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A Discovery Journey to Mathematics, Sciences and Engineering Through Technology

ATCM 2020, Virtual Format, Radford University, Virginia, USA and Suan Sunandha Rajabhat University, Thailand

Most presentations with videos are available here.

Abstracts for Invited Papers

Abstract for 21784

Sketching Graph of Function using Software

Authors:	VLADIMIR NODELMAN
Affiliations:	Holon Institute of Technology

One of the typical tasks in the study of functions is sketching of their graphs. The acquired skills, as well as the ability to read graphs, are notably useful in the later life.

The software used in teaching mathematics automatically builds ready-made graphs. While studying sketching these graphs are unacceptable. Traditionally, sketching is done by hand on paper. Nowadays (rarely) this can be done on a computer monitor as a freehand drawing. The resulting curves are very approximate and rough.

This paper illustrates the method of sketching graphs with intensive use of software. In general, the types of student’s activities do not depend on the specifics of functions. They explore a common model with the help of author's non-profit software "VisuMatica”.

This model includes a function f(x) with a hidden graph and the ability to visualize its characteristic properties:
• Intervals of sign constancy,
• Discontinuities,
• Local max/min,
• Supremum/infimum,
• Critical points,
• Asymptotes,
• Domain/Range,
• Inflection points.

Using this show, the student builds a sketch of the graph (one or more of its branches), by setting control points. The program connects them with appropriate smooth curves. These curves can be edited by dragging, exact locating, adding and removing control points. If one suspects a function periodicity, it is enough to sketch a curve at a proper interval and select the option "replicate along the X-axis".

The result is checked by unhiding the graph of f(x) and comparing it with the constructed sketch.

The model is universal: to build a sketch of a graph of another function, it is enough to redefine f(x) and the whole show (except of old sketch) rebuilds automatically.

Abstract for 21785

Multiple-choice questions in Mathematics: automatic generation, revisited

Authors: Kosaku Nagasaka

Affiliations: Kobe University

The multiple-choice question is one of very common assessment tools in the e-learning environment. Especially in mathematics learning, the multiple-choice question is used mainly for assessing lower-level cognitive processing (e.g. definitions, simple computations and so on), and there are not so many known studies on the multiple-choice question in mathematics learning: benefit, guiding principle, automatic question generation and so on. In this paper, we show our guiding principle, our whole system based on Moodle and Python (with Jupyter notebook), and some examples of automatic question generators in linear algebra and fundamental calculus.

Abstract for 21786

GeoGebra Reasoning Tools for Humans and for Automatons

Authors: Zoltan Kovacs, Tomás Recio

Affiliations: The Private University College of Education of the Diocese of Linz, Institute of Initial Teacher Training, Universidad de Cantabria Santander, Spain

We present two recent tools, integrated in the dynamic mathematics program GeoGebra, for automated proving and discovering in elementary geometry. First of all, the GeoGebra Discovery module, with the Relation, Prove, ProveDetails and LocusEquation commands. They are for humans because it is a human who must introduce the objects the human person wants to Relate, the thesis the human wants to Prove or the missing hypotheses the human wants to discover with the LocusEquation command. Moreover, we will describe some tools we have developed within GeoGebra for automatons, such as the Discover(X) and the WebDiscovery. We conclude the paper with reflections on the pros and cons and on the potential impact of these reasoning tools in the educational world.

Abstract for 21788

Group Testing Estimation Using R

Authors: Md Sarker

Affiliations: Radford University, Radford, VA 24142, USA

Group testing (pool testing) has long been used in public health applications for monitoring and detection of infectious diseases. In group testing, pools comprised of individual specimens (blood, swabs, etc.) are tested initially, and then individuals from positive pools are tested subsequently for case identification. This procedure and its variants can offer an enormous amount of cost savings in testing cost. Unfortunately, group testing data are naturally complex, and the statistical methods that model the data are complicated. Consequently, using group testing models in practice is non-trivial, especially for the public health officials who do not have much background in statistics. Recognizing this as an important issue in surveillance programs, we develop a user-friendly R package called groupTesting to estimate disease probabilities from group testing outcomes. The package provides R functions with a great deal of flexibility and generality for group testing problems, with both single and multiple infections. Computing efficiency of the R programs is greatly enhanced by using compiled FORTRAN subroutines. The work is illustrated using simulation as well as chlamydia and gonorrhea data collected from the Nebraska Public Health Laboratory.

Abstract for 21790

Use of silent video tasks in the mathematics classroom

Authors: Bjarnheiður Kristinsdóttir, Zsolt Lavicza, Freyja Hreinsdóttir

Affiliations: University of Iceland School of Education, Johannes Kepler University Linz, Austria

Starting with an innovative idea from mathematics teachers and teacher educators in a Nordic-Baltic collaboration project, Bea has designed and developed silent video tasks and their instructional sequence within a design-based research project in Iceland.

Silent videos are ½-2 minutes long animated video clips, showing mathematics dynamically without sound or text. In a silent video task, students get to add their voice-over to a silent video, either by creating a screen recording or by recording a sound file. First, the teacher chooses a silent video displaying some previously studied mathematical ic and shows it to the whole class. Next, students get assigned into pairs to view the video as often as they want whilst they prepare and record their voice-over to the video. Students are free to choose what they include in their voice-over, but one can expect some explanations, descriptions, or narratives. All students’ responses to the task get listened to and reflected on in a whole group discussion. Teachers can highlight some shared knowledge present in students’ responses. Also, topics such as precision in language use and misunderstandings can be addressed and discussed.

Results from the design-based research study indicate that silent video tasks can be used for formative assessment. Teachers can gain insight into students understanding and students get an opportunity to share and become aware of their own knowledge about the mathematical ic shown in the video. Furthermore, it was observed that during implementation of the silent video task, students would participate in the discussion and talk about mathematics with their peers. This was also the case in classrooms where students normally worked silently and individually on problems from their textbooks and were not used to participating in discussions about mathematics.

Abstract for 21794

Safety zone in an entertainment park: envelopes and Maltese Cross related to an offset of an astroid

Authors: Thierry Noah Dana-Picard

Affiliations: Jerusalem College of Technology

There exist different, non totally equivalent, definitions of an envelope of a parameterized family of plane curves. Using software, it is possible to explore the different approaches, either via geometric constructions and automated commands or using analytic methods. In this paper, we explore examples using joint work with a Dynamic Geometry System (DGS) and a Computer Algebra System (CAS). Each package provides its own contributions, and together they contribute to the exploration, to obtain parametric presentations and implicit equations on the one hand, and to have benefit of automatic animations and mouse-driven dynamic work on the other hand. Zooming and increasing precision of approximations are crucial. We study an envelope of a family of circles centered on an astroid, i.e. an offset of this astroid, and explore its physical meaning to determine a safety zone of a concrete device.

