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1.
Abstracts
for Invited Papers
2.
Abstracts for
Full Papers
3.
Abstracts
for Presentations with Abstract Only
4.
Abstracts for Hands-on workshops
Abstracts for Invited
Papers
Abstract for 21945
Olympic geometry problems: human vs. machine
Authors: Belen Ariño-Morera, Tomas Recio, Piedad Tolmos
Affiliations: Universidad Antonio de Nebrija,
Madrid, Universidad Rey Juan Carlos, Madrid
We discuss, through a collection of examples, the behavior of
GeoGebra Discovery automated reasoning tools concerning the solving of some
difficult elementary geometry problems, such as those proposed in
mathematics contests, or in entrance exams for talented students’ training courses
(e.g. ESTALMAT https://www.estalmat.org ), or in
selection processes for becoming a mathematics teacher for the public
administration (Spanish: “oposiciones”). Considering
just statements coming from these sources, and such that GeoGebra Discovery
is currently programmed to deal with (e.g., not involving inequalities in
the hypotheses), we observe, on the one hand, the good behavior of GeoGebra
in many instances and, in the other, the remarkable coincidence on the
perception of the difficulty, for both human and machine solvers (see, for
example, [1]). It is surprising to verify, once more, that there is some hidden
coincidence between the difficulty of solving the given problems, for
humans and for machines, even considering only those cases that machines
can address without restrictions. See [2], where it is remarked how
Computer Algebra troubles for deriving conclusions from equalities through
rewrite rules, coincide with-- and may actually help understanding--
students’ difficulties with such tasks, proposed in the well-known in the
70’s, Chelsea College Concepts in Secondary Mathematics and Science (CSMS)
Project. We think that both facts (the use, in relevant contexts, of test
items for humans that can be solved by a machine; the ability to detect the
idea of “difficulty” through the behavior of a machine) should be further
explored and discussed, regarding their potential consequences in mathematics
education. In this respect we would like to call the attention of the
community of educators about the need to understand and to compare the
notion of “difficult” geometric problem, both for humans and for GeoGebra
automated reasoning tools, as it could
a) help improving the performance of GeoGebra, by advertising the
user beforehand that a sought query is of high difficulty and that might
expect a delayed or no answer, or by selecting, in the Discover command output,
to exhibit only interesting theorems, avoiding obvious, trivial ones, etc.
Likewise, it could
b) help improving and adapting GeoGebra’s reasoning tools to the
needs of students with high capacities. Finally, as the most direct
consequence, a deeper consideration of the concept of difficulty for
geometric problems, regarding the machine vs. human behavior, could
contribute to
c) foster the potential role of GeoGebra concerning geometric
problems posed in mathematical contests, such as the mathematical
Olympiads, etc.
[1] Ariño-Morera, B. (2022): GeoGebra Discovery en la (European Girls’ Mathematical Olympiad) EGMO 2022. Actas de las Jornadas de Aprendizaje y Enseñanza de las Matemáticas,
(JAEM 2022). Valencia.
[2] Recio, T. (1998): Didactical relevance of meaningless
mathematics. International Journal of Computer Algebra in Mathematics
Education (IJCAME), vol.5, no. 1, 15-27.
Abstract for 21946
Spreadsheets: A Technological Nexus between Big Ideas in Mathematics
and Computational Thinking in Mathematics Classrooms
Authors: Weng Kin Ho, Jonaki Ghosh, Berinderjeet Kaur, Chee Kit Looi
Affiliations: Nanyang Technological University, Department of
Elementary Education Lady Shri Ram College for Women University of Delhi Delhi, India, National Institute of Education Mathematics
and Mathematics Education Nanyang Technological University Singapore
Recent years in Mathematics Education research saw the emergence of
‘Big Ideas in Mathematics’ and ‘Computational Thinking’ as two areas of
intense research. This paper highlights the technological and pedagogical
affordances of electronic spreadsheets, which make them a convenient and
practical technological nexus between ‘Big Ideas in Mathematics’ and
‘Computational Thinking’ in a Mathematics classroom. To demonstrate how
such a connection is realized in authentic classroom settings, some
instructional exemplars that have been designed and deployed in Asian
(senior) high schools are provided here. Our present approach for
generating such mathematics lessons may be considered as one of the ways
for mathematics teachers to transform their understanding of big ideas of
mathematics into tasks and lessons in the classroom.
Abstract for 21948
Ordering Question with Clue in Moodle
Authors: Kosaku Nagasaka, Takahiro Nakahara
Affiliations: Kobe University, Sangensha
LLC
The ordering question is one of the third-party question types for
the quiz activity in Moodle. It displays several draggable items in a
random order, that may include a couple of mathematical expressions
rendered by MathJax or KaTeX.
The students are required to rearrange/drag them in the correct order
specified in the question text. This question type is very useful to
evaluate or drill the both of procedural and conceptual knowledge in
mathematics if the questions in use are well considered and structured. In
this paper, we propose a new feature for the ordering question type, that
allows some items to be fixed as clues (static/non-draggable items). This
feature helps the students to understand how to solve the problem and force
the students to think deeply the hidden relationship among the given items.
We also show our actual ordering questions with clues in use, that are
pre-class learning activities as one of self-assessment tasks in linear
algebra lectures.
Abstract for 21949
Ellipsoid is Tangent to its Locus under a Linear Transformation,
Isometries and Sheared Maps
Authors: Wei-Chi Yang
Affiliations: Radford University
In ([10]) and ([9]), we describe an antipodal linear transformation L
on an ellipsoid S; and see S is inside and tangent to L(S): In this paper,
we discuss how two geometry figures are congruent and are related by an
isometry through this linear transformation L. We describe how a locus
ellipsoid L(S) can be written as a standard form of XMX^t
= 1, and how the rotated ellipsoid Sr stays tangent to XMX^t
= 1: Next, we also explore how the ellipsoid, XMX^t
= 1, can be tilted so its minor and medium axes form a circle. We first
note that the minor and mean axis of XMX^t = 1
span a plane P that intersects the ellipsoid in the smallest possible
ellipse. We rotate this plane by keeping the mean axis fixed, and tilting
the minor axis towards the major axis. At some unique point, one obtains a
plane P that intersects the ellipsoid in a round circle. We shall explore finding
such sheared map T. This paper will benefit those students who have
backgrounds in Linear Algebra and Multivariable Calculus. In particular, we
need the eigendecomposition for the ellipsoid of
L(S).
Abstract for 21950
Shift and Vigenère Ciphers with Maplets
Authors: Rick Klima, Neil Sigmon
Affiliations: Appalachian State University, Radford University
Cryptology, the art and science of communicating in secret, provides
an excellent tool for illustrating practical uses of mathematics. Topics
from number theory, linear and abstract algebra, probability and
statistics, and other areas all appear prominently throughout cryptographic
methods and their cryptanalysis. Although historical, or
"classical," ciphers are no longer widely used in our modern
digital society, they can still be used to directly connect mathematics and
cryptology, with advanced technology significantly enhancing how classical
ciphers can be implemented and broken. As examples of this, in this paper
we describe and illustrate the implementation and cryptanalysis of shift
and Vigenère ciphers. To help with this,
technology involving Maplets will be used.
Abstract for 21951
Computational thinking in mathematical modelling: an investigative
study
Authors: Keng Cheng Ang, Liang Soon Tan
Affiliations: Nanyang Technological University, 1 Nanyang Walk,
Singapore 637616, Academy of Singapore Teachers Ministry of Education
Singapore
It has been suggested that computational thinking, based on
fundamental concepts of computing science, provides a useful approach to
everyday problem solving. It has also been seen that computational
approaches can play a major role in the work of professionals in various
fields, and it is therefore pertinent that computational thinking be given
some attention in schools to prepare students for the future workforce. One
way to do so is to expose students to modelling challenges, and through
these, provide opportunities for students to learn, practise
and refine their skills and competencies in both computational thinking and
practical problem solving. In this paper, we describe the interaction and
interplay between computational thinking and mathematical modelling through
students’ experiences in an international mathematical modelling contest.
