematics to
everybody at all levels. It aims also to show rich techniques of
investigation within DGS and CAS environments. A final problem in relation to
Marden’s theorem will be investigated within DGS, leading to a very
nice conjecture, which is proved, with a blend of DGS and CAS. An
original way to prove that the Steiner ellipse is the ellipse of maximum area
inscribed in a triangle will be shown in an important part of
this paper: the way this very last work was conducted could be an
important resource for techniques of investigation or proofs to know in order
to use DGS and CAS relevantly.
Abstract for 21709
An Introduce of Dynamic
Mathematical
Digital Resources Open
Platform
Author: Guan Hao
Affiliation: Chengdu Institution of Computer
Application, CHINA
In
response to the principle of achieving shared improvement through collaboration,
relevant actions taken on the aspect of the digital education resources have
become the important contents and research highlights of the present
information and communications technology (ICT) in
education. After years of researches and constructions, the digital education
resources still have not been fully valued, and what is worse is that
comments such as the so-called "resources island" and "digital
ruins" are presented. This phenomenon is mainly because the construction
of the existing resource platform lacks sufficient openness
and scientific correlation. This paper proposes a model of the educational
resources open platform based on the PaaS structure. By combining the
techniques such as the dynamic geometry, the computer algebra, and the
automated geometric theorem proving, a dynamic mathematical educational
resources open platform is designed and implemented by means
of a micro-service architecture. Moreover, the OAuth2.0 technology is applied
to provide authentication and authorization to a third-party application and
a user, as well as hierarchically customized source materials and
capabilities for editing dynamic mathematical contents. This paper proposes
an overall design of the open platform, gives a hierarchical strategy and an
authentication process for applications and user permissions thereof, and
introduces the process of customizing the open resources and the tools.
Currently, the open platform serves a plurality of third-party applications
and is widely applied.
A
collection of video clips associated with this presentation is available
online. They can be found at http://atcm.mathandtech.org/EP2019/videos/21709/.
Abstract for 21710
Limit and Continuity
of a Function. Software aspect
Author: Vladimir Nodelman
Affiliation: Holon Institute of Technology, ISRAEL
The
studies of fundamental concepts of limit and continuity of a function cause
difficulties: students for the first time meet here definition with
quantifiers.
This paper
illustrates the methods of teaching and learning these concepts with
intensive use of software. In general, the types of student’s
activities do not depend on the specifics of functions (whether they are real
or complex), whereas, the supporting models are significantly different.
By means
of author’s non-profit software, "VisuMatica"
students not only use some ready models but construct proper models by
themselves and explore with their help the studied contents.
Abstract for 21712
Realizing Computational
Thinking in the Mathematics Classroom: Bridging the
Theory-Practice Gap
Authors: Weng Kin Ho, Chee Kit Looi, Wendy Huang, Peter Seow, Longkai Wu
Affiliations: Nanyang Technological University, SINGAPORE
With the
impact of computer technology on human civilization in the 21st century,
Computational Thinking has become an important topic of research and
discussion in the area of education over various non-computer science
disciplines; for example, mathematics, sciences, languages, social sciences,
etc. By now, Computational Thinking has often been referred to as a paradigm
of knowledge and problem solving by which the problems and their solutions
can be implemented using an effective means, e.g., by a computer, though it
never really possess a
universal definition. In this paper, we invite the reader to revisit the
original meaning of the word “Computational Thinking” as intended
in 1980 by its inventor, Seymour Papert. By so
doing, we bring into focus the concrete issues that a mathematics teacher need to
consider so as to realize Computational Thinking in his or her lessons. We
analyze the design principles put forth earlier by the authors, and understand these principles in the context of
mathematics teachers’ professional development and classroom
implementation.
Abstract for 21713
Poncelet's Porism and Its Connections with Algebra, Analysis, Mechanics, and Dynamical Systems: A Technology-Based Approach
Author: Guillermo Davila-Rascon
Affiliation: University of Sonora, Department of
Mathematics, MEXICO
In 1822,
Jean-Victor Poncelet published his fundamental work in which
he demonstrated a remarkable result that became known as
Poncelet Closure Theorem or Poncelet''s Porism, and can
be enunciated as follows: Let C and D be two smooth
conics in the projective plane. If there is a polygon of $n$
sides inscribed in C and circumscribed about D, then there are infinitely
many such polygons having the
same number of sides n. Moreover, each point of C is a
vertex of such a closed polygonal line.
In this
talk, we will
explore some of the remarkable connections of this
result with some others in different fields, showing us the
richness of ideas and methods that originated from this theorem. For
example, we will connect the Poncelet's porism with the theory
of elliptical billiards, especially; we are interested in
deriving conditions for the periodicity of billiard’s trajectories. In
addition, we will present the relation of the theorem with the theory of elliptic
integrals, as well as algebraic geometry, etcetera.
We will be
using GeoGebra and Maxima for exploring some of the scenarios
presented in the talk. For example, modelling the reflections
of light beams inside ellipses and the integrability
of two dimensional elliptical billiards.
Abstract for 21719
Robot for Mathematics
College Entrance Examination
Authors: Hongguang Fu, Jingzhong Zhang, Xiuqin Zhong, Mingkai Zha, Li Liu
Affiliations: University of Electronic Science and
Technology of China,
School of Computer Science
and Engineering,
University of Electronic Science
and Technology of China,
Southwest Minzu University, Chengdu, CHINA
Automated
mathematics has attracted more and more interests to mathematicians and
computer scientists. In this article, we propose a new solution, Robot for
Mathematics College Entrance Examination (RMCEE), to automatically solve
elementary mathematical problems. RMCEE took the college entrance exam of
China in 2017 and scored 105 points out of 150. RMCEE takes as input Chinese
natural language and outputs human-readable solution processes. It leverages
artificial intelligence technologies in multiple domains such as the
knowledge graph, natural language understanding, cognitive reasoning, and
deep learning. Our project outperforms other similar projects such as Todai Robot of
Japan in that RMCEE proposes a natural language understanding model of entity
combinations based on knowledge graph, and implemented human-readable solution processes
based on a novel cognitive reasoning model.