Abstract for 21797

An overview of the evolution of DGS in the 21st Century: it is time for algebra

Authors: Eugenio Roanes-Lozano

Affiliations: Universidad Complutense de Madrid

The early dynamic geometry systems (DGS): Cabri Géomètre and The Geometer’s Sketchpad were introduced in the early ‘90s, providing a whole new world of possibilities for geometric exploration. They were manly oriented to education, but can also be used for research.

At the end of the ‘90s the DGS Cinderella was introduced, including the possibility to work in non-Euclidean geometries. It also performs the internal computations in the set of complex numbers, what is the key for the continuity of some animations.

In 2001 GeoGebra is presented as another classic DGS. But it has a difference with respect to the previous ones: it is free and is willing to be extended through the collaboration of the community of users. It becomes a great success.

A possible evolution of DGS is moving from 2D to 3D. Some present a 3D version (Cabri 3D), others include 3D possibilities from a certain version onwards (GeoGebra) and others are developed directly as a 3D-DGS (Calques 3D).

But the most fruitful development is the approach of DGS to the possibilities of computer algebra systems (CAS). CAS have two main characteristics:

they can handle unassigned variables, that is, variables in the mathematical sense, not in the computational sense,
they work by default in exact arithmetic, instead of in floating point arithmetic (what makes numerical computations reliable).

Already back in 2001 the author detailed in a plenary lecture at ICTMT-5 the need for cooperation between DGS and CAS: DGS should incorporate algebraic capabilities. Different approaches have been followed in the 21st century:

a new DGS that has a small internal CAS and/or can communicate with an external CAS is developed (GDI, Discovery, Geometry Expressions),

a computational “bridge” between existing DGS and CAS is built (paramGeo, paramGeo3D),

an existing DGS incorporates algebraic capabilities from a certain version onwards (GeoGebra).

The last step of this evolution is the autonomous work of the algebraic engine of the DGS for automatic theorem proving and discovery (GG-ART).

These evolutions have clearly made DGS much more powerful tools.

Abstract for 21799

Recognizing the Polish Efforts in Breaking Enigma

Authors: Rick Klima, Neil Sigmon

Affiliations: Appalachian State University, Radford University

The work of British and American codebreakers led by Alan Turing at Bletchley Park in breaking the Enigma cipher machine during World War II has been well-documented, and rightfully recognized as one of the most extraordinary achievements of the human intellect. However, without the success of Polish codebreakers led by Marian Rejewski in the 1930s on an earlier version of Enigma, the work by the British and Americans in the 1940s might have taken much longer, prolonging the war at the potential cost of untold additional lives. The mathematics integral to the Polish method for breaking Enigma involved some basic theory of permutations. The purpose of this paper is to present an overview of these ideas and how they served to this effect. To assist in demonstrating this, technology involving Maplets will be used.

Abstract for 21800

Synergistic relationship between computational and mathematical thinking: Implications for teacher education programs

Authors: Jonaki Ghosh

Affiliations: Lady Shri Ram College, Delhi Universityy

The invention of the computer has changed the way we think about mathematics teaching and learning. Papert, in the early 1960s, had referred to the computer as “a mathematics speaking being” and had proposed that children be encouraged to use the computer as “an object to think with”. He talked about “computer cultures”, and delved into how working with computers can influence thinking and reasoning. His pioneering work led to concretizing the term computational thinking (CT), which, in recent times has been identified as an important skill to be developed in children right from the school years. While CT encompasses a broad skill set applicable across contexts and domains, it is also intimately connected with mathematical thinking (MT). 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 and engaging in multiple paths of inquiry are some of the skills common to both CT and MT. Thus mathematics as a compulsory school subject, becomes the natural playing ground for integrating CT based activities in the K – 12 curricula. However, developing appropriate tasks, which elicit both CT and MT in students continues to remain a key pedagogical challenge and teacher preparation needs to address this aspect. Mathematics courses in teacher education programs (TEPs) generally cater to school mathematical content and related pedagogy. However, they do not offer any opportunity to specifically address CT.

This talk will focus on the synergistic relationship between computational thinking and mathematical thinking by illustrating examples of CT – MT integrated tasks from school mathematics as well as from outside school mathematics. The suggested tasks, both mathematically and computationally rich, were integrated in a foundational mathematics course in an undergraduate pre service teacher education program. The students who attended the course were from diverse backgrounds in terms of their mathematical ability and interest. Their prior mathematical knowledge included topics taught at the senior secondary level in school, such as, permutations and combinations, probability, trigonometry, coordinate geometry and calculus. The integrated tasks covered a wide range of topics emerging from Fractal explorations, Chaos game, coin weighing problems and cake cutting algorithms. The talk will highlight the potential of such tasks to enable students to engage in the processes of visualization, recursion, iteration, scaling, generalizing, forming decision trees and analyzing algorithms, which are important from both computational as well as mathematical perspectives. Evidence of progression in students’ thinking as they engaged with these tasks and their positive feedback led to a convincing argument for integrating such tasks in the mathematics courses of the program. The supporting role of technology in mediating CT and MT was also an important take away from the study.

Abstract for 21809

A Browser Based Mathematical Investigation With GXWeb and WolframAlph

Authors: Philip Todd

Affiliations: Saltire Software, Tigard, OR USA

The combination of Geometry Expressions with commercial CAS systems such as Mathematica or Maple makes a formidable tool kit for mathematical exploration. However, these systems are not appropriate for casual use, as they require installation, and are not free. In this paper, we demonstrate the use of the free browser based version of Geometry Expressions: GXWeb [1], along with the free browser based CAS tool WolframAlpha [2]. Both have taken great strides to enhance usability, while retaining the power of their underlying technologies. We root the discussion in an investigation of the Tschirnhausen cubic, the curve which appears as the catacaustic of parallel oblique beams of light reflecting in a parabolic mirror. We highlight techniques for moving information between GXWeb and WolframAlpha and for exploiting WolframAlpha’s permissive approach to mixing mathematics with natural language.