Students’ ability to apply computational thinking in the contest was
inferred and investigated via case studies. Data sources in the form of
report artefacts, videos, interviews and judges’ comments form the basis of
the case studies. The investigation reveals that the constructs of
computational thinking such as pattern recognition, abstraction,
decomposition and algorithm creation play a critical role in the successful
completion of the students’ modelling tasks.
Abstract for 21952
Real Quantifier Elimination in the Classroom
Authors: Tomás Recio, Zoltan Kovacs
Affiliations: The Private University College of Education of the
Diocese of Linz, Institute of Initial Teacher Training, Nebrija
University, Madrid, Spain
We present the experimental command RealQuantifierElimination
in GeoGebra Discovery. The command provides quantifier elimination over the
reals. We describe how this new command can be used in certain classroom
situations.
In our examples we focus on mathematical logic and elementary
calculus (in particular, on definitions of basic notions and proving
inequalities). Finally, we conclude a potential impact of this new command
in the educational world.
Abstract for 21955
Riemann Sphere and Complex Plane Transformations with Sphere
Movements (Software Aspect)
Authors: VLADIMIR NODELMAN
Affiliations: Holon Institute of Technology
There are various ways to visualize complex functions, but most of
them provide only passive show, even with support for manually controlled
and/or parameterized animations.
The Riemann sphere offers a very different instrument for modeling
complex plane transformations, often allowing them to be defined as the
result of a transformation of the sphere itself.
In this paper, we present the use of the Riemann sphere model in discovering
the features of complex functions and the construction of these functions
as results of sphere movements with the help of the author’s non-commercial
software VisuMatica.
Abstract for 21958
THE POSSIBILITIES OF GEOGEBRA IN RESEARCH IN BRAZIL
Authors: CELINA A. A. P. ABAR
Affiliations: Pontifical Catholic University of Sao Paulo
This paper aims to present the contribution of GeoGebra in research
carried out in Brazil. Dynamic geometry systems (DGS) have evolved
significantly and the contribution to research and education is noticeable
in the papers presented here. The easy access and dynamism offered by
GeoGebra make it possible to reduce the gaps between what is taught at
school and the context of the students, in addition to contributing greatly
to the training of teachers. Between 2009 and 2022, researchers identified
140 studies aimed at teacher training throughout Brazil and, in another
study, on papers published in a specific journal on GeoGebra, it appears
that all of them focus on didactic issues, concerning about the analysis of
the effects on the teaching and learning process of students and analysis
of the types of thinking/reasoning developed in the proposals presented. In
the research, we identify strategies that enable teacher training that
reflects positively on schools and indicates ways to improve teaching
practice. Hence the importance of some theoretical contributions presented
and considered in the studies, which allow validation of the results
obtained. It appears that using GeoGebra is an alternative in the search
for ways to build situations that help overcome teaching and learning
difficulties, not only in Mathematics, but also in other contexts of
science. The available and constantly evolving tools, as in the
experimental proposal of GeoGebra Discovery, make it go beyond the context
of mathematics to other sciences, revealing multidisciplinary aspects.
Abstract for 21963
Deployment of Mathematical Resources to a Philippine High School
through a Community LTE Network
Authors: Ma. Louise Antonette De Las Penas, Maria Alva Q. Aberin,
Agnes D. Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie
Marie B. Verzosa
Affiliations: Ateneo de Manila University, University of Southern
Mindanao
In the Philippines, one challenge that continues to be faced by the
Department of Education in bringing educational content in a blended
learning modality is the lack of internet access of the learners. This
paper discusses the distribution, through a community LTE network, of
mathematical resources for Grades 7 to 10 to teachers and students of a
particular high school in the Philippines. It also gives details on
particular technological tools (mathematical applications) that were
created to help the mathematical learning of students in a remote setting.
Abstract for 21964
Sphere and Spheric Geometry: The Power of
Visualization and Investigation of Dynamic Geometry
Authors: Jean-Jacques Dahan
Affiliations: IRES of Toulouse
This article aims to provide a dynamic approach to the basic notions
of spherical geometry. We will use the power of visualization of Cabri 3D to make more comprehensible the detail of the
proofs establishing the formulas giving the area and the volume of a
sphere. Experimenting with real spheres is a challenge already overcome
with half hollow and transparent plastic balls on which you can stretch
strings and write with markers. The use of Cabri
3D greatly enriches such a teaching of spherical geometry in facilitating
the 3D representation of the objects of this geometry as well as their
manipulation. We will show how. All the results presented here are known,
but it is the way in which they are approached and detailed that
constitutes the originality of this article.
Abstract for 21966
Exploration of parameterized families of surfaces: envelopes, offsets
and canal surfaces
Authors: Noah (Thierry) Dana-Picard
Affiliations: Jerusalem College of Technology
The study of envelopes and offsets requires a strong dialog between
algebraic computations and graphic representations. Both are available
using a Computer Algebra System, and sometimes accompanied by a Dynamic
Geometry System. The two kinds of software have different affordances,
whence different characteristics of the animations. Visualization raises
specific problems. We illustrate this with examples of 1-parameter and
2-parameter families of surfaces in 3D space, in particular canal surfaces
and pipe surfaces. In certain cases, the envelopes have non-isolated
singularities; we study them switching between parametric and implicit
presentations. Finally, networking between them and between visualization
and symbolic computations is discussed.
Abstract for 21968
Link to an expanded abstract
7-Circle Waltz
Authors: Jen-chung Chuan
Affiliations: Department of Mathematics, National Tsing Hua
University, Hsinchu, Taiwan 300
Evelyn, Money-Coutts, and Tyrrell first published the Seven
Circle Theorem in 1974. It shows that there are many beautiful
relationships involving only lines and circles on a plane still waiting to
be discovered. The earliest study of polyhedra
dates back to Apollonius, Pappus and Archimedes some 23 centuries ago. The
author first read about the “circumscriptible
tetrahedron”. The term is used to define a tetrahedron whose six edges (not
produced) are tangent to the same sphere. Our project here has constructed,
with the dynamic geometry software Cabri 3D, a
set of 27 mathematically curious animations of the 7 circles formed with
the faces of a circumscriptible heptahedron.
Each animation offers a concrete example in the discipline of:
1) Graph Theory: the contact graph formed with the 7 circles in each
animation remains the same.
2) Topology: The 27 heptahedra accompanying the animations are
topologically distinct.
3) Geometry: For each animation there exists a pair of circles having
the same axis throughout the animation.
4) Combinatorics: There could be more than one pair
of circles for the same circmscriptible
heptahedron.
5) Connections between 2D and 3D: Each “snapshot” of the animation
can be transformed under the stereographic projection into a Sangaku figure of 7 circles among which two are
concentric.
6) Prism: The term “porism” is obscure.
Michel Floréal Chasles
showed his appreciation of the interest in the Porisms
from the point of view of modern geometry. With Cabri
3D this work leads a new perspective of a generalization of Stein''s Prorism.
Since each animation is based on a simple harmonic motion, we simply
call it a “7-Circle Waltz”.
Abstract for 21969
Augmented intelligence with GeoGebra and Maple involvement
Authors: M. Pilar Vélez, Tomás Recio
Affiliations: Universidad Antonio de Nebrija,
Escuela Polit�cnica Superior Universidad Antonio de Nebrija
Madrid, Spain
We reflect on the necessary interaction between human and machine in
the mathematical activity of our days. The emergence of computers, and more
recently everything related to artificial intelligence, has shaped a new
way of doing and learning mathematics. The role of mathematics in this scenario
is twofold. On the one hand, mathematics is the hidden support of
artificial intelligence and, therefore, of the digitization of everything;
on the other hand, personal computers provide digital tools that perform
incredible calculations (including most of the tasks required in the
current mathematics curriculum) or facilitate the drawing of dynamic graphs
that help visualize mathematical objects, and even perform mathematical
demonstrations. Clough’s conjecture example will illustrate these items from
our experience.