Abstract for 21723
例说动态数学系统在数学教育中的作用
(The Role of Dynamic
Mathematics in Mathematics Education)
Authors: Chuan-Bo Zuo, Jian-Lan Tang
Affiliations: Hawgent Technology Centre in Mathematics, Gangxi Normal University, CHINA
动态数学系统(Dynamic
Mathematics System)在数学教育中能够发挥什么作用？这取决于数学问题的类型以及解决问题的策略. 在这个报告当中，我们根据不同的数学教学问题进行了分析、研究与思考，从而提出了动态数学系统在数学教育教学过程中所具有三个层次或方面的价值与作用：一、动态数学系统是一种工具；二、动态数学系统仅仅是一种工具；三、动态数学系统从不仅仅是一种工具.
(What role
can the Dynamic Mathematics System play in mathematics education? It depends
on the type of mathematics problem and the strategy to solve the problem. In
this report, we analyze, study and think according to different mathematics
teaching problems, and then propose three levels of dynamic mathematics
system in the process of mathematics education and teaching. First, the
dynamic mathematics system is a tool. Second,
the dynamic mathematics system is only a tool. Third, the
dynamic mathematics system is more than just a tool.)
Abstract for 21726
Some Opportunities for
Computational Thinking in the Mathematics Classroom
Author: Jonaki Ghosh
Affiliation: Lady Shri Ram College, Delhi
University, INDIA
Computational
thinking has been identified as an important skill for students who wish to pursue
mathematics and mathematics related disciplines as a career. This has called
for a special focus on CT activities in the K – 12 curriculum. While
many definitions of CT may be found in the literature, all of them seem to
focus on specific skills, such as, the ability to deal with challenging
problems, representing ideas in computationally meaningful ways, creating
abstractions for the problem at hand, breaking down problems into simpler
ones, assessing the strengths and weaknesses of a representation system and
engaging in multiple paths of inquiry. These skills are also critical for
mathematics learning and there is a common consensus on the understanding
that CT skills have to be
developed in mathematics classrooms right from the school years. However finding
appropriate tasks which help to develop and elicit such thinking remains to
be a key pedagogical challenge. Further teachers need to be empowered to
create as well as integrate CT tasks in their lessons. This article hopes to
suggest a guide map for preparing and integrating CT based activities in the
mathematics classroom. It also attempts to highlight how technology can play an pivotal
role in engaging students and in steering them towards computational
thinking. Examples of tasks ranging from iteration and recursion in fractal
constructions to exploration of chaos and simulation of queues and games
which were conducted with secondary school students in the Indian context
will be discussed.
Abstract for 21737
Fixing Education for
the AI Age
Author: Conrad Wolfram
Affiliation: Wolfram Research, UK
The
importance of quantitative understanding for jobs, society and management has
exploded over the last few decades. Meanwhile, the mainstay of preparation
for this computational thinking--mathematics education--increasingly
struggles to match up with these requirements. Why has this chasm opened up and how
can it be bridged? Understanding the changing role of computers and
automation of knowledge is crucial. What will be the future role of humans in
solving problems--in the workplace or in society--given increasing artificial
intelligence? Which human skills must we focus on developing for everyone for
day-to-day survival? What are the top value-added skills for the highest
value contribution?
Conrad
Wolfram will address these questions, explaining the role of computers and a
renewed, broad, core computational subject in transforming education for the
AI age. He will give live demos throughout the talk and answers questions
afterwards.
Abstract for 21738
The Mathematics behind Cryptocurrencies and Blockchain
Authors: Juan Medina Molina, Elena Soledad Jiménez-Ayala
Affiliations: Universidad Politécnica de Cartagena, SPAIN,
Universidad Politécnica de Cartagena, SPAIN
In
day-to-day education, when we introduce a new mathematical concept in class,
students often ask: what is its purpose? It is then useful and enriching to
be able to present some interesting current technology to which the
mathematics can be applied. We show some of the mathematics that underlies
cryptocurrencies, specifically bitcoin and the technology behind it, known as
the blockchain. Many people talk about the blockchain as being one of the
most important innovations of recent times, since it can be applied in a wide
variety of fields, from economy to education.
A vital
aspect of the mathematics present in cryptocurrencies and the blockchain is
cryptography, mainly in connection with elliptic curves. Having some
knowledge of cryptography, therefore, may be appropriate for economists, engineers,
scientists in general, and mathematicians. However, the way to present it to
each of these groups should be different.
We examine
the approach and the contents by which this topic should be introduced in class, and distinguish
to whom the training is aimed.
Abstract for 21748
Proving Nonnegativity of Polynomial with Computer
Authors: Bican Xia, Haokun Li, Lu Yang
Affiliations: Peking University, School of
Mathematical Sciences, CHINA,
Peking University, CICA, CHINA
Chinese Academy of
Sciences, CHINA
Proving a polynomial is nonnegative (either globally or under some
constraints) is a basic and important problem in the field of real algebraic
geometry and has many applications in other fields. This article reviews some
of our works on this topic with emphasis on how to use our tools to prove
nonnegativity of polynomial with computer. Furthermore, a concept
of block SOS decomposable polynomials is introduced which
characterizes a class of polynomials whose SDP matrices (corresponding to
their SOS decompositions) can be block-diagonalized. It is proved that the
set of block SOS decomposable polynomials is measure zero in the set
of SOS polynomials.
Abstract for 21752
Creative Technology-Assisted Approaches to Foster Innovative Mathematics Learning Environments in South
Africa
Author: Werner Olivier
Affiliation: Nelson Mandela Metropolitan
University, First Rand Chair in Maths Education, SOUTH
AFRICA
In this paper the author describes and demonstrates a number of creative
components of an offline Techno-Blended teaching and learning model (TBM) for
mathematics. This model was developed by the Govan Mbeki Mathematics
Development Centre at the Nelson Mandela University with the aim of
addressing some of the key education challenges in under-resourced schools
from rural regions in South Africa. It incorporates modern interactive
digital materials with innovative technological features alongside Android
applications to create innovative 21st century offline learning environments.