Abstract for 21810

A Haskell Implementation of the Lyness-Moler''s Numerical Differentiation Algorithm

Authors: Weng Kin Ho, Chu Wei Lim

Affiliations: Kobe University

This paper describes a computational problem encountered in numerical differentiation. By restricting the problem to a proper subclass of differentiable functions, a numerical solution first proposed by Lyness and Moler is considered and implemented in the functional programming language Haskell. The accuracy of the calculation of the numerical derivative using the Lyness-Moler's method crucially lies in our recursive algorithm for computing contour integrals.

Abstract for 21812

Technology use in secondary mathematics education: A comparative perspective with international large-scale assessment data

Authors: Christian Bokhove

Affiliations: University of Southampton

In the past decades technology has been used in mathematics education in a variety of ways, ranging from LOGO in the early days of the computer, to Computer Algebra Systems and now, among other applications, for dynamic geometry and online applications. Not all applications of technology are successful, though. Recent meta-studies have shown that especially intelligent tutoring systems or simulations such as dynamic mathematical tools were significantly more beneficial than other uses. In many cases, the effectiveness increased if digital tools were used in addition to other instruction methods and not as a substitute. These two developments provide a compelling challenge to classroom resource; on the one hand, there are the existing classroom resources like textbooks, and on the other hand there is technology that can augment and improve these existing instruction methods. Both could be combined in digital mathematics books, but for this to happen, several stars must align, not in the least the general technology uptake for secondary mathematics education in a country.

In this paper, using data from TIMSS 2015 and PISA 2018, I first will give an international comparative overview of technology and resource use in secondary mathematics education. I will show that technology uptake in countries vastly differs for students and teachers. For example, in Australia more than half of students are asked by their teachers to use computers at least monthly for exploring mathematics principles and concepts. In Japan this is only 3%. I will give an overview for more countries and will also include an analogue analysis on internet use. I will explore whether different use is associated with differing achievement levels. The results show vast differences between countries, with some countries integrating numerous technology resources in their secondary mathematics education, and others showing limited technology use. Possible explanations are discussed. I then relate these findings to existing research on the most effective uses of technology in secondary mathematics education, and sketch scenarios for adequate and useful technology uptake. I present several case examples of effective technology use as well. I conclude by integrating the two lines of inquiry. Firstly, we need to focus on the most effective uses of technology for secondary mathematics education. Secondly, for each country, we must explore more fully what stands in the way of successful uptake of these successful methods. In some final thoughts, I sketch a vision where digital mathematics books could combine and harness many of the affordances of technology use in secondary mathematics education worldwide.

Abstract for 21814

The Role of Technology to Build a Simple Proof: The Case of the Ellipses of Maximum Area Inscribed in a Triangle

Authors: Jean-Jacques Dahan

Affiliations: IRES of Toulouse

We know that there is a unique ellipse inscribed in a triangle and passing through the midpoints of its sides. This ellipse is known as the Steiner ellipse. Among the properties of this special ellipse, one states that it is the ellipse of maximum area inscribed in a triangle. The first complete proof of this property was given in 2008 by Minda and Phelps. Their proof uses lots of properties of complex numbers and especially the complex forms of some transformations. When I read this proof for the first time, I was unpleasantly surprised by its complexicity. From this moment, I worked on an approach of this property using dynamic geometry and Computer Algebra System. My aim was initially to find investigations that could lead to this property. I was successful but what was astonishing is that I could build a proof of this property following the stages of the previous investigations. This paper will discribe first, how the investigations conducted with technology led to the expected conjecture and secondly how a simpler proof could be built in translating with CAS the stages of the investigations ([1’]). This process is really unusual because, it is known that there is a gap between the conjecture and the proof in an experimental process of discovery mediated by technology (or not). The story of this research will give an example of bridging the stage of conjecture and the stage of proof ([2’]). We will also have the opportunity to show how the possibilities of a software can influence our constructions and the way to conduct our proofs: here we will conduct a backward reasoning which is the core of the simplification provided by my proof. As usual in any research work, we will give some extra results met during our investigations (construction of all ellipses inscribed in a triangle, simple constructions of isoptics…).

Abstract for 21820

The geometry of impossible figures

Authors: Alasdair McAndrew, Jacob Baker

Affiliations: Victoria University, Melbourne Australia, Mathematics Department Alexandra Park School Bidwell Gardens, London N11 2AZ UNITED KINGDOM

"Impossible figures" are those that can be drawn with perspective in two dimensions, but cannot exist in the physical world. Well known examples are the Penrose triangle, the Penrose staircase, and the "impossible trident". The Dutch artist Maurits Escher (1898--1972) took great delight in such figures and incorporated them into many of his works. Less well known is the Swedish artist and graphics designer Oscar Reutersvärd (1916--2002), who drew and developed hundreds of such figures, and who has been honoured by some Swedish postage stamps showing his designs. Some art installations now include such figures, but which only seem impossible from one particular perspective. In this article, we explore the geometry of such figures, and discuss how such figures can be drawn using standard programming tools. The mathematics required is elementary, but not without subtlety, and with the delight of producing some lovely diagrams.

Abstract for 21823

NetPad: Using Technology to Promote the Reform of Mathematics Education

Authors: Hao Guan, Gang Yao

Affiliations: cas, jzjy

With the development of computer technology, the dynamic geometric system is constantly innovating. From the perspective of application scenarios, we divide it into three main development stages: application stage, Internet stage and mobile Internet stage. In the mobile Internet stage, the positioning and coordination of different devices and the organization and sharing of digital resources are major challenges. NetPad is a dynamic mathematical digital resource platform conceived and developed in the mobile Internet stage, and includes a two-dimensional and a three-dimensional dynamic geometric system. Examples will be given to illustrate the functions, interaction methods and main application scenarios of its dynamic geometric system, resources and platform.