Abstract for 21973
Exploring some elementary results of Ramanujan with modern tools
Authors: Alasdair McAndrew
Affiliations: Victoria University, Melbourne Australia
The Indian
mathematician Srinivasa Ramanujan (1887--1920) was one of the most
extraordinary mathematicians in history. Almost entirely self-taught, he produced
results of such originality that nobody understood him until he gained the
confidence of the English mathematician Godfrey Harold Hardy. As one of the
most expert mathematicians of his time, even Hardy was forced to admit that
some of Ramanujan''s results ``defeated me
completely; I had never seen anything in the least like them
before''''~\cite{hard37}. Hardy and Ramanujan worked together for five
years (during which time Ramanujan was admitted to both the Royal Society
and to a Fellowship of Trinity College, Cambridge), after which Ramanujan,
by then a very sick man, travelled home to India where he died aged only
32. His results have kept scores of mathematicians busy for the last
century---indeed some have devoted their lives to his work---and his
influence is if anything even greater now. Many of his results are deep and
difficult, and quite beyond an article such as this. But there are also
some lovely gems which are more easily grasped; and of varying difficulties
to prove. In this paper we explore a few of his simpler results with the
aid of modern technology.
Abstract for 21977
Mathematics and Technology: Does it work?
Authors: Vanda Santos
Affiliations: Research Centre on Didactics and Technology in the
Education of Trainers, University of Aveiro, Portugal, Centre for
Informatics and Systems of the University of Coimbra
The objective of this paper is to show that technologies have a great
impact on the teaching and learning of mathematics. Technologies can be
programs, applications, or even automatic deduction systems that can be
used to teach one or several mathematical concepts. The use of learning
environments with or without tutors, which integrate a dynamic geometry
system or another, can be used in the teaching and learning of mathematics.
Active methodologies that involve students in the learning process have as
their fundamental objective to develop mathematical skills that allow them
to know how to solve problems. Some tasks that were developed will be
presented, either with the use of programs or teaching and learning
environments, online or offline. The results have been favorable in the
teaching and learning of mathematics, with the use of technological tools
and involving active methodologies
Abstract for 21982
Using virtual reality to teach linear algebra with a focus on affine
geometry
Authors: José L. Rodríguez
Affiliations: University of Almería
We present an innovative experience of the use of virtual reality in
a first undergraduate course of mathematics at a Spanish university carried
out during the last 3 academic years. This complements the theoretical and
practical classes of the subject of linear algebra with notions of affine
geometry that will be used in later courses. Mathematics, with the use of
technological tools and involving active methodologies.
Abstract for 21987
Understanding Geometric Pattern and its Geometry, (part 9) - On
Walking Pentagons and Isfahani Inflation
Authors: Miroslaw Majewski
Affiliations: New York Institute of Technology, Abu Dhabi Campus
We introduce Isfahani inflation, a simple
inflation technique for decagonal tessellations. We discuss the creation of
geometric patterns using Isfahani inflation.
Using examples from Bukhara and Iran, we show how one can reconstruct them
with this inflation and produce numerous variants. Some extensions of Isfahani inflation will also be mentioned.
Abstract for 21989
A Computer Algebra Approach to Billiards
Authors: Setsuo Takato, Jose A Vallejo
Affiliations: Universidad Autonoma de San Luis Potosi, Toho University
Billiards are very interesting examples of mathematical objects where geometry, analysis and physics merge. From a dynamical systems perspective, they offer examples of integrable and chaotic behavior, so they are quite appropriate to illustrate the main features of these. In the talk, we will review the basics of billiards and we will see how to study them with the aid of the free packages Maxima and KeTCindy.
Abstract for 21991
A Topological View of Curves and Surfaces Inspired by 2D and 3D Locus Problems
Authors: Wei-Chi Yang, Guillermo Dávila
Affiliations: Radford University, Universidad de Sonora
Motivated by some locus problems discussed in [8], and further in [9] and [10] for 2D and 3D cases, we explore scenarios in which if two topological manifolds are topologically equivalent with technological tools. We derive some interesting facts about topological equivalence that could be used in the classroom.
Abstract for 21995
Is it so time consuming to start using a new piece of mathematical
software?
Authors: Eugenio Roanes-Lozano, Carolina Fernández-Salinero
Affiliations: Universidad Complutense de
Madrid
In this paper we summarize an experience carried out with pre-service
teachers, students of the Master's Degree in Secondary Teacher Training
(MFPES) of a public university, about their ability to self-learn the use
of the computer algebra system for smartphones “Maple Calculator”. It is
focused on determining if they were able to find in a short session the main
features of the new software and the advantages and disadvantages of its
use compared to the use of “Maple” on a computer (note that even if the
students handled the latter, it does not resemble the smartphone software).
This research has a qualitative approach, of an ethnographic nature. The
responses to the questionnaire have shown great maturity, highlighting the
expected points and pointing out others.
Abstract for 21996
Upskills Teachers’ Competencies in Constructing Sangaku
Puzzles with the Geometer’s Sketchpad
Authors: Krongthong Khairiree
Affiliations: International College, Suan Sunandha Rajabhat University Bangkok Thailand
The purpose of this study was to describe how to increase mathematics
teachers’ knowledge and skills in using the Geometer’s Sketchpad to
construct Sangaku puzzles. Survey research was
conducted in Bangkok, Thailand in the year 2021. A total of 35 mathematics
teachers participated in this study. Based on the research findings, the
teachers revealed that because of the Covid-19 pandemic, they must teach
mathematics through an online platform until the year 2022. More than 50%
of the teachers wanted to use the Geometer’s Sketchpad to design Sangaku puzzles as e-learning materials that made
students’ learning challenging and fun. The Sangaku
puzzle was not easy to construct with a compass and a ruler. The Geometer’s
Sketchpad enhanced teachers’ competencies to construct Sangaku
puzzles easily, correctly, and precisely.
Abstract for 30001
Visualizing the Derivative Relationship Between “Volume” and “Surface
Area”
Author: Douglas B. Meade
Affiliations: Department of Mathematics, University of South
Carolina, Columbia, SC 29208 USA
Many students note the obvious derivative relationship between the
“volume” and “surface area” of a sphere or circle, but that it fails for a
cube or square. In this presentation we explore this topic both
analytically and visually. Of particular interest whether this is
relationship is just a curiosity or whether it can be observed in other
regions and in other dimensions.
Abstract for 30006
“What the majority of mathematics teachers are missing.”
Author: Douglas Butler
Affiliation: iCT Training Centre, UK
The latest research suggests that only 20% of mathematics teachers are making any use of online resources in their teaching. As a result, the majority are therefore missing out on the many possibilities to enhance their students’ understanding through visualisation and interaction. In this talk Douglas will run through a number of possibilities using items selected from his wide-ranging TSM RESOURCES website, covering topics from junior levels to advance higher, and he will include the use of the latest web-version of Autograph.
Abstracts
for Regular Full Papers
Abstract for 21941
Research on Sangaku and the use of ICT.
Authors: Hideyo MAKISHITA
Affiliations: Shibaura Institute of Technology
The author proposes geometry teaching materials based on Sangaku, the mathematical culture of the Edo period, together with utilization of information and communications technology (ICT). As described in this paper, the author proposes the use of computer algebra systems (CAS) and dynamic geometry software (DGS) as ICT supporting mathematics education in junior and senior high schools, and reports the use of CAS for algebraic equations expressed by algebraic equations and the use of DGS for drawing diagrams of Sangaku problems.
Abstract for 21942
Computations of statistical power in R
Authors: Sharad Silwal
Affiliations: Radford University
Hypothesis testing is one of the foundational topics in statistics
and a must teach in every introductory statistics course. The entire theory
of hypothesis testing rides on the concept of power. Yet, its computation
is generally perceived to be daunting and is avoided by most introductory
courses in statistics. For instance, it is not covered in AP Statistics
curriculum. Understanding of power, on the other hand, is reinforced when
you know how to compute power against an alternate hypothesis. This paper
presents an exposition of computations and illustrations of the critical
value and statistical power for a t-test and its nonparametric analog in R.