Successes with Tablet-assisted learner incubation programmes will be
discussed with reference to qualitative and quantitative impacts of recent large scale pilot
projects. The use of the TBM model to implement an in-service professional
learning network programme for teachers that focuses on Technology Pedagogy
and Content Knowledge (TPACK) will also be discussed. Finally, aspects of the TBM that
focuses on STEAM education awareness and creative problem-solving skills for
4IR will be discussed and demonstrated.
Abstract for 21756
Augmented Reality and
Blended Learning: Engaging Students Learn Word Problems with Bar Model and the
Geometer’s Sketchpad
Author: Krongthong Khairiree
Affiliation: International College, Suan Sunandha Rajabhat University, Bangkok, THAILAND
The purpose of this study aims to explore the students’ perceptions
of teaching approaches using Augmented reality, blended learning in
mathematics via smartphone. In the 2019, action research was conducted in
mathematics class of a lower secondary school in Bangkok, Thailand. The total
of 35 Secondary Year 1 students participated in this study and the duration
of the action research was about three months. In mathematics classroom, the
researcher created mathematics lessons, activities and learning instructions
of her lectures. The students studied mathematics word problems and used the
Geometer’s Sketchpad outside classroom. They used smart phone to scan
QR Code Reader to explore mathematics animations and mathematics activities
prior attending class. The research findings indicated that the blended learning
was new teaching strategy that combined the learning on mathematics in the
classroom and outside classroom via technology. The students brought
assignments/exercises of mathematics concepts inside the classroom via
learning activities. The research findings shown that the students’
engagement in blended learning were higher than the using traditional
classroom. Based on the students’ interviews they revealed that using
blended learning incorporated mathematics word problems, animations
using Geometer’s Sketchpad via smart phone, Augmented reality and QR
Code Reader methods they were able to manage their learning pace and learned
remotely. This learning methods made learning mathematics fun and
challenging.
Abstract for 21757
Exploring Reflections
That Are Inspired by A Chinese Exam Problem
Author: Wei-Chi Yang
Affiliation: Radford University, USA
We use technological tools to explore the reflections on
circles. The discussions in this paper were
inspired by a college entrance practice exam from China. We see if we choose
the incoming and outing light beams are at a specific angle within a circle,
we shall create many nice geometric patterns. Secondly, we replace the straight lines for
light beams by two symmetric curves with respect to the corresponding normal line
at the point on the circle, we will create nice patterns involving curves.
Finally, we explore some known facts regarding the reflections along ellipses
with technologies.
Abstract for 21758
Innovative Strategies:
Visualizations for Teaching and Learning Mathematics
Author: Lila Roberts
Affiliation: Clayton State University, USA
The last 20 years have seen a dramatic evolution of software and hardware
tools that can be used for creating demonstrations and models for teaching
and learning mathematics. From flat 2D representations of three-dimensional
objects, to robust 3D representations using sophisticated graphics software,
to tactile objects manufactured using 3D printing, the important role of
visualizations in teaching and learning mathematics cannot be overstated.
Visualizations increase student understanding and learner motivation. 3D
models of mathematically significant objects provide access to students who
have low vision and have benefits for all students. In this paper, we
investigate various free and proprietary software tools for generating 3D
visualizations, both graphical representations and models created using 3D
printers. Some practical aspects of 3D
printing are also discussed.
Abstract for 30005
Future Knowledge in
Engineering Mathematics and
PCET Calculator - Latest Research Results
(工程数学和PCET计算器的未来知识最新研究成果)
Author: Peter Chew
Affiliation: PCET Multimedia Education, Bukit Mertajam, MALAYSIA
In the talk, Peter Chew will discuss some of his vision regarding his
research in Engineering Mathematics and his development in the PCET
calculator latest research results. One area is to create new rules, methods
or theorems to complement necessary information that can enhance certain area
of engineering mathematics. The new discovery can make solving certain
engineering mathematics problems easier, which in turn can assist our
mathematics teaching and learning. He also will share his PCET
calculator special functionalities, where he will cover the following two
main areas, Peter Chew Rule in solutions of triangle, as well as some special
features of the PCET calculator, uses future knowledge in PCET calculator
design such as Peter Chew Rule. He will present current issues, techniques
and methods in his field of research and introduce his latest research
findings.
Recently,
mathematics has become a challenging course for high school students around
the world. Some mathematics researchers and educators have adopted different
approaches to solve this challenge. Technical tools have had a major impact
on advanced mathematics teaching and mathematics learning. Today's online
calculators and math applications, photo math applications and calculators
contain only the knowledge already stated in the book such as the sine and
cosine rule. However, some areas of mathematics today are not complete, which
leads to a certain field where some of the same questions are difficult to
solve or cannot be solved. Therefore, a new product with some complete
mathematical fields is needed today to help teach and learn in higher
education, which is the main goal of the PCET calculator. In author’s
opinion, the PCET calculator covers some specific areas of mathematics, and
its design contains some knowledge that has not yet been covered in any
textbook as of today. Another goal of the PCET calculator is to help students
to gain interests and promote effective learning in mathematics.
(摘要-在演讲中，周贻德将讨论他对工程数学的研究以及在PCET计算器最新研究成果。未来知识研究的目标是创建新的定律，方法或定理，以补充必要的信息，从而增强工程数学的某些领域。新发现可以使解决某些工程数学问题变得更加容易，从而可以帮助我们进行数学教学。他还将分享PCET计算器的特殊功能，其中将涵盖以下两个主要领域 周贻德定律在任意三角形，以及PCET计算器的一些特殊功能，使用未来知识在 PCET 计算器设计例如周贻德定律.他将在他的研究领域介绍当前的问题, 技术和方法，并介绍他最新研究成果。
最近, 数学已成为全世界中学学生的挑战性课程。一些数学研究和教育工作者采用了不同的方法来解决这一挑战。技术工具对高等数学教学和数学学习产生了重大影响。现今的在线计算器和数学应用程序，照片数学应用程序和计算器只包含已经在书中陈述的知识例如正弦定律和余弦定律. 可是现今数学的某些领域还没有完整，这导至该领域某些同题难以解决或无法解决。因此，现今需要一个具有某些完整数学领域的新产品，以帮助高等教育中的教导与学习，这是PCET计算器的主要目标。 PCET计算器具某些完整数学领域， 因PCET计算器设计包含一些未来的知识，这些未来的知识还没有说明在现今任何高等教育书籍中。一些未来知识可以解决一些目前无法解决的问题。 PCET计算器的別一个目标是帮助学生维持兴趣，促进数学的有效学习。)
Video
clips can be
downloaded from the following URLs: (https://youtu.be/0sSVPZpzvpo (English) or https://youtu.be/6C92IWy_24U (Chinese).