Abstract for 21824

Computational thinking as habits of mind for mathematical modelling

Authors: Keng Cheng Ang

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

The growing interest in computational thinking and its use in problem solving had led teachers and educators, as well as other researchers, to ponder over what it means and how best to introduce such a notion to students in schools. Many ideas on “teaching computational thinking” have also been suggested, and in many countries, courses on coding have been made very popular as more people begin to believe that the ability to write code is an important skill in this increasingly digital world. In this paper, we focus on the habits of mind that are related to computational thinking and that can be developed from learning to code. Some of these habits include looking at trends in data and analyzing them, examining a process and simulating it, and systematically constructing a solution to a problem. More specifically, we shall discuss how these habits of mind can enhance and support one’s skills and competencies in the context of mathematical modelling, using three examples. Individually, each example illustrates some aspects of computational thinking applied to the modelling tasks. Collectively, through these examples, we attempt to demonstrate that the related habits of mind of computational thinking, developed through coding exercises, could strengthen one’s ability and expand one’s capability of tackling modelling tasks in a significant, albeit sometimes subtle way. The paper concludes with a brief discussion on possible directions of work that could further exploit computational thinking in mathematical modelling.

Abstract for 21825

How important is the user-interface to dynamic software?

Authors: Douglas Butler

Affiliations: iCT Training Centre (Oundle, UK), Autograph-Maths

Autograph is now free to download, thanks to La Salle Education and "Complete Maths", so joins Desmos and Geogebra on the give-away table. This is a useful opportunity to compare the three very different user-interfaces, and to evaluate their effectiveness.

Autograph is still a desk application, and relies on a well tried system of object selection then right-click. The right-click menu lists the options that are relevant to the object selection. Geogebra uses the opposite selection process: choose the operation then the objects (as did Cabri). Sometimes this is to be preferred, but not always. Geogebra gets a lot of its power from the use of command line entries, which some teachers find quite demanding. Desmos was born in the cloud, so has the best web performance and online participation. However Desmos has the smallest feature list as it is not really dynamic object-based software.

By the time of this presentation a web version of Autograph will be nearing completion.

This presentation will take a number of topics from the high school curriculum and see how the three platforms compare.

Douglas Butler
Twitter: @douglasbutler1
Home page: www.tsm-resources.com

Abstract for 21826

Maple in the Classroom: Strategies, Experiences and Lessons Learned

Authors: Douglas Meade, Paulina Chin

Affiliations: Maplesoft, University of South Carolina

Interactive applications that demonstrate mathematical concepts are valuable tools for students, whether they are used in a classroom setting or for self-study purposes. Instructors can easily find a large number of ready-made applications for a variety of subjects. However, sometimes you need to build your customized interactive resources.

Prof. Meade will show various applications that he has developed over the past 30 years for use in calculus, linear algebra, and differential equations classes. These include Maplets for Calculus, a collection of 201 Maple applets designed for use by students and instructors in calculus and precalculus. He will talk about his philosophy and current best-practices for building these applications, using them in the classroom and adapting them for different audiences.

All the applications described in this talk were created in the mathematics software package Maple. Dr. Chin will describe the current tools available in Maple that allow instructors to quickly get started in creating their own interactive educational resources. These tools make it easy to incorporate Maple’s extensive library of mathematical functions with ready-made graphical components.

The presentation is accessible and meaningful to all Maple users, novice and experienced, and even to non-Maple users as the pedagogical philosophies and best-practices are not software specific.

Abstract for 21827

Understanding Geometric Pattern and its Geometry (part 3) – Using Technology to Imitate Medieval Craftsmen Designing Techniques

Authors: Miroslaw Majewski

Affiliations: New York Institute of Technology, Abu Dhabi Campus

TThe medieval artists produced incredibly complex geometric art using very basic tools – a ruler, simple compasses and a number of templates drawn on a parchment or on a paper. This was all what they had and all what they needed. They did not have computers, AutoCAD or printers. Nowadays with all the modern tools we still have problems with reconstructing correctly the old geometric art and our easy-to-use tools do not help much.

In this paper we will explore the possible ways of creating geometric patterns using a simple geometry software and following the old XV century methods.

Abstract for 21829

Exploring Locus Surfaces Involving Pseudo Antipodal Points

Authors: Wei-Chi Yang

Affiliations: Radford University

The discussions in this paper were inspired by a college entrance practice exam from China. It started with investigating the locus curve that involves a point on the given curve and a pseudo antipodal point with respect to a fixed point. With the help of several technological tools, the problem leads author to explore 2D locus for some closed curves.

Later, we investigate how a locus curve can be extended to finding the 3D locus surfaces on surfaces like ellipsoid, cardioidal surface and etc. Secondly, we use the definition of a developable surface (including tangent developable surface) to construct the corresponding locus surface. In robotics it is well known that antipodal grasps can be achieved on curved objects. In addition, there are many applications already in engineering and architecture about the developable surfaces. We hope the discussions regarding the locus surfaces can inspire further interesting research in these areas.

Author will make use technological tools so we can leave the complicated computations behind and make the key concepts more intuitive through graphical representations. Contents are accessible to undergraduate level students. Technological tools that will be used are: Maple, Geometry Expressions, Netpad (Chinese developed web-based software) and etc. Example using Netpad can be found in this URL:https://www.netpad.net.cn/resource_web/course/#/222555.

Abstract for 21830

Designing Mobile Apps to Address Mathematical Gaps in the Context of a Developing Country

Authors: Ma. Louise Antonette De Las Penas, Debbie Marie Verzosa, Jumela Sarmiento, Mark Anthony Tolentino, Mark Loyola

Affiliations: Ateneo de Manila University, University of Southern Mindanao

Developing countries typically do not perform well in international benchmarks of mathematics achievement. This may be partially explained by students’ immersion in classrooms characterized by superficial strategies or rote-learning methods. This paper reports on the design of mobile applications (apps) developed by the authors as part of an ongoing project funded by a national government agency and intended to promote structural thinking and statistical reasoning. It describes the general features of the apps, as well as the pedagogical principles upon which the apps’ designs were anchored on. These principles are grounded on research and established practices on number sense and statistical learning. Collaborations with the Philippine Department of Education for widespread implementation and sustainability are also discussed.