Abstract for 21959
Combining Brute Force and IT to Solve Difficult Problems
Authors: Jozef Hvorecký,
Lilla Korenova, Tomáš Barot
Affiliations: University of Ostrava, Ostrava, Czech Republic,
Institute of Technology and Economics, České
Budějovice, Czech Republicc,, Faculty of
Pedagogy, University of Ostrava, Ostrava, Czech Republic
The brute force method is a typical approach to solving unknown or
non-standard problems: without having a more appropriate tool, one tries to
test all relevant candidates whether they are or are not the result using
the trial-and- error approach. During the process, one may look for a clue
or a hypothesis leading to more effective solution and/or to its
generalization. The brute force allows learners to solve tasks which are
for them otherwise unsolvable because they require other – more
sophisticated, beyond curricula – methods. In the paper, we demonstrate two
principal steps of the method: the generation of the space of relevant
candidates and their testing. Depending on the space size and complexity of
calculations, testing may last long. We accelerate is using spreadsheet
calculations.
The problem-solving method is explained using examples. First, we
find out a brute force solution and then discuss it. Depending on the type
of problem, the discussion hypothesizes “theory-based” solutions,
generalizes the findings and outlines similar problems which can be solved
using brute force.
Abstract for 21961
Different types of test questions and examining systems to assess
students'' knowledge in Applied mathematics for Informatics
Authors: Helena Brozova, Jan Rydval, Milan Jelínek
Affiliations: Czech University of Life Sciences, Faculty of Economics
and Management, Dep. of Systems Engineering, Faculty of Economics and
Management, Czech University of Life Sciences Prague Czech Republic,
Faculty of Economics and Management, Czech University of Life Sciences
Prague Czech Republic
Appropriately chosen teaching and testing methods enable students to
adequately understand the taught matter through direct contact teaching in
classrooms and through distance e-learning and self-study at home as well.
When teaching the subject Applied mathematics for Informatics, students
must not only be able to recognize which mathematical model to apply to
solve a given problem, but also to analyze and interpret their obtained
results. In this paper, we demonstrate our approach of teaching and testing
Applied mathematics for Informatics using e-learning system Moodle for
students of the Bachelor's degree at Czech University of Life Sciences.
Within the framework of Applied mathematics for Informatics teaching,
students are provided with practical seminars in addition to classical
lectures. In these seminars’ students solve specific problem situations
from practice, through which they learn to recognize which mathematical
models to apply to solve the problem situation and students are encouraged
to work independently and think critically. Students demonstrate this
knowledge in the final exams, which are designed as "open book"
standardized examination system, and contained a practical management story
in which students as managers are forced to solve many practical problems
corresponding to different mathematical models. Students can use their
notes, books and all resources available in Moodle. The method of teaching
and testing knowledge is chosen to increase the students'' ability to
understand the problems taught in Applied mathematics for Informatics,
increases the ability to recognize and apply the appropriate mathematical
model to solve a given practical problem and to analyze and interpret the
results obtained.
Abstract for 21962
Applying Flipped Classroom to Increase Students’ Achievement and
Investigating students’ Satisfaction in Learning Mathematics
Authors: Supotch Chaiyasang,
Asst.Prof. Dr. Supotch Chaiyasang
Affiliations: Suan Sunandha
Rajabhat University, Bangkok, Thailand
The objectives of this classroom action research were to increase
students’ mathematical achievement and to survey students’ satisfaction in
learning by using flipped classroom. The participants were 32 grade 11
students who enrolled in the second semester of the academic year 2019 at a
high school. The topic used in this study was Vectors in Three Dimensions.
The instruments were 7 lesson plans, achievement test and satisfaction
survey. Learning management by using flipped classroom comprised 3 steps:
1) before class, students studied online learning through video clips,
handouts and quizzes, 2) during class, teacher reviewed key concepts and
students discussed the contents that they had studied from home, solved
harder problems, and got individual help from teacher and 3) additional
skills or extended knowledge. Data were collected from pretest, posttest,
and satisfaction survey. Data were analyzed by using effectiveness index,
mean, mode, and standard deviation. The results showed that: 1) the effectiveness
index of the flipped classroom was 0.8 which revealed that students’
achievement was increased 0.8 from the beginning and 2) students’
satisfactions 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 21965
Carral Geometric Proof of a
Steiner Ellipse Property Attempt of Generalisation
Authors: Jean-Jacques Dahan
Affiliations: IRES of Toulouse
In this paper, we will first prove using the solution proposed by
Michel Carral, that the ellipse inscribed in a
triangle of maximum area is its Steiner ellipse. This proof is based on a
purely geometric reasoning which greatly simplifies the first complete
proof proposed by Minda and Phelp
([5]), in the sense that it uses more basic tools and knowledge. Recall
that in a previous paper ([6]), an approach with dynamic geometry had
already allowed a very simplified approach even if a step was incomplete
insofar as it was only justified experimentally. As I said above, this
problem was solved geometrically by my colleague Michel Carral
to whom I had submitted it. He has included it as an exercise in the area
geometry book he is finalizing. I thought that his solution deserved better
than an exercise in his geometry book and I decided with his agreement to
write it trying to respect the spirit of the author but detailing it enough
to be understood by all. I will then propose an attempt at generalization
to ellipses inscribed in polygons. In passing I will propose a still purely
geometric proof of the fact that polygons of minimum area having a given
inscribed circle are regular polygons. Eventually a construction under the
New Cabri, using macros, illustrates the sequence
of polygons circumscribed to a given ellipse approaching the polygon of
minimum area circumscribed to this ellipse.
Abstract for 21967
Multiple choice questions using STACK with partial score and feedback
Authors: Kentaro Yoshitomi
Affiliations: Osaka Metropolitan University
Online testing systems in mathematics education are useful tools for
both teachers and students. STACK is a system that is widely used in Europe
and other parts of the world, and it is a question plugin for Moodle, a
Learning Management System (LMS). On the other hand, the use of
multiple-choice questions in mathematics has been limited due to the
randomization problem. The use of multiple-choice questions with STACK
solves this problem, but the method described in the help document does not
support partial score and feedback, which are important features of a
learning tool. In this paper, we introduce a method for providing partial
score and feedback by devising a coding method that utilizes the framework
of STACK's multiple-choice questions, and present a template. In addition,
we will present some examples in which multiple-choice questions, together
with incorrect answer patterns, are considered to be important educational
resources.
Abstract for 21970
Understanding the Problem Structure in Computational Thinking in
Mathematics Classrooms
Authors: Masanori Fukui, Yuji Sasaki
Affiliations: Center for University Education, Tokushima University,
Graduate School of Media and Governance, Keio University
Understanding the structure of problems is essential not only in
mathematics education but also in all subjects. Particularly in structured
problems such as those in mathematics, it is crucial to understand the
problem structure before solving it to improve the solution method. It has
been reported that problem making, or problem-posing, is effective in
promoting creativity and understanding problem structures. However, it is
not always easy for majority of the students to create problems, and it is
not clear whether creating problems is connected to problem solving. Thus
far, other scholars have proposed �modified problem-posing� as a method
to enable many students to solve problems. However, it is unclear whether
this method improves problem-solving ability in mathematics. This study
proposes a methodology to enhance problem-solving skills by focusing on the
relationship between modified problem-posing and computational thinking.
Abstract for 21971
Engaging Learners through Data: Senso Eskwela Pilipinas
Authors: Mark Anthony Tolentino, Ma. Louise Antonette
N. De Las Pe�as, Maria Alva Q. Aberin, Agnes D.
Garciano, Mark L. Loyola, Jumela
F. Sarmiento, Juan Carlo F. Mallari, Debbie Marie B. Verzosa
Affiliations: Ateneo de Manila University, University of Southern
Mindanao
The use of real data in teaching and learning statistics has been
recommended in the literature. This paper talks about the development and
implementation of the Senso Eskwela
Pilipinas, the first database in the Philippines
that builds and provides real data with the intention of making the study
of statistics engaging, understandable, relatable, and relevant for
Filipino learners.