Abstract for 30010
Towards Dynamic
Mathematics with Cabri: Where do we stand? Where do we go?
Author: Jean-Marie Laborde
Affiliation: CNRS Univ. Grenoble Alpes Cabrilog, FRANCE
It is common to say
that technology and its impact on society is moving fast. Is that so sure? In
the early 1980s, the rise and success of the Graphical User Interface or GUI concept,
in direct manipulation, made possible the invention of dynamic geometry.
It took some time for
Dynamic Geometry Systems (DGS), namely Cabri and just after
Geometer's Sketchpad, to spread throughout the various educational systems.
For a long time, only the most innovative teachers have understood the real
potential of the revolution brought by such environments.
Nowadays, we must
admit that dynamic geometry, and more and more widely and recently, dynamic
mathematics have not yet completely revolutionized the learning and teaching
of mathematics.
In my presentation, I
will explore the limitations of making profound, technology-based changes in
mathematics education. I will present evidence of these constraints,
but will also explain the
evolutions and the solutions that the Cabri team is working on,
especially with regard to the availability and maturation of the new Cabri-Express. Cabri Express being free of
charge and running on the Internet on any device.
Abstract for 30100
The Evolution of Computer
Algebra in the Teaching and Learning of Mathematics: Differential Equations
Author: Douglas B. Meade
Affiliation: University of South Carolina –
Columbia, USA
In this talk I will
provide a quick tour through some of the different ways in which I have used
Maple to improve student
understanding of traditional topics in an introductory differential equations
course, such as direction fields, the phenomenon of beats, and
developing an understanding of solutions to first-order systems in
phase space. In addition to highlighting improvements that became possible as technology,
particularly Maple, has improved I will also discuss additional technological
advances that can bring additional educational benefits for
differential equations.
The following two
screenshots show two of the interactive examples that will be discussed in
this talk.
A
collection of video clips and other resources ssociated with this
presentation is available online. They can be found at http://atcm.mathandtech.org/EP2019/videos/30100/.
Abstracts for Full Papers
Abstract for 21689
Scientific Calculators to Improve Students’ Critical Thinking Skills: An Evidence from Mathematical Exploration in Mathematics Classroom
Authors: Ariyadi Wijaya, Heri Retnawati,
Wahid Yunianto, Pasttita Ayu Laksmi,
Mutia Meilina, Pientha Glenys Amanti
Affiliations: Universitas Negeri Yogyakarta, SEAMEO QITEP in
Mathematics, INDONESIA
Casio INDONESIA
In
Indonesia, most teachers hold negative perspectives toward the use of
scientific calculators for learning mathematics. Many teachers are worried if
calculators will weaken students’ fluency in performing calculation and
hinder students’ understanding of mathematics concepts. Considering
this situation, the present study is aimed at exploring scientific evidences
that calculators are beneficial for developing students’ conceptual
understanding and critical thinking skills. The present study used a
quasi-experimental research with a pretest-posttest control-group design. A
total of 940 tenth graders from 21 schools in nine provinces in Indonesia
participated in the study. The experimental groups learnt the topic of linear
and quadratic functions by using scientific calculator Casio Classwiz, whereas
the control groups learnt the same topic in regular activities utilizing
paper-and-pencil approach. The use of Casio Classwiz in the
experimental groups was not as a calculation tool, but as a tool to explore
and investigate mathematics concept. The data analysis shows a significant
difference for students’ critical thinking in which the experimental
group (M =17.40, SD=21.13) outperformed the control group (M = 12.97, SD =
20.00); p = .000. This finding serves as a scientific evidence that using
scientific calculators in exploratory mathematics activities could improve
students’ critical thinking.
Abstract for 21692
Visualizations of Vector Fields and Ordinary
Differential Equations with KeTCindy
Authors:Takeo Noda, Setsuo Takato
Affiliations:Toho University, JAPAN.
Toho University, JAPAN
In this paper, we present some examples of visual
teaching materials which are made by using KeTCindy and used
in courses of ordinary differential equations and vector calculus. In
undergraduate mathematics education, simple and accurate figures sometimes
help learners to understand mathematical concepts. KeTCindy is a
powerful tool for generating such mathematical figures. It uses Cinderella as
a graphical user interface and creates TeX codes for
the graphics. The outputs can be implemented not only in printed materials,
but also in slides for screen presentation. Furthermore, KeTCindyJS, which is
an extended version of CindyJS, can make
those figures into interactive content, which can be viewed and manipulated
on web browsers.
Abstract for 21718
Connecting with Data:
Exploring Statistical Concepts Using R
Author:Leslie Chandrakantha
Affiliation:John Jay College of Criminal Justice of CUNY, USA
R is a
language and environment for statistical computing and graphics. R has proven
to be an excellent tool for understanding and visualizing statistical
concepts. In this paper, we present how to use R for data analysis,
elementary simulation, and understanding concepts in an introductory level
statistics course. We consider examples from descriptive statistics, normal
distributions, sampling distributions, confidence intervals, and hypothesis
testing to demonstrate the use of R.