Abstract for 21832

What’s in a name? Using a scientific calculator for mathematical exploration in schools

Authors: Barry Kissane

Affiliations: Murdoch University

This paper identifies a problem that calculators are often interpreted as devices whose sole purpose is to undertake numerical calculations, with the result that their educational significance in secondary schools is not understood well, in contrast to other forms of ICT, for which the software capabilities are recognised as the key features. It is suggested that the potential for educational use of calculators in many Asian contexts is undermined by this limited understanding of their capabilities. An important use of calculators in secondary schools beyond mere calculation involves mathematical exploration, which is described in the paper. Several examples of ways in which features of scientific calculators might be productively used for mathematical exploration are outlined, to indicate the range of contexts of relevance. Ways in which such features might be used in schools are described

Abstract for 21834

Maths in the Time of Corona: Experiences in Remote Education

Authors: Dóra Szegõ, Ildikó Perjési-Hámori, György Maróti

Affiliations: University of Pécs, Faculty of Engineering and Information Technology, Department of Engineering Mathematics

This presentation reflects on the spring semester of the 2019/2020 academic year. The COVID-19 global health crisis has brought traditional university education to a halt. At the University of Pécs we had eleven days to make the transition to remote education. In trying to overcome the obstacles some new methods were developed to teach Mathematics in the Department of Engineering Mathematics: Microsoft Teams, Zoom, Möbius TA, Neptun, Unipoll or even YouTube were utilized. The presentation covers the experiences of Mathematics for Information Technology 2 in detail: how the classes were held, the kind of homework given, the structure used for grading, and most importantly how Möbius TA was used in the final exams.

Computer aided test and assessment is widely used to support the teaching and learning of mathematics [1, 2]. During the design of the questions Bloom’s taxonomy [3] was taken into account (the levels are knowledge, comprehension, application, analysis, synthesis, evaluation). All questions’ title refer to the taxonomy level.

Phases of development:

Planning: what, to whom, at which level. Detailed development of curriculum
Data acquisition: selection of the types of exercises, splitting the exercises into parts, weighting, finding the correct wording, correct answer
Programming, close teamwork between curriculum developer and IT expert.
One-by-one testing
Construction of different assessments for different purposes (practicing, self-regulation, exam)
Collecting feedback from students and teachers, revision of questions.
In our presentation, the results of students with and without on-line test and assessment will be discussed. Our goals were

for students: assessing their own knowledge of a particular ic,
for teachers: getting feedback from the level of knowledge of learning material.
References:

[1]
Winkler, S., Körner, A., Breitenecker, F.(2016). A New Approach Teaching Mathematics, Modelling and Simulation Proceedings of the 9th EUROSIM & the 57th SIMS, 416-419, Oulu, Finland, DOI: 10.3384/ecp17142416
[2]
Ronning, F., (2017). Influence of computer-aided assessment on ways of working with mathematics Teaching Mathematics and Its Applications 36, 94-107 DOI:10.1093/teamat/hrx001
[3]
Pelkola, T., Rasila, A., & Sangwin, C., (2018). Investigating Bloom’s Learning for Mastery in Mathematics with Online Assessment Informatics in Education, Vol. 17, No. 2, 363–380 DOI: 10.15388/infedu.2018.19

Abstract for 21835

Transfigurations of Polyhedra

Authors: Jen-chung Chuan

Affiliations: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300

In this study, we are to present animations in the form of short video clips showing how polyhedron A can be changed in appearance to polyhedron B, where A, B are particular types of Catalan solid, Archimedean solid or Platonic solids. Since each such transfiguration is in one to one correspondence with the nets of a particular polyhedron, and since the algorithm for generating all such nets is yet to be developed, the author would welcome your feedback on improvements in making a more efficient video production. Expanded abstract can be found in this link.

Abstract for 21836

Using technology in mathematics teaching and learning: Sure, but why and how?

Authors: Michael Bosse, Anthony Dove

Affiliations: Appalachian State University, Radford University

There is little doubt regarding the value of technology in mathematics teaching and learning. Most research and practices even seem to accept this unquestioningly. But, is this enough? We must begin to consider more deeply why and how we use technology in the mathematics classroom. In this session, we will discuss Instrumental Genesis, Representational Determinism, Uses of Technology, the IGS framework, and Implications of classroom implementation of mathematics learning technology.

Instrumental Genesis. Instrumental Genesis (IG) recognizes that a tool (with its constraints and possibilities) and a subject (with his/her knowledge and work ethic) interact as an instrument through which to do a task (Artigue, 2002; Lagrange, Artigue, Laborde, & Trouche, 2003; Trouche, 2005). Trouche (2018) recognizes instrumentation as how the tool affects the subject, instrumentalization as how the subject affects the tool, and mediation as the interaction of the two. Thus, discussing either technology or the teacher/students independent of the other is nonsensical.

Representational Determinism. Traditional mathematical representations include: numeric (or tabular), symbolic (or algebraic), graphical (or pictorial), and verbal (written or oral). More recently, the literature has recognized dynamic math environments (DMEs) and dynamic technology environments (DMEs) as an additional type of mathematical representation (Brown, Bossé, & Chandler, 2016). All representations have inherent strengths and weaknesses. Any representation or manipulative provides only a partial embodiment of underlying mathematical ideas, while ignoring or even slightly distorting others (Goldin & Shteingold, 2001). In a given mathematical domain or task, the representation itself not only impacts the information that can be directly perceived and used, but also limits the range of possible cognitive actions by allowing some, prohibiting others, and impacting behavior. (Bossé, Lynch-Davis, Adu-Gyamfi, Chandler, 2016)

The term, representational determinism (Zhang, 1997), defines how the form of a representation affects: what mathematical information can be perceived or distorted; what mathematical processes can be activated; and what mathematical structures can be explored and discovered. Thus, the selection and use of a representation resides not only in the mathematics being addressed but also in the determinism of the representation. In order for representations to be used correctly, users must understand each representation’s associated, contextualized determinism (Bossé, Lynch-Davis, Adu-Gyamfi, Chandler, 2016). Unfortunately, the seeming simplicity with which some believe that technology can be implemented in the classroom can lull some to use technology in means which may lead to lessened pedagogical and epistemological benefits.

Uses of Technology. There are three primary uses of technology in the classroom: Presentation; Pedagogical (teaching) – to teach a concept, to enhance/extend a concept, to assess student understanding, and to remediate a concept; Epistemological (learning). These dimensions are very different applications of technology, and must be thoroughly understood by educators intending to employ technology in the mathematics classroom. Any plans to use technology should include more than just a list of activities for students to perform; plans and activities should be founded upon why it is being used in such a manner.

Interactive Geometry Software Framework. The Interactive Geometry Software (IGS) Framework considers whether the use of technology acts as an amplifier (students could achieve the same goals without the technology) or as a reorganizer (the mathematical goal of the task would be difficult to achieve without IGS) (Hollebrands & Dove, 2011; Sherman & Cayton, 2015). Understanding this framework helps the educator to understand the nature of the activities and technology use, how students interact with the technology, and what affordances the technology provides the learner. (Note how this circles back to IG.)