Abstract for 21972
Develop Computational Thinking in Portuguese Mathematics Curricula
with Collatz Conjecture
Authors: José Manuel Dos Santos, Alexandre Emanuel Batista Trocado, Zsolt Lavicza
Affiliations: Centre for Research and Innovation in Education (inED), Center for Research and Development in Mathematics
and Applications (CIDMA), School of Education - Johannes Kepler University,
Linz, Austria
Recently several countries have adopted as a strategy the
introduction of Computational Thinking (CT) in the curricula of compulsory
education. In Europe this movement has been driven by decisions of the
institutions of the European Union, arguing that the technological capacity
of citizens must go beyond their use, and it is necessary to promote the
development of CT. In this context, some European countries have included
the development of CT as a capacity to develop in mathematics. Portugal was
one of the countries that adopted this strategy, which is object of public
debate. With this work we intend to analyze some of the potentialities of
the introduction of CT as an ability to develop in the mathematics
curriculum, namely those related to the type of mathematical activity that
can be developed in the classroom. The Collatz
Conjecture (CC) will be the context for us to show how we can work with a open mathematical problem,
simultaneously developing Mathematical Thinking and different concepts and
procedures of CT. The CC approach, as a classroom task, may illustrate how
a contemporary subject of mathematics can help itself from computing,
highlighting the use of various technological tools or programming
languages depending on the age student group.
Abstract for 21976
Link to extended abstract
The Enjoy Origami on Mathematics and Science Education in STEAM
Authors: Minoru Itoh
Affiliations: Tokyo University of Science
Abstract: The origin of Japanese origami culture came from the
Ancient China as the Buddhist tradition (around the 6th to 7th centuries).
Especially, the paper on which the Buddhist scriptures are written is the
root of thin and durable Japanese paper. Washi, called very traditional
Japanese paper, is still used in various places even in modern Japanese
society. Origami paper is very popular for young children in primary school
in Japan. Therefore, origami is great material for mathematics education.
In Japanese mathematics education, using origami as a teaching material
that is very familiar to children stimulates not only children�s
intellectual academic ability but also emotional aspects, and is improving
the educational effect. For example, in Euclid geometry, angle trisection
and doubling problems are famous as impossible to draw on mathematics, but
it is possible by using origami. Similarly, the problem of drawing with a
ruler and compass can be easily drawn by children using geometric PC
software; GeoGebra, Grapes, Cinderella, etc. By using origami and geometric
software in combination, children can expect more effective mathematics
education than ever before. On the STEAM, why don�t you go on a fun
geometry learning journey with your children and math teachers using origami?
Abstract for 21979
Limit calculation outside the domain of definition of real functions
using computer algebra systems: an educational panoramic view
Authors: Enrique Ferres-López, Eugenio
Roanes-Lozano, Angélica Martínez-Zarzuelo
Affiliations: Complutense University of
Madrid, Centro Universitario de Tecnología y Arte Digital
We recently realized that one of the best-known pieces of
mathematical software (GeoGebra)
evaluated the limits of certain functions at a point outside their domain of
definition
in different ways according to the so called “View” used (GeoGebra is a
very powerful dynamic geometry system with algebraic capabilities). The
examples used would classically be classified as “removable
discontinuities” or “jump discontinuities”. In a previous paper we
described this fact and compared the output of GeoGebra with the output of
the computer algebra system Maple. In this new paper we have checked the
output of some of the best-known computer algebra systems in more examples,
providing a panoramic view of the situation. Clearly, the behavior of the
pieces of software depend on the decisions made during the design step, and
condition their applications on mathematics teaching.
Abstract for 21984
Scissors, Cardboard and GeoGebra: Technology as instrument, not only
as artefact
Authors: Mathias Tejera, Franco Mariani, Zsolt Lavicza
Affiliations: Johannes Kepler University, CICATA-IPN
This concept paper presents an example of technology integration by
modifying an optimisation problem as an initial
activity of the calculus course in the last year of high school. This
proposal articulates three ideas; the importance of the instruments used
for the mathematical activity, the concrete, pictorial and abstract model,
and the notion of instrumental genesis. Technological tools appear in this
proposal initially as an artefact, but this design generates that they
become an instrument for learning progressively. Experimentally noted that
the activity generates a high level of commitment, causing students to put
in play and refine their ideas about working with functions to model
reality and make better decisions. This model for technology integration
into the mathematics classroom by modifying existing tasks could promote
teachers to integrate technology in an easy and more meaningful way.
Abstract for 21985
How to prepare a digital geometric model which is enclosed by an
assembly of surfaces for 3D printing
Authors: Petra Surynková
Affiliations: Department of Mathematics Education, Faculty of Mathematics
and Physics, Charles University
In this article we address the process of manufacturing of 3D
geometric models on 3D printers for the educational purposes. The
manufacturing of the geometric model includes the design, 3D computer
modeling with Constructive Solid Geometry (CSG), 3D computer modeling of
parametric surfaces based on differential geometry, 3D scanning of real
objects, and the process of fabrication itself. Students can join the whole
process of designing the models for 3D printers or its parts and the
printed models can be included in teaching and learning geometry at every
stage of education (at the university and the secondary school in our
case). We present the possibilities how to model geometric objects in 3D
computer modeling software; in addition to commercial ones in free GeoGebra
dynamic system too. We present particular constructions of selected
geometric models whose boundary consists of parametric surfaces. All
examples of printed geometric models presented in this article are intended
to be used in mathematics instructions at the secondary school and in the
undergraduate courses on descriptive geometry at Charles University
(mandatory courses for secondary pre-service mathematics teachers who study
teaching mathematics and descriptive geometry). All phases of designing the
models for 3D printing together with physical 3D printed models bring a new
light in teaching and learning geometry. It engages students in real-world
problem solving and promotes students� knowledge in geometry while
introducing them into 3D computer modeling and 3D printing technologies. 3D
virtual models and 3D printed models themselves can serve as the
educational manipulative aids.
Abstracts for Abstract Only
Abstract for 21937
Multiple-Choice questions using STACK
Authors: Kentaro Yoshitomi
Affiliations: Osaka Metropolitan University
We have developed Mathematica-programs to generate XML files of
abundant multiple-choice questions (MCQ) for using on Moodle with random
question function. However, the problem is the correctness of the
questions. In some cases. there are bugs which are almost impossible to be
fixed since scale of the number of questions. On the other hand, STACK can
provide MCQ, but does not have feedback messages, which are quite important
for the students'' self-study. We have developed STACK question template,
which can provide partially scoring and appropriate feedbacks.
Abstract for 21938
Review of stochastic volatility option pricing models
Authors: Abby Tan
Affiliations: Universiti Brunei Darussalam
The aim of this work is to review extension to the Black-Scholes
pricing model. More specifically, we look at various models where the
constant volatility assumption is relaxed. Perhaps the simplest model is
the one where volatility function follows a deterministic process. A
natural extension of this model is to consider a diffusion process for
volatility process. We consider a range of diffusion processes with varying
‘memory’ parameter. For such cases, there are no closed form solutions for
option prices. One non-conventional option pricing model is to allow risk
to exist and price the risk into the option pricing model. The risk
manifested itself as pricing bands or confidence interval around classical
Black-Scholes prices. An interesting feature of this risk is that it is
independent of detailed statistical characteristics of the volatility
process. To take into account memory effects, we
can define specific ‘moments’ exhibited by the volatility process which
will result in different pricing bands. These pricing bands give good
approximation to market price. Interestingly, the volatility ‘smile’ curve
can be recovered.