Abstract for 21722
The Delivery Role and
Assessment Role of Computer-Based Technology in a Flipped University
Mathematics Course
Authors: Wee Leng Ng, Kok Ming Teo, Khoon
Yoong Wong, Kang Ling Michelle
Kwan
Affiliations: National Institute of Education, SINGAPORE
Nanyang Technological
University, SINGAPORE,
National Institute of
Education SINGAPORE
In recent years, computer-based technology (CBT)
has enabled university lecturers to teach their courses using non-traditional
pedagogies. One such pedagogy is the flipped learning model. Under this
model, students learn the basic content on their own using pre-class tasks
and then come to class to engage in more challenging work such as solving
difficult problems. CBT can play two important roles in flipped learning, namely to deliver learning materials efficiently and to
assess student achievement effectively. This paper describes how these two
roles were applied to a flipped Linear Algebra II course in the National
Institute of Education (Singapore), taken by a group of student teachers (n =
15) over a 12-week period from January to April 2018. Their perceptions of
flipped activities were gathered using weekly surveys, mid-semester survey,
end-of-course survey, and end-of-course interviews. They generally agreed
that flipped learning using CBT was helpful and enjoyable. As flipped
learning becomes more common among university lecturers in Asian countries,
it is beneficial to share experiences of utilising CBT to
promote active learning of mathematics among university students.
Abstract for 21727
What does Research Say on the Use of Calculator to Improve Indonesian Students’ Mathematics Achievement?
Authors: Pasttita Ayu Laksmiwati, Ariyadi Wijaya,
Heri Retnawati, Wahid Yunianto,
Pientha Glenys Amanti
Affiliations: SEAMEO QITEP in Mathematics, INDONESIA,
Yogyakarta State
University, INDONESIA,
SEAMEO QITEP in Mathematics, INDONESIA,
Casio Singapore Pte Ltd, SINGAPORE
Jakarta Rep Office INDONESIA
Technology
has essential roles in mathematics teaching and learning. So, it is crucial
to facilitate students with access to technology, such as the use of
calculators in their learning process. This study was aimed to investigate
the effectiveness of the Classwiz scientific
calculator on the improvement of students’ mathematics achievement.
This study was conducted in nine provinces of Indonesia, involving eleven senior
high schools. The researchers employed a quasi-experimental research study
with pretest-posttest control-group design with both qualitative and
quantitative data collected and analyzed. Five lessons with context-based
activities as interventions in the experimental group were designed to offer
students OTL. The qualitative data were collected by using a mathematics test
involving pre-test and post-test. Moreover, the study used classroom
observation and field notes to collect qualitative data. The main
focus of the research was students’ mathematics
achievement. The students’ mathematics achievement was also analyzed
based on the perspective of gender and school location (western, central, and
eastern Indonesia). The investigation showed that the use of the calculator
gave a significant impact on the students’ mathematics achievement. In
conclusion, the finding of the study suggests that the use of calculators in
mathematics learning could improve students’ mathematics achievement.
Abstract for 21729
How to Enhance
Students’ Participations in Mathematics
Learning Using Calculator?
Authors: Heri Retnawati, Ariyadi Wijaya,
Wahid Yunianto, Pastita Ayu Laksmiwati,
Mutia Meilina, Pientha Glenys Amanti
Affiliations: Universitas Negeri Yogyakarta, Mathematics
Education Department Mathematics and Science Faculty, INDONESIA,
Universitas Negeri Yogyakarta, INDONESIA,
SEMEO QITEP in Mathematics, INDONESIA,
Casio Education, SINGAPORE
One of strategy
to improve the quality of mathematics learning is increasing students''
participations in learning. During this process, students are guided to find
mathematical concepts through exploration, so that concepts can last longer
in their minds to be utilized in problem solving. One strategy that can be
used to enhance students in mathematics learning is integrating calculator
utilization. This study was to describe the strategy to enhance
students’ participations in mathematics learning in high school and
vocational school using a calculator. This research is a narrative
qualitative study. Data was collected by observation of 21 teachers from 8
provinces in Indonesia who integrate teaching and learning using calculator
and documenting students’ responses to worksheets developed by
researchers. Data analysis was carried out using Cresswell’s steps. The
results showed that the teacher’s keywords
to enhance students in mathematics learning on the topic function was
integration the use of a calculator starting from the lessons design,
prepared appropriate work sheets and carry out learning, guided students to
discover concepts through learning activities, and facilitated students to
collaborate and communicate during the process learning. The steps of learning
that integrate calculator to explore mathematical concepts in detail are then
discussed.
Abstract for 21735
Making the Mathematics
Enjoyable in Science
Author: Minoru Ito
Affiliation: Tokyo University of Science, JAPAN
An introduction
to current Japanese mathematics and science education for enhancing
children’s motivation to concern about the nature of phenomena around
us; for example, the size of the universe etc. We discuss how teachers can
apply mathematics to science using materials that I have
developed. We shall see some of those contents in details, with which
science teachers can apply and
make their mathematics
and science education classes more enjoyable.
Abstract for 21769
Teaching
Binary Number Concepts using Mathematic Magic Card
Trick
Author: Janchai Yingprayoon
Affiliation: International College, Suan Sunandha Rajabhat University,
THAILAND
Mathematic
Magic Card Trick is a creative mind-reading trick based on binary system that
uses 5 tables. The tables are constructed from a
principle of conversion between decimal and binary system. This magic cards can be used as an induction set before teacher
starts introducing the binary system. This can make classroom fun and
meaningful.
Abstracts for Presentations
with Abstract Only
Abstract for 21743
Comparison of Some Properties of Triangles and Tetrahedrons
Author: Younbae Jun
Affiliation: Kumoh National Institute of
Technology, SOUTH KOREA
The
triangle is the simplest polygon, and the tetrahedron is the simplest polyhedron.
They have very similar characteristics, and in many cases, similarity can be
explained by analogy from 2D to 3D.
Many
properties of a triangle can be constructed with a ruler and a compass, but
their construction in a tetrahedron is relatively difficult. Thanks to
advanced technological tools such as interactive and dynamic geometry
software, 2D and 3D figures can be easily constructed.
In this
paper, we compare some properties of triangles and tetrahedrons in terms of
analogy, construct them using software, and improve students'' creativity by
learning analogies.