Implications. The implications of these dimensions are myriad and are important to consider when employing technology. For instance: not all uses of technology improve learning; technology use in teaching and learning is not a panacea; and technology use can both improve strengths and accentuate weaknesses among student learners (Jobrack, Bossé, Chandler, & Adu-Gyamfi, 2018).

References

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International journal of computers for mathematical learning, 7(3), 245-274.
Brown, M., Bossé, M. J. & Chandler, K. (2016). Student errors in dynamic mathematical environments. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.org.uk/journal/bosse8.pdf
Bossé, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal of Mathematics Teaching and Learning 17(3). Retrieved from http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/37/22.
, G. A., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics (pp. 1-23). Reston, VA: NCTM.
Hollebrands, K. F., & Dove, A., (2011). Technology as a tool for creating and reasoning about geometry task. In T. P. Dick & K. F. Hollebrands (Eds) Focus in high school mathematics: Technology to support reasoning and sense making (pp. 33–52). Reston, VA: National Council of Teachers of Mathematics.
Jobrack, M., Bossé, M. J., Chandler, K., & Adu-Gyamfi, K. (2018). Problem solving trajectories in dynamic mathematics environments. International Journal of Mathematics Teaching and Learning, (1) 69-89. file:///Users/bossemj/Downloads/72-Article%20Text-669-2-10-20180830%20(4).pdf
Lagrange, J. B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 237-269). Springer, Dordrecht.
Trouche, L. (2005). An instrumental approach to mathematics learning in symbolic calculators environments. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument (pp. 137-162). New York: Springer.
Trouche, L (2018). Instrumentalization in mathematics education. In the 2018, Encyclopedia of Mathematics Education. Retreived from https://www.academia.edu/37155584/Instrumentalization_in_mathematics_education
Zhang, J. (1997). The nature of external representations in problem solving. Cognitive Science, 21(2), 179-217.

Abstract for 21847

How technology affects problem-posing activities?

Authors: Zoltán Kovács

Affiliations: Eszterházy Károly University, University of Debrecen

Problem-posing is a priority area for the development of mathematical competence in addition to problem-solving. In the problem-posing activity, whether we start from a known problem or a real-life situation, we must first discover the case, come to conjecture, or even test one of our inferences on additional examples. So, the flexibility of computer-based technologies (including programming) for facilitating exploration and experimentation seems relevant to problem posing. This situation naturally raises the question: How can technology be used in problem-posing activities? (Singer, Ellerton, & Cai, 2015).

In the first part of my lecture, I will give a brief overview of how technology appears in Hungarian mathematics textbooks (grades 5-8). I then examine examples of the problem-posing activities of teacher candidates, primarily in terms of didactical coherence (Abramovich & Cho, 2015). In conclusion, I argue that the application of technology can open up new curriculum perspectives in the teaching of mathematics in a didactically consistent way.

Although geometric tasks appear to be particularly well suited to the dynamic visualization power of computer-based tools to aid in problem posing, I also investigate technological tools in other mathematical contexts.

References

Abramovich, S., & Cho, K. E. (2015). Using digital technology for mathematical problem posing. In F. M. Singer, N. F. Ellerton, & J. Cai, Mathematical Problem Posing (old.: 71-102). New York: Springer.
Singer, F. M., Ellerton, N. F., & Cai, J. (2015). Mathematical Problem Posing. New York: Springer-Verlag.

Abstract for 21848

Delivering a computer-based maths curriculum

Authors: Alec Titterton

Affiliations: Computer-based Maths, Wolfram Research

This talk will explore how the contents and delivery of the mathematics curriculum change when you assume that computers exist and students will be encouraged to learn how to use them for solving problems. From the very process used to define the makeup of the curriculum, to the desired outcomes for learning, to the mechanisms used to track progress, the assumption of computer use changes many traditional approaches and raises many challenges to long held beliefs about the nature of the subject and what is required for today''s AI age.

Abstract for 21854

ExDiD: Trendy Teaching Method to WOW Your Students

Authors: haslinda ibrahim, Masnita Misiran @ Bakun Misiran @ Bakun, Norhayati Yusof yusof

Affiliations: school of quantitative Sciences, universiti Utara Malaysia, kedah 06010 Malaysia, school of quantitative Sciences, universiti Utara Malaysia, kedah 06010 Malaysia

ExDiD(Explore, discover, develop) method is being adopted for creating ambiance learning environment to meet future demands and challenges. This innovative teaching method is based on three main criteria, namely “Explore, Discover, and Develop” to create a curious mind in learning mathematics by engaging students in the learning of the subject. Students were coached to solve problems based on the ExDiD method. The first phase, which is called “Explore” is the process where the students are free to explore the material/problem given to them. This phase is the basic principle in understanding ideas or concepts related to the given scenario. In this category the students are trained to do brainstorming for any given problems they have to solve. Then, the “Discover” phase is where the students execute some possible arrangements or enumerations for several cases that are appropriate to the given problems. This task is crucial in the investigation of the relationship towards providing solutions to the problem. Finally, the “Develop” phase is where the students construct the design for the solution. In this phase, students eventually construct the formulae, procedures, algorithms, or plans for the concluding solutions. To facilitate deep learning, the activities are conducted in small groups of four to five students. Collaboratively, each group shall explore the nature of the problem, then discover the patterns of solving problems from various aspects and finally, they shall develop an optimal strategy to reach the solution. This novel teaching method ExDiD forms a strategic chain of core processes in building critical thinking, which is fundamental in problem solving and decision making. This article will showcase the voyage of ExDiD in teaching and learning.

Abstract for 21855

Using Computer Algebra and Computer Numeric Systems to support a deeper understanding of Applied Mathematics

Authors: Alexander Edthofer, Milena Sipovac, Stefanie Winkler, Andreas Körner

Affiliations: TU Wien, Institute of Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

At the TU Wien different methods and concepts are applied to teach students the power and possibilities mathematics provide for engineering science. The last semester has shown that it is important to use computer systems to enable individual feedback and learning. Different tools are applied for different lectures and exercises. On the one hand, there is the basic math courses for engineers. On the other hand, there are various courses given in the field of mathematical modelling and simulation. This field may already suggest the usage of computer systems. But in both subjects the basic theory is an important aspect of studying. The only remained question is how to enable the self-education for the exercising part of the courses.