Abstract for 21940
Presentation: The Survey Toolkit Curriculum for Researching
Information, Survey Development, and Data Analysis Using TinkerPlots�
Author: Thomas Walsh
Affiliations: Ames Community Schools (retired), Iowa State University
The Survey Toolkit project and use of the curriculum with upper
elementary (middle school) students is presented. The curriculum is
discussed as a field-tested program found to be effective in guiding
students choosing research questions, writing a research report using a
paragraph cluster information strategy, developing unbiased survey
questions using reliable sampling, analyzing survey data with TinkerPlots®, and sharing results. The development and
understanding of data analysis is most important
for students living in an era of misinformation and unreliable findings
from surveys used to influence the choices for decision-making.
The PowerPoint presentation will focus on these topics about The
Survey Toolkit:
• Integration of the curriculum with other disciplines including
language arts studies.
• The design model and development of the curriculum for collecting
and organizing information for testing and analysis.
• Application of the design model following a student project on
Alternative Energy from choosing a research question (goal), writing a
report using an inquiry-based composing process to support the development
of survey questions, developing the survey questions, hypothesis testing of
survey questions, choosing a sample to administer the survey, analyzing survey
data with TinkerPlots®, and sharing results on a
poster board.
• Examples of other student projects showing various research topics,
questions, and data plots on Indian culture, color affects
on mood, interest in Rome, usefulness of video cameras, and understanding
earthquakes are displayed.
The presentation focuses on the author’s implementation of The Survey
Toolkit using TinkerPlots® with student project
examples provided following a lesson plan sequence in the text and
integrated with supplemental activities provided in The Survey Toolkit
Resource Manual. Following the PowerPoint, a demonstration of the TinkerPlots® software will be presented. Access to The
Survey Toolkit, TinkerPlots® and resource manual
are available from the author’s site at
https://sites.google.com/site/tomwalshjrhome/. Journal publication links
discussing use of the curriculum and teaching strategies along with a
literature review on teaching statistics with students is provided. The
author is currently conducting a literature review focused on the use of TinkerPlots® by elementary and middle school students
in the schools. The Survey Toolkit Resource Manual is available as a pdf
download at the web site. A reference business card will be provided, with
a QR code, for access to the site.
The need for further research to evaluate the effectiveness of the
curriculum materials, student learning, alternative teaching strategies,
use of TinkerPlots®, and staff development is
needed. Students show different levels of understanding of statistical data
and reasoning, which needs teacher scaffolding and support to evaluate
graphs. This author has found supporting students learning through mediated
teacher intervention using TinkerPlots® has been
effective to support creation and understanding of data set graphs for
reporting findings and making inferences. Evaluation of The Survey Toolkit
curriculum will be needed to improve students’ ability to think
statistically, since data analysis and statistical reasoning are becoming
part of the mainstream school curriculum in many countries.
Abstract for 21957
EXPLORING PLANE GEOMETRY WITH GEOGEBRA DISCOVERY
Authors: CELINA A. A. P. ABAR, Alexandre Matias Russo, Tomas Recio
Affiliations: Pontifical Catholic University of Sao Paulo, Pontifical
Catholic University of São Paulo Brazil, Universidad Antonio de Nebrija Spain
This contribution is about some work that is part of a doctoral
dissertation, in progress, in the context of geometry education. More
precisely, it deals with the study of plane geometry properties through an
experimental version of GeoGebra called Discovery, which has some Automated
Reasoning Tools (ART). The objective is to identify if there are
contributions to the geometry learning process of students in the 9th year
of Elementary School and if the tools available in Discovery allow the
development of geometric thinking, through constructions and conjectures
passing through the levels proposed by Van Hiele.
In our presentation we will describe the development of the exploration of
an activity on a circumference, and the corresponding reflections presented
by a pair of students working on this activity, all this in the framework
of the Design Research methodology. Students were asked to address this
activity through GeoGebra Discovery. It can be concluded that the Relation
and Discover tools from GeoGebra Discovery helped in the process of exploring,
verifying, and validating the students'' conjectures, pointing out relevant
contributions to the teaching and learning of plane geometry properties.
Abstract for 21960
Exploring the Nature of Online Discussion Forums in Mathematics
Authors: Pragashni Padayachee
Affiliations: University of Cape Town
Mathematics plays a fundamental role in engineering studies. Students
need to successfully navigate learning in mathematics to apply mathematical
knowledge and skills to other engineering courses. However, mathematics
poses a challenge for students, delaying graduation and contributing to
increasing student attrition rates. Online discussion forums provide an
added pedagogical opportunity to encourage student engagement with
mathematics concepts in an online mathematics community of learning.
Careful consideration should be taken in designing this course activity so
that it encourages, facilitates and reflects a deep level of student
learning. An expectation exists in this anytime available and open to all
asynchronous activity for students to take responsibility for their own
learning and to share knowledge with their peers. Commonly used in other
disciplines, not much is written about discussion forums in the often
traditionally taught undergraduate mathematics courses. This research
sought to understand students'' approaches to learning in mathematics
discussion forums. students taking Vector Calculus during 2020 in an
engineering support program at the University of Cape Town were the focus
of this research. This qualitative research study rooted in constructivist
theories of learning employed a conceptual framework to explore student’s
discussion forum participation. The three-pronged framework focused on
content, interaction and objective measures. Quantitative and qualitative
data are used to evaluate the nature of the discussion forums based on the
11 categories set out by this framework. Key findings indicate a positive
correlation between student engagement in discussion forums and student
learning and achievement in the vector calculus course.
Abstract for 21998
Learning mathematics through 3D printing in Secondary Education: a
case study in Spain
Authors: Miguel Angel Fuertes-Prieto, Bárbara María Alonso-Ruano, María Álvarez-Díez,
Laura Delgado-Martín
Affiliations: Universidad de Salamanca, Colegio Sagrado
Corazón – Salamanca
The progressive affordability of printers and printing material has
made 3D printing go from being a technology used only in professional and
higher education environments to being a teaching resource available in
many primary and secondary schools [1]. The introduction of 3D printing
technology in the field of education has been considered by some
researchers as a great advance compared to current traditional education
[4], having a positive effect on the general performance of students in
their technical and mathematical skills [3]. Learning environments centered
in the students and with integration of technology produce students who are
better able to think critically, solve problems, collaborate with others
and engage deeply in the learning process. When teachers know how to effectively
use technology features, they can better address the different cognitive
strengths and needs of the different students [3].
In this presentation, a case study where 3D printing has been used in
Secondary Education in a Spanish school will be described, in relation with
the main ways in which 3D printing is being used in the educational system,
according to Ford and Minshall [2].
It has been a cross-curricular project carried out mainly in the
areas of mathematics and technology, but also with integration of other
areas. Secondary students have learnt about 3D printing, it has been used
as support technology during teaching, not only to produce artefacts that
aid learning but also to support outreach activities and even community
services.
In the technology area, students learnt all the steps of the 3D
printing process, from the design to the making. That knowledge was applied
in the mathematics area to calculate areas and volumes of simple and
composite shapes, experimentally verify the results of mathematical
calculations, or carry out experimental verifications of mathematical
statements such as the Pythagorean Theorem.
Preliminary results show that the learning process of most of the
students has been improved when using 3D printing and almost all the
students gave very positive feedback of it.
References
[1] Canessa, E., Fonda, C. and Zennaro, M. (2013). Low cost 3D printing for science,
education and sustainable development. Trieste: ICTP—The Abdus Salam International Centre for Theoretical
Physics.
[2] Ford, S. and Minshall, T. (2019). Where
and how 3D printing is used in teaching and education. Additive
Manufacturing, 25 131-150. https://doi.org/10.1016/j.addma.2018.10.028
[3] Kwon, H. (2017). Effects of 3D printing and design software on
students’ interests, motivation, mathematical and technical skills. Journal
of STEM Education, 18(4).
[4] Sun, Y. and Li, Q. (2017). The application of 3D printing in
mathematics education. In 2017 12th international conference on computer
science and education (ICCSE) (pp. 47-50). IEEE.