Abstract for 21744
Mining Cryptocurrency
for Mathematics Applications
Author: Russel Carson
Affiliation: BYU-Hawaii, USA
Cryptocurrencies,
such as Bitcoin, provide practical examples of a host of different kinds of
mathematical tools. However, many math educators are not familiar enough with
them to use them as examples when teaching math. Some of the mathematical
tools involved in cryptocurrencies are non-invertible and non-linear
functions, modular arithmetic, convergent geometric series, and Boolean
algebra. The basic mathematical structure of a cryptocurrency will be
discussed, followed by some examples of applications that could be used in
mathematics classes.
Abstract for 21745
Development of Animation of Sine Curves to Teach the Concepts of Trigonometric Functions
Authors: Koji Nishiura, Setsuo Takato, Kunihito Usui
Affiliations: National Institute of Technology,
Fukushima College, Faculty of
Sciences, Toho University, JAPAN,
Control Engineering,
National Institute of Technology, Kisarazu College, JAPAN
In this study,
we develop an effective method for teaching mathematics and enhanced
materials for teaching problematic concepts to students of upper secondary
and higher education.
Students
often find understanding the concepts of trigonometric functions difficult;
therefore, we selected trigonometric functions as a suitable topic to create
enhanced teaching materials. We developed the animation of sine curves using KeTCindy mathematical
software.
The second
author developed KeTpic to
simplify the process of producing high-quality graphics in TeX documents.
Further, he developed KeTCindy, which
serves as an interface between KeTpic and
Cinderella dynamic geometry software, and KeTCindyJS, which
integrates the functions of KeTCindy to CindyJS, enabling
easy creation of various interactive materials.
Using KeTCindy and KeTCindyJS, we
created a teaching material that includes the animation of sine curves along
with the explanation of some mathematical concepts and problems. Furthermore,
we conducted experiments involving eye movement measurement to analyze the
effectiveness of the created teaching material. In this talk, we will present
the animation of sine curves and the results of
the experiments.
Abstract for 21747
Visualization of Complex Function Integral with GeoGebra
Author: Shigeki Ogose
Affiliation: Kawaijuku, JAPAN
You can
visualize not only the result of a complex function integral but also how the
partial sum (∑f(z)dz ) while z is a
complex number) converges to the integral along its pass with GeoGebra. And
it' is easy.
Once you write the main program with GeoGebra, all you have to do is to
input a function and
compose a path with a mouse for almost all integrals found in undergraduate
textbooks.
Abstract for 21767
Animations and
Dissections of Rhombic Polyhedra
Author: Jia Yao
Affiliation: National Tsing Hua University,
TAIWAN
In this
paper, we will show 18 sets of animation of dissection of rhombic polyhedra: (1)
Animation of Rhombic Polyhedra of type (2k+1,2k), k>1; (2) Animation of
Rhombic Polyhedra of type (n,n+1), n>3; (3) Dissection of Rhombic
Polyhedra of type (2k+1,2k); (4) Dissection of Rhombic Polyhedra of type
(n,n+1); (5) Animations of Dissection of Rhombic Polyhedra of type (2k+1,2k)
into Rhombohedra; (6) Animation of Dissections of Rhombic Polyhedra of type
(n,n+1) into Rhombohedra; (7) Animation Connecting a cube of 48-face Rhombic polyhedra; (8)
120-face Rhombic Polyhedra; (9) 48-face Rhombic Polyhedra; (10) Six Cylinders
each touching four others at one point; (11) Linkage; (12) Diagonal Burr; (13)
Space Filling Polyhedra; (14) Pennyhedra in the
form of Dodecahedra; (15) Pennyhedra in the
form of Tricontahedron; (16) 12
Sticks; (17) Rhombic Polyhedra Complex; (18) Two-Piece Interlocking Puzzle.
This work
is valuable for 3D demonstration in a science exhibition. The geometric
construction and animation serve as a good training for hand-eye
coordination. Visual Geometry has attracted people’s attention for a
long time. This work shows how the interactive geometry software Cabir3D can
concretely develop new ideas in this field.
Abstract for 30002
The Different Meaning of the Pythagorean Theorem
and the Area
Author: Michel Carral
Affiliation: Université Toulouse, FRANCE
Through
the different demonstrations of the theorem of Pythagoras, we show the different
meanings of the Pythagorean Theorem even though they have the same statement. We look
vertically the notion of “area” as a Euclidian notion and
algebraic notion (is an affine invariant) from the primary to the university.
We show the links between the trilinear (Cartesian, Barycentric, normal
…), and some actions of the affinity.
Abstract for 30200
Integrating Hawgent Dynamic Mathematics
into Teaching “The Formula for the Area of a Circle” from a TPACK Perspective
Authors: Jian-Lan Tang, Jun-Yu Wang, Jia-Zhen Song
Affiliations: Guangxi Normal University, 15 Yucai Road, Qixing District, Guilin, P.R.CHINA 541004
The
formula for the area of a circle is an important content of the sixth-grade
mathematics, and it is a good material for students to cultivate their
mathematical reasoning. Reasoning of the formula for the area of a circle has
been a difficult point and focus of teaching. Aiming at the issue "why
is the formula for the area of a circle like S= πr²? What is the relationship
between the formula for the area of a circle and that of a
rectangle or a triangle?" more than
90% of teachers and students only know the formula S= πr², but
don’t know why the formula is like this, in a "knowing it but do not
know why, let alone knowing how to know it" . This paper attempts to
explore this issue through integrating Hawgent Dynamic
Mathematics into teaching “the Area of a Circle” from a TPACK
perspective.
Abstracts for the Hands-On
Workshops
Abstract for 21675
Generating Educational Videos
Author: Juan Medina
Affiliation: Universidad Politécnica de Cartagena, SPAIN
Educational
videos are very popular nowadays, from MOOC courses to videos that can be
found on online platforms such as Youku or YouTube. In this workshop session
we will tell of our own experience in the creation of mathematics videos,
which began in December 2005 with our portal lasmatematicas.es – one of
the first educational video portals in the world. We will discuss a variety
of procedures for the creation of educational videos and also talk about
how to translate videos into other languages efficiently.