Abstract for 30001

Three Aspects of Maple for Education

Authors: William C. Bauldry

Affiliations: Appalachian State University, North Carolina

We discuss three aspects of utilizing the computer algebra system Maple to enhance learning. First, we consider Maple as platform to develop both static and dynamic images and displays for classes and for students for their studies. Second, we consider Maple as a student exploration tool under the Action-Consequence-Reflection Principle where a student acts on a mathematical object, observes the consequences of their action, and reflects on the mathematics of the situation. Third, we look at Maple as a tool to support mathematical exposition via linking to documents, posting worksheets in the MapleCloud, and by creating packages of routines and programs to support a document.

Abstract for 30002

Incorporating Online Mathematics Teaching in Practice in China - Implications from experiences during the pandemic

Authors: Yiming Cao

Affiliations:

In this paper, an investigation of the challenges that mathematics teachers in China faced when the nation switched to online teaching during the pandemic was reported; it was also examined that how teachers incorporating technology use into teaching practice during online teaching. A total of 152 mathematics teachers from 20 cities (municipalities) or provinces were interviewed. The analysis of data shows that many teachers face with challenges in technology use and instructional practices during online teaching. How teachers addressed the challenges from technology use during online teaching were examined. Implications are discussed as to how to integrate technology with instructional practice, the critical role that teachers play in online teaching, and possible factors that determine the effectiveness of online teaching.

Abstract for 30006

Effective Strategies in Teaching Using the Hyflex Model

Authors: Haitham S. Solho

Affiliations: American University in Dubai (United Arab Emirates)

It is safe to say that one of the major effects of the COVID-19 pandemic was forcing educators to reconceptualize the learning experience, and rethink how students engage with the instructor, content, and peers. It required educators to learn how to use technology tools as well as various classroom strategies to ensure that students can still receive an adequate learning experience. In this paper, I discuss some of the strategies used at the tertiary level in a small university setting. I give an overview of some of their strengths and weaknesses of some of the tools used to deliver the content (namely Blackboard Collaborate and Zoom), and use data collected from courses completed using both tools that suggests that there are still substantial steps to be taken to ensure the students’ conceptual understanding of the content. My hypothesis is that students’ overreliance on the technological tools, along with the absence of the physical interaction elements (eye contact and physical proximity) makes it difficult to capture the essence of the traditional physical classroom settings. I discuss some of the techniques I used to enable students to further enhance their conceptual understanding of the content, all while providing them with the interactive engagement needed to understand content. Some of the techniques (like polling, flipped classroom, and student-driven discussions) have been very effective in delivering and ensuring a better and more rewarding educational experience for the students.

Abstracts for Full Papers

Abstract for 21780

Enhancing the Problem Solving Skills of Selected Grade 11 Students of Highway Hills Integrated School Through One Word Problem a Day (OWPaD)

Authors: Reynaldo Jr Collado

Affiliations: Highway Hills Integrated School, Department of Education-Schools Division Office of Mandaluyong

Problem solving is one of the major components in learning mathematics. It elicits learners’ higher order and critical thinking skills. To be able to draw out a learner’s potential and problem solving, one must provide a stable foundation of its basics. This study is about enhancing the problem-solving skills of selected Grade 11 students of Highway Hills Integrated School through One Word Problem a Day (OWPaD). The study used 55 students who are under the class of the teacher-researcher. It employed the quasi-experimental design. A pre-test was conducted to determine the existing problem-solving skills of the respondents. The scores obtained were used to determine the level of problem-solving ability of the respondents ranging from poor (0%-58%), good (59%-79%) and satisfactory (80%-100%). This was used as the basis in conducting the day to day intervention for two months. OWPaD is an intervention designed to enhance the problem solving skills of learners by using the Law of Exercise and Learning by Doing Theory of Thorndike and Dewey respectively. Every day before the start of the lesson, the researcher gives a word problem for the students to solve. A post-test was done after 2 months of implementation. Results were tested at 0.05 alpha level of significance using a t-test which indicated that there was a significant difference between the means of pre-test and post-test scores of the respondents.

Abstract for 21782

Learning Action Cell as a School-Based Continuing Professional Development Program

Authors: Ryan Jay Verbo

Affiliations: Department of Education, Philippines, Schools Division Office

The purpose of the conduct of this study entitle “Learning Action Cell (LAC) as a School-Based Continuing Professional Development” is to determine the effect of LAC to the content knowledge and instructional performance of the secondary mathematics public teachers in Mandaluyong. Mixed method design were used in the study. The researcher asked permission/approval to the Schools Division Office of Mandaluyong in utilizing the COT-RPMS (Appendix J.3) rating of the respondents as well as the copy of percentage of “Passed and Failed” of the students for 2nd Quarter and 3rd Quarter rating periods for School Year 2019-2020, respectively.

As revealed in the study the content knowledge and teaching ability of the teachers has improved after the conduct of LAC and it was validated during the observation of classes before and after the conduct of LAC. There is a significant difference on the teaching ability of the teachers before and after the conduct of LAC. Likewise, data shows that there was an increase in the over-all performance of the students before and after the LAC as reflected from the over-all mean grade of 82.79 (Approaching proficiency) and 87.52 (proficiency), respectively. This implies that LAC enhances the students’ performance.

The researcher conducted an interview among the teachers as to the challenges they encountered in the conduct of LAC. These constitute three challenges which were specified as follows: a) lack of preparation and professional development; b) excessive academic load for the students; and c) integration of lessons in real-life context.

Abstract for 21783

Model of e-Teaching and e-evaluation Methodology for Mathematics during COVID-19 Pandemic in Indonesia and Pakistan

Authors: Faqir Bhatti, Dr. Eka Miranda

Affiliations: Riphah Institute of Computing and Applied Sciences Riphah International University, Raiwind, Lahore. Pakistan Information Systems Department, School of Information Systems Bina Nusantara University, Indonesia.