Abstract for 21999
Computational Thinking in the Spanish Secondary School Curriculum of
Mathematics. Meaning and implications.
Authors: Belen Palop, Juan José Santaengracia, Luis José Rodríguez-Muñiz
Affiliations: Universidad de Valladolid, Universidad de Oviedo
(Spain)
The digital transformation of our society has opened a new gap
between those who can understand and control the technology that surrounds
us and those who don’t. For this transformation to happen, we need on the
one hand, the digital competence that needs to be learned and taught,
especially since 2020, when 99% of Spanish households with dependent children
have smartphones and access to the internet Instituto Nacional de estadística (INE, 2021). On the other hand, we have to
achieve an even more ambitious goal, which has been included by the Spanish
Ministry of Education in the new K-12 curricula [LOMLOE,22]: the
development of children’s Computational Thinking.
We can define Computational Thinking (CT) as the way of reasoning
that allows people to tackle a problem using input data with the aim of
having a computer solve it [Diaz&Palop]. This
definition is based on three main computing aspects: Algorithms, Data and
Problems, and includes all dimensions of CT (Abstraction, Pattern
Recognition, Decomposition, Implementation, Debugging, Parallelization,
Simulation, Data collection, Data analysis and Data representation, Modellization and Generalization).
The broad meaning of the term that some authors simply define as
“thinking as a Computer Scientist”, makes it a big challenge to include CT
in K-12 curricula. Many questions on how this should be done are still
unanswered, from the best learning paths to aspects such as when is the
child’s mind ready to apprehend certain abstract concepts. To name an
example that has received special attention in teaching: when are
children’s minds ready to open the black-boxes of Machine Learning and
fully understand the Computational Thinking behind the cat-picture vs.
dog-picture classifiers?
With all these aspects in mind, in this work we analyze the new
Spanish Compulsory Secondary School Curriculum regarding the actual meaning
of each of the 30 appearances of the concept. Among those, one appears
under the generic term of Digital Competence; 3 in the Biology and Geology
course description; 14 in the Technology courses; 1 in Basic Vocational
Training and 10 under the description of the Mathematics courses. Our
research questions are: (1) What components among Algorithms, Data and
Problems is the Mathematics curriculum proposing to work on? (2) When
explicit descriptions are given, which of the cited 12 dimensions are addressed?
and (3) Can these components/dimensions be added or infused in the
traditional Mathematics curriculum?
Diaz, I. & Palop, B. A holistic
approach to Computational Thinking in K-12 Education [Unpublished
manuscript]. U. Oviedo, U. Valladolid.
INE. (2021). Hogares que tienen acceso a Internet y hogares que tienen ordenador. Porcentaje de menores usuarios de TIC.
Madrid: Instituto Nacional de Estadística.
Ministerio de Educación y Formación Profesional [MEFP]. (2022). Real Decreto
1105/2014, de 26 de diciembre, por el que se establece el currículo básico de la Educación Secundaria Obligatoria y del Bachillerato..
Boletín Oficial del
Estado, 03/01/2022.
Abstract for 22000
A didactic process for learning the logical conditional and its
correct application through the use of computer tools with prospective
Primary teachers
Authors: Laura Sánchez-Pascuala, Eloísa Montero
Affiliations: Centro Universitario Escuni,
Universidad Complutense de Madrid
The objective of this communication is to present a possible didactic
process to be followed in order to facilitate the understanding and use of
the conditional and its operation by prospective Primary teachers (PPT).
The optional subject "ICT for Mathematics in Primary" of
the Primary Education Degree seeks to develop competences such as: i) Discovering the possibilities of various ICT tools
for the teaching of Mathematics in Primary, and ii) Knowing how to
translate to mathematical language and know how to deal with ICT tools some
problems of daily life. In this communication we will focus on two of its
objectives: i) Discover the possibilities of the
three large groups of software for Mathematics Education: Logo/Scratch,
Dynamic Geometry and Computer Algebra; and ii) Begin to program in a
computational language.
At Escuni University Center for Education
(Madrid, Spain) we have planned the aforementioned subject with the aim
that PPT can develop these skills and objectives, among others, so that
they learn how to design teaching-learning experiences for their future
Primary students through the learning of three software pieces: Scratch,
GeoGebra and Excel. The use of conditionals is among the basic learnings to
be developed in this subject, in addition to the use of these software, so
that its assimilation is not a goal itself, but a knowledge required to
complete different projects associated with the PPT’s professional
development. The goal of this communication is to introduce a didactic
process to facilitate the understanding of the logical value of a
conditional expression and its operation, in order to implement it in a
practical way in daily life and to develop the computational thinking
skills.
The associated computational language comprehension process consists
of different levels, beginning with a written natural language (or close to
it) (Scratch) to end with an abstract computational language (Excel), going
through an intermediate stage (GeoGebra). Our goal is to plan the learning
of computer tools based on this progression in the use of computational
languages.
For PPT located at the first level we recommend the use of Scratch.
The fact that this software has a visual interface allows learners to focus
on understanding the conditional itself and how to use it empirically, with
a language close to written language.
At the second level, the use of the GeoGebra program is appropriate
because this software’s interface remains essentially visual. Carrying out
self-correcting exercises is a good context to motivate PPT. Some of the
examples in which this concept appears are: when we give a condition for
the appearance of an object or when we describe the functionality of a
created button.
For PPT of the last stage the use of Excel is possible. In this
program we find a very basic level of the use of the conditional, such as
the conditional formatting of cells, and a wide range of formulas that can
help us work on this concept, from the simplest ("IF", "IF.ERROR") to other more complex uses such as the
concatenation of conditionals.
Abstract for 22001
Math trails in initial teacher training with MathCityMap
and Augmented Reality
Authors: Alvaro Nolla de Celis, Angélica Benito, Ariadna Gomezescobar, Elena
Sánchez, Carlos Ajenjo
Affiliations: Universidad Autónoma de
Madrid, Universidad a Distancia de Madrid, IES Ángel Corella
We present an ongoing project in teacher training at Universidad Autónoma de Madrid (UAM) which incorporates math trails
with mobile technologies. In particular, it includes the use of MathCityMap and the Augmented Reality (AR) capabilities
of GeoGebra in math trails and proposes the creation of math trails by the
students as a rich activity in initial teacher training.
Designing a math trail is a creative activity that starts from the
consideration of the surroundings as an educational space in itself. It is
presented as an open challenge and becomes a mathematical learning process
which requires the creation of contextualized tasks, allowing a shift from
usual academic settings to real-life mathematical situations. The inclusion
of math trails in initial teacher training is presented as an opportunity
to develop problem-solving and problem-posing skills in prospective
teachers, and to provide them with a creative and collaborative
mathematical experience that can incorporate in their professional future.
In addition, the use of mobile technology has been successfully
implemented in several outdoor learning proposals. These tools give more
flexibility and autonomy during the activities, provide teachers with the
possibility to monitor and interact with their students and may include
gamification features. Learning how to use and experiment with these tools
give prospective teachers the confidence and opportunity to include them in
their own math trails.
We will describe the work carried out by the project since the
academic year 2019-2020 with students of mathematics subjects of Early
Childhood, Primary and Secondary Education Degrees and Masters at UAM. The
project followed two steps: (i) Students
experience a math trail using MathCityMap and
GeoGebra AR with pre-design routes, and (ii) students in groups create math
trails aimed for their future pupils. The routes were mostly designed at
various locations around the city (streets, parks, museums), highlighting
the connections of mathematics with architecture, history, nature, arts…
which shows the STEAM nature of the project. For some groups of students,
the trails were designed around the UAM Campus, and it was possible to
carry out an evaluation session with a peer (group) review process.
The project has had a very positive evaluations by the students. They
mostly found the inclusion of MathCityMap and
GeoGebra engaging and motivating, and the creation process of math trails
as meaningful.