Abstract for 21679
Exploring and Visualizing
Statistical Concepts
Using
R Programming Environment
Author: Leslie Chandrakantha
Affiliation: John Jay College of Criminal
Justice of CUNY, USA
This workshop session will highlight the use of the R programming environment as a teaching tool in understanding basic statistical concepts. Introductory statistics concepts are relatively abstract for many students. Research has shown that the use of technology enhances the understanding of basic concepts. The following topics will be explored: descriptive statistics and charts, probability distributions, sampling distributions and the central limit theorem, hypothesis testing and confidence intervals. Participants will have hands-on experience in learning how R can be used to reinforce their teaching of statistical concepts in the classroom.
Abstract for 21681
Revolutionary Maths with a Revolutionary Freeware: Cabri Express
Authors: Jean-Jacques Dahan, Jean-Marie Laborde
Affiliations: IRES of Toulouse, FRANCE
Cabrilog, FRANCE
In the
same platform, Cabri Express provides
an environment for 2D and 3D DGS, for coding and for algebra : you will approach math in a so different and
motivating way. You will see how to use the online as well its offline
version.
Abstract for 21686
Design and Implementation
of Web-Based Dynamic Mathematics Intelligence Education Platform
Author: Guan Hao
Affiliation: Chengdu Institution of Computer
Application, CHINA
The
information and communications technology (ICT) in education can effectively
promote the development of ICT in subject by going to depth of a subject, and can
practically assist the teaching process and improve the teaching quality. A
dynamic mathematics intelligence education platform (DMIEP) is a tool of ICT
in subject that goes to the depth of the mathematics subject. We will briefly
reviews the development of the web-based dynamic mathematics software;
proposes that the design principles of the web-based, especially a mobile
internet-based, DMIEP software should be “opening and sharing”;
and provides goals to be achieved, such as seamless integration with a system
or a third party application in a cross-terminal manner, good expansibility,
and intelligence. Under the guidance of the principles and goals, an opening
and sharing DMIEP has been designed and implemented, having functions such as
relationship-based drawing, geometric graphic transformation, dynamic
measurement, dynamics and parameters iteration, geometrical theorem automatic
reasoning, and opening interfaces. At present, the platform has been widely
used in the mathematics teaching process of primary and secondary schools.
Abstract for 21691
Cabri 3D Workshop on Circumscriptible
Hexahedron of type
(4,4,3,3,3,3)
Author: Jen-Chung Chuan
Affiliation: Department of Mathematics, National
Tsing Hua University, Hsinchu, TAIWAN 300
In this
workshop, we are to construct, with Cabri 3D, a
polyhedron that has two quadrilateral and 4 triangular faces, such that all
edges are tangent to a sphere.
Step 1:
Planar construction
Construct
this configuration:
Here PB/BQ =
Golden Ratio
Step 2:
Inversion
Invert
points A, B, C to A’, B’, C’ respectively w.r.t. a sphere
(not shown) tangent to the xy-plane at
O.
Step 3:
Quadrilateral face
Construct a the plane U
parallel to the xy-plane
passing through the center of inversion.
Let
PA’ meet the plane U at S.
Let T be the reflection
of S across the z-axis.
Let
TC’ meet PB’ at U.
Construct
the quadrilateral PSTU.
Step 4:
Convex hull
The convex
hull of PSTU and its reflection across the z-axis is the required hexahedron
Step 5: Verification
Verify
that each edge of the hexahedron meets the sphere (with center of inversion
as its south pole) at exactly one point.
Abstract for 21618
Discovering the Online
Freeware Cabri Express
Authors: Jean-Jacques Dahan, Jean-Marie Laborde
Affiliations: IRES of Toulouse, FRANCE
Cabrilog, FRANCE
We will
discover the possibilities of this free online calculator which environment contains
both a 2D and a 3D DGS. We will see how to record the created files online
and to open online files created by anybody. We will also see that this
freeware allows the users to open activities (that can be multipage
activities) created with the New Cabri.
Abstract for 21703
A Potpourri of Activities for the Classroom by using Free Software
Author: Guillermo Davila-Rascon
Affiliation: University of Sonora,
Department of Mathematics, MEXICO
This
hands-on workshop is intended for undergraduate students and we will present some
computer activities with GeoGebra and Maxima, for
1)
applying modular arithmetic for residue design
2)
exploring the reflections of light rays in curves, especially, in conics
3)
modeling and synchronizing chaos
The workshop
material is intended for two sessions of one hour each, and the
materials (programs) will be provided by the instructor.
Abstract for 21730
How to Use KeTCindyJS to Produce Interactive Materials
in HTML Format
Authors: Setsuo Takato, Koji Nishiura, Takeo Noda
Affiliations: Toho University, JAPAN,
National Institute of
Technology, Fukushima College, JAPAN,
Toho University, JAPAN
LaTeX is a
great tool to produce high-quality educational materials containing finely-tuned mathematical
expressions. However, it is not that easy for mathematics teachers to handle
scientific artwork on their classroom materials. KetCindy enables
them to overcome this limitation and prepare high-quality mathematical
figures in PDF format through intuitive, user-friendly operations. In short, KeTCindy is a
computer collaborative system based on two major components: the dynamic
geometry software Cinderella, and LaTeX drawing tool KeTpic, the
latter being a tool developed by ourselves. We organized a workshop on KeTCindy in
ATCM2016.
Recently,
we have developed a powerful follow-up of KetCindy, called KeTCindyJS. It is a
collaborative system of KeTCindy itself and CindyJS (https://cindyjs.org)
to produce interactive materials in HTML format from KeTCindy. KeTCindyJS does not
create LaTeX files, but HTML files, which are closely related to LaTeX files
from KeTCindy. Lots of
samples of KeTCindy and KeTCindyJS can be
found at the URL: https://s-takato.github.io/ketcindysample/
Both
systems, KeTCindy and KeTCindyJS, are
provided for free, so they can be freely used anytime and anywhere. The
package KeTCindy,
including KeTCindyJS, is fully
downloadable from CTAN (Comprehensive TeX Archive
Network). Go to CTAN (https://ctan.org) and search for ``ketcindy", or
proceed directly to: CTAN/ketcindy (URL:
https://ctan.org/pkg/ketcindy).
This
workshop will be organized as a brief introduction to KeTCindy and KeTCindyJS. KeTCindy needs
LaTeX, R and Maxima to produce PDF files via LaTeX, so some samples will be
only briefly demonstrated. The rest of the time will be assigned to
experiences of KeTCindyJS. Teachers
who are not necessarily frequent LaTeX users, but are interested in using better figures in their
interactive materials, are highly welcomed.
Abstract for 21755
Designing Mathematics
+ Computational Thinking Lessons
Author: Weng Kin Ho
Affiliation: Nanyang Technological University, SINGAPORE
This
workshop provides the participants with a hands-on experience in designing
lesson using the four design principles (Complexity, Data, Mathematics,
Computability) that teach mathematics to high school students, harnessing on
computational thinking paradigm.
Abstract for 21765
利用Hawgent皓骏创建个性化的动态数学软件
(Creating Personalized Dynamic Mathematics Software with Hawgent)
Authors: Chuan-Bo Zuo, Chu-Biao Lin
Affiliations: Hawgent Technolgoy Centre in Mathematics, CHINA,
Foshan Guicheng Middle School, CHINA
动态数学软件发展至今已有30多年，功能也越来强大、越丰富. 但是，我们发现，无论选择哪一款动态数学软件，都会感到有些非常实用的功能它没有实现. 事实上，现在或将来任何一个团队开发的任何一款软件都无法做到这一点，即：满足所有使用者的千变万化甚至是不断变化的需求. 那么允许每一位使用者创建个性化的、满足个性需求的工具与菜单就显得非常重要.
在Hawgent皓骏当中，你可以直接调用她内部的所有函数，还可以直接定义属于你自己的函数，甚至也能够直接运行C#中的所有函数，从而为我们创建个性化的动态数学软件而服务.
在本工作坊当中，我们将通过几个具体的案例指导大家如何利用Hawgent皓骏创建个性化的动态数学软件工具与菜单.
(Dynamic
mathematics software has been in development for more than 30 years, and its
functions are becoming more powerful and richer. However, we found that no
matter which dynamic math software you choose, you will find some very useful
functions that are not implemented. In fact, now or in the future, any
software developed by any team cannot do this, that is, to meet the
ever-changing needs of all users. It is very important that the software allow each
user to create personalized tools and menus that meet individual needs.
In Hawgent, you can
directly call all
of her internal functions, or you can directly define your own
functions, and even run all the functions in C# directly, thus serving us to
create personalized dynamic math software.
In this
workshop, we will guide you how to use Hawgent to create personalized
dynamic math tools and menus through several specific cases.)
Abstract for 21768
Creative Mathematics Hands-On Activities in the
Classroom
Author: Janchai Yingprayoon
Affiliation: International College, Suan Sunandha Rajabhat University,
THAILAND
Many
children find that Mathematics is difficult and boring. Nevertheless, 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 to learn Mathematics. The
workshop will show ways to develop creativity in Mathematics and Technology
Education to increase intellectual curiosity, to develop problem solving and
thinking skills, to promote discovery as well as to unleash creativity. In
the workshop, the participants will share with each other how to make
Mathematics lessons more meaningful, effective and interesting, how to
cultivate intrinsic motivation for learning Mathematics, and how to develop
thinking abilities, problem-solving skills and creativity.
Every
participant will receive a fun and creative activity pack. Samples of
creative hands-on activities will be demonstrated as follow: Curves in
Nature, Reaction Time Test, Simple Balance, Mathematics of Robot arms.
Abstract for 30000
Mathematical
Explorations using Spreadsheets
Author: Jonaki B Ghosh
Affiliation: Department of Elementary Education, Lady Shri Ram College for
Women University of Delhi, INDIA
Spreadsheets
such as Microsoft Excel or LibreOffice Calc can be very useful tools for
performing scientific calculations and statistical data analysis. They enable
us to simulate problems and
also create, visualise and analyse mathematical
models. The power of spreadsheets can be leveraged in a course on
mathematical modeling where problems may be explored through simulations and
graphical analysis. This hands-on workshop will focus on the use of a
spreadsheet for exploring some mathematical concepts and problems, which lend
themselves to investigations. Problems discussed in this session will include
interesting paradoxes related to probability such as the Birthday Paradox and
the Monty Hall problem. It will also include explorations in chaos and
dynamical systems, simple regression analysis and applications of mathematics
to cryptography. Participants will get a hands-on experience
Abstracts for the Poster Session
Abstract for 21707
About Decimal
Expansion (Approximate Value) of Irrational Numbers
Author: Kimio Seishi
Affiliation: Tokyo University of Science, JAPAN
It is easy
for the junior high school students to understand the size of displaying
fractions and irrational numbers as decimal approximations. However,
understanding is difficult because the definition is complicated, especially in
the case of irrational numbers.
In junior
high school in Japan, the image of the square root is described using a
figure such that the length of one side of the square is the square root of
the area of the square. However, in order to calculate an approximate value,
the length of one side is estimated and it is calculated by calculating how
close the square is to the area of the square to be obtained. In other words,
it uses the method of calculating the approximate value by calculating many
times each time while increasing the decimal places one by one.
Here, I
will introduce two methods systematically to calculate the approximate
values. We set the length of one side of a square to the square root of its
area.
First, we
consider a rectangle of the same area instead of a square, and from the
average of the vertical and horizontal lengths of this rectangle. We find the
next new vertical and horizontal length. Repeat this operation. However, the
rectangle is transformed into a square to obtain the length of one side. (I
will refer this as Horizontal and Vertical Averaging.)
Second, we
consider a rectangle in which one square is known and the other square to be determined is mixed
and halved. The length of the square, which is
known to be half the area and the other side. To create a new square, we repeat
this operation to find the
length of one side. (I will call this as Square
Dichotomy.)
From the
above, the approximate value of P, for example, can be easily calculated
systematically as follows by using a graph calculator.
At first,
after entering the length of the
first rectangle, enter (ANS + P / ANS) / 2 and repeat
until the value no longer changes.
Second,
enter the length of one side of the square you know, then enter (ANS^2 + P) /
2 / ANS and repeat until the value no longer changes.