The rapid spread of the Covid-19 pandemic through the world has also created a disruption in the field of education. Students are unable to go to schools due to the Covid-19 pandemic. Technologies, such as the Internet tare widely used to support online learning. The objective of this paper is to discuss the result of e-teaching for Mathematics in Indonesia and Pakistan. This study examines student’s performance in Mathematics in Indonesia and Pakistan. Data has been collected from a private university in Indonesia and Pakistan. They are Bina Nusantara (Binus) University and Riphah International University for the even semester 2019/2020. This study has examined the students’ performance in Calculus and Linear Algebra for Undergraduate students. This study has found that the students could adapt to learning method changes in Calculus and Linear Algebra, from Blended/Hybrid (e-learning) to fully Online (e-learning) during the Covid-19 pandemic. The e-learning method could be implemented in Mathematics if the e-learning system is equipped with complete features and a complete learning system. This study has revealed rubric for each discipline must be carefully constructed looking at the ground reality and it may differ from country to country

Abstract for 21801

Authors: Leslie Chandrakantha

Affiliations: John Jay College of Criminal Justice of CUNY

Dengue fever is fast emerging mosquito-borne viral disease with more than one third of the world’s population is at stake. The objective of this paper is to predict the risk status (high or low) of dengue transmission based on climate factors using artificial neural networks and the logistic regression method. Previous studies have shown that climate factors influence dengue transmission. The rainfall, temperature, and relative humidity are considered as input for both models. The artificial neural networks possess the ability to identify complex relationships in data without any specific assumptions. Both models fared well and showed minimal false predictions.

Abstract for 21802

Connections between mathematics and digital technology in problem-solving: evidences of techno-mathematical fluency

Authors: Hélia Jacinto, Susana Carreira

Affiliations: Institute of Education, University of Lisbon, University of Algarve, Faro, and UIDEF, Institute of Education, University of Lisbon, Lisbon, Portugal

In this paper we discuss the connections established between mathematical and technological knowledge that emerged from mathematical problem solving with digital technologies in a beyond school competition. We argue that mathematical problem solving with technologies is a synchronous activity of mathematization and expression of mathematical thinking, which leads to the emergence of conceptual models, and that the connections between mathematical and technological knowledge enhance the solving-and-expressing of the techno-mathematical solution of a problem. From an interpretative stance, we present the activity of a middle-school teenager working on a covariation problem and focus our analysis on the key aspects of the simultaneous use of mathematical facts and procedures and the digital tools she resorts to, in developing a conceptual model of the situation. We conclude that the resources available shape her mathematical thinking during problem-solving, that the connections established between these two types of knowledge open way to a progressive mathematization of the situation, allowing the production of a solution that displays a techno-mathematical discourse, which we explain expanding on the notion of techno-mathematical fluency.

Abstract for 21806

Web-based system for teachers to create teaching materials on a browser

Authors: Takuya Kitamoto, Masataka Kaneko, Setsuo Takato

Affiliations:

Due to the influence of the new corona-virus, the need for ICT education in elementary schools, junior high schools, and high schools is increasing. Currently, the introduction of IT equipment such as personal computers and tablets is progressing in these schools.

However, to realize effective ICT education, software as well as hardware is also an essential element, and it is said that the software is not as complete as the hardware. Although there are some practical examples of ICT education, it is hard to say that it is being used in school education, mainly because of problems with cost and system flexibility.

In order to spread educational activities utilizing ICT, this paper proposes a web-based system that allows teachers of schools to create teaching materials on the browser. Our system is able to create various teaching flexibly, and it is easy for school teachers to create their own materials including auxiliary teaching materials used in classes and E-learning teaching materials for exercises. This paper gives some examples of creating teaching materials for class lessons. This paper also presents a configuration example of a simple E-learning system using a computer algebra system.

Abstract for 21808

Teaching of the Graph Construction Techniques Using integer partitions

Authors: Faqir Bhatti, Iqra Zaman, Ms. Tabasum NAZ

Affiliations: Riphah Institute of Computing and Applied Sciences, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore. Pakistan

In this paper, we give new ideas to construct graphs using Integer Partitions. Integer Partition is very useful area of Combinatorics and very fascinating for mathematicians. Integer partition is the study of integers by partitioning them into smaller integers. The graphs constructed in this paper are completely based on Integer Partitions and their graphical representations.

Abstract for 21815

Questioning The Unquestioned: How Primary School Teachers In Yogyakarta Perceive Calculator Use In Mathematics Lessons

Authors: Russasmita Sri Padmi, Wahid Yunianto

Affiliations: Russasmita Sri Padmi, Wahid Yunianto SEAMEO QITEP in Mathematics

The use of calculator in Indonesia is heavily stigmatized due to its allegedly detrimental effect on the students’ learning. On the contrary, public education system in many developed countries has embraced calculator as part of educational technology, supported by myriad positive findings regarding its use in mathematics learning. Considering calculator is one of the most affordable and accessible options for educational technology, calculators can be a promising alternative to introduce educational technology in developing country such as Indonesia. Therefore, changing the stigma is necessary, which can be made possible through appropriate intervention. This study investigated teachers’ perception regarding the use of calculator in mathematics learning in primary school. Open-ended questionnaire was assigned to 30 primary school teachers’ in Yogyakarta, followed by qualitative data analysis. The result suggests that calculator use in primary school mathematics classroom is not a common occurrence in Yogyakarta. Most teachers see calculators simply as calculating device and serve little educational benefit beyond that. The result is hoped to shed light on teachers’ perception regarding calculator, in order to devise suitable and fruitful intervention in the future.

Abstracts for Hands-On Workshops

Abstract for 21844

Creating Math Applications with Maple

Authors: Paulina Chin, Douglas Meade

Affiliations: Maplesoft, University of South Carolina

The Maple mathematics software package allows you to easily create and share interactive applications that take advantage of its natural math notation and extensive library. Examples of these can be found in the Maple Application Center, https://www.maplesoft.com/applications, and they are used in both educational and research contexts.

In this workshop, we will cover the following topics to help you generate your own applications:

Authoring documents in Maple that include math and visualizations.
Creating applications that include interactive components.
A brief look at Maple’s programming language and its mathematical and scientific library.
Sharing your work in the Maple Cloud or the Maple Application Centre.

This workshop complements Prof. Meade and Dr. Chin’s invited presentation, “Maple in the Classroom: Strategies, Experiences and Lessons Learned", as it will explain how to build a number of the applications shown in that talk (though attendance at that event is not required). Some familiarity with Maple is helpful but not essential for this workshop.

All registrants will receive a limited-term license for Maple that they can use during and after the workshop.

Abstracts for Papers with Abstract Only

Abstract for 21772

Surface roughness and deformation effect on the performance of hydromagnetic fluid based squeeze film on rough porous truncated Conical Plates

Authors: RAKESH PATEL, J