The most experimental part of the project was the inclusion of AR
features in one of the pre-designed routes, which consisted of a MathCityMap trail augmented with GeoGebra 3D applets
which were linked at every task. This augmented math trail contains various
uses of AR in this outdoor setting, and the ones that required more
interaction with a GeoGebra 3D model to solve the task were considered more
engaging by the students. The AR experience with future Secondary School
math teachers showed good responses in participation and motivation, as
well as noticing room for improvements.
Abstracts for Hands-on Workshops
Abstract for 21943
Workshop: Exploring Computer Science with Lynx to Learn Geometry and
Logo Programming Code
Authors: Thomas Walsh
Affiliations: Ames Community Schools (retired), Iowa State University
Research on Logo programming
contributing to student learning has appeared in the literature during the
last four decades. Empirical and meta-analysis studies support of teaching
Logo coding in developing student cognitive problem-solving skills has been
documented using teacher guided instruction. Utilizing guided instruction
with teacher-mediated scaffolding Exploring Computer Science with MicroworldsEX (Walsh 2013-2017) has been found as an
effective curriculum in preparing the author’s elementary and middle school
students to apply Logo code language to create geometric graphics,
animation, and gaming projects. The instructional curriculum e-book updated
to a cloud-based platform Exploring Computer Science with LYNX (Walsh 2020)
is anticipated to provide continued support to students and teachers in
learning Logo coding. Michael Quinn is the lead designer of LYNX and
president of Logo Computer Systems Incorporated (LCSI). Quinn reports about
99% of the users of LYNX are students and teachers in grades 4 to 9
including use reported by graduate students for their program of study.
LYNX is part of the Canada CanCode Program
started in 2017 to support digital skill development to Canadian youth
(K-12) and providing teachers with professional development.
The e-book is published by
LCSI and posted at https://lynxcoding.club/ on the cloud. Visiting the website the user can get started exploring LYNX on their computerat the
Home Page by:
• Viewing the Learner Mode
and Advanced folders showing math projects.
While opening the projects,
by selecting the EDIT button, grey words in the
Procedures Pane explain the
commands.
• Selecting the Help Section
documents and videos are available along with
downloads for the Getting
Started Guide and Activity Cards. In this section
Exploring Computer Science
with LYNX is available under Resource
Materials.
Returning to the home page
at https://lynxcoding.club/ select the yellow link CREATE A LYNX PROJECT when ready to code exploring and creating explore and
create your own project.
The workshop will introduce
LYNX coding to participants with no previous experience using Logo or other
coding languages. A PowerPoint presentation with provide an overview of the
use and need to teach coding in the schools along with a brief background
about the development and features of Logo. Research support in the
literature for teaching Logo is presented along with a sample of the
author’s student projects. On the participant’s computer (Mac or Windows) an introduction to coding using LYNX will be provided experimenting with turtle commands for creating graphics. Time will then be
provided for applying the commands to create a Logo program.
Experience teaching Logo on
changing platforms has supported the author at the elementary and middle
school level for over 30 years. The classroom field experience along with
research on Logo programming, based on dissertation study, has contributed
to development of the e-book curriculum. More research will be needed to
study teacher scaffolding and mediation skills to support learning Logo
using the LYNX platform along with transfer to other domains including
programming environments like Python or JavaScript. Future employment of
computer-programming jobs will be best for applicants with experience in a
variety of programming languages and newest programming tools (Bureau of
Labor Statistics, 2021).
Abstract for 22002
Developing Mathematical and Computational Thinking through
Spreadsheets Authors: Jonaki Ghosh, Weng Kin Ho
Affiliations: Lady Shri Ram College, Delhi University, National
Institute of Education, Mathematics and Mathematics Education, Nanyang
Technological University, Singapore
We assume Excel is installed in participants' computer prior to the workshop. The workshop will illustrate
the possible linkages between the educational goals of the ‘Big ideas in
mathematics’ and ‘computational thinking’ through the use of spreadsheets.
Electronic spreadsheets, if used appropriately, can serve as a nexus
between these two domains in mathematics education. Mathematics teachers
need to able to convey the ‘Big ideas’ to their students by engaging them
in meaningful problem solving and explorations. Spreadsheets, equipped with
advanced numerical and graphing capabilities can be great enablers in this
regard and can be used as primary vehicles for exploration in many
mathematical tasks.
Technological and pedagogical
affordances, offered by spreadsheets in exploring mathematical concepts,
which in turn foster computational thinking, will be the focus of the
workshop. The easy accessibility and powerful features of spreadsheets make
them conducive to designing inquiry-based tasks. In fact, spreadsheets are
easily accessible to school students, as they are easy to use and do not
require an extensive knowledge of coding. The workshop will emphasize the
synergistic relationship between mathematical and computational thinking
whereby participants will be given the opportunity to visualize and analyze
problems using MS Excel. The problems will be drawn from a range of topics,
which illustrate the ‘Big ideas’, such as exploring numerical patterns,
graphing and analyzing data, simulating experiments in probability and
working with matrices.
Abstract for 30002
Introduction to Sage: Part 1
Author: Alasdair McAndrew
Affiliation: Victoria University, Melbourne, Victoria, Australia
We assume participants installed Sage in their computers prior to the workshop. Sage (https://www.sagemath.org) is an open-source computer algebra system which has been in continuous development since 2004. The original aim was to collect the best of open source mathematical software together under the one interface; this being the programming language Python. Currently Sage consists of nearly 100 different packages covering almost all branches of mathematics, as well as many tens of thousands of lines of code specifically written for it, many contributed by the leading researchers in their fields. It also contains interfaces to commercial software systems. It remains fully open source.
The first workshop will introduce Sage briefly, provide a whistle-stop tour of its major components, including its documentation and its interfaces, and look at some undergraduate-level material: algebra, calculus, linear algebra, geometry.
Abstract for 30003
Introduction to Sage: Part II
Author: Alasdair McAndrew
Affiliation: Victoria University, Melbourne, Victoria, Australia
We assume participants installed Sage in their computers prior to the workshop. The second workshop will delve a bit deeper, looking at some of Sage's more advanced capabilities, such as animated graphics, Gröbner bases and geometry theorem proving, number theory, optimization, and proposals from the first workshop.
No particular expertise will be expected, and the only thing that participants need to bring is enthusiasm.
The aim of these workshops is to provide the participants with enough information to be able to determine whether Sage might be useful for their own work, and how they can teach themselves further.
These two Sage workshops will be delivered using Zoom, as the presenter is unable to be physically present at the conference.
Presenter:
Alasdair McAndrew is a long time user of Sage (more or less since its inception) and is a developer - he created the initial version of the Derangements package: see https://bit.ly/3C0AVNw. He has written about Sage extensively in articles and on his blog. He has also written a book "Introduction to Cryptography with Open-Source Software", based around Sage. See https://amzn.to/3ya6seF for details.
Abstract for 30004
GeoGebra in Action: Dynamic Geometry in 2D and 3D
Author: Petra Surynková
Affiliation: Charles University, Faculty of Mathematics and Physics, Department of Mathematics Education, Praha, Czechia
We need everybody to install GeoGebra 5 or 6, the GeoGebra 6 is prefered, before joining this workshop. (See https://www.geogebra.org/download?lang=en). We will introduce the GeoGebra 6 dynamic system and the bases of using the software. We will work with dynamic features of GeoGebra, 2D and 3D Graphics View, and Computer Algebra System.
In the first part of the workshop, we will solve geometric constructions in the Euclidean plane, for instance circumscribed and inscribed circles of a triangle or common tangent lines to two circles. We will demonstrate known theorems and statements in the planar geometry, such as Pythagorean and Thales's theorems. For the pedagogical purposes, we can show the differences in using defined GeoGebra’s functions and constructions which simulate the hands-on drawing using only the ruler and the compass.
In the second part of the workshop, we will focus on analytic and differential geometry in the two- and three-dimensional space. We will combine defined tools for geometry and computer algebra system to solve equations such as constructions of conic sections, the intersection of a plane and a line in the three-dimensional space, or the intersection of surfaces.
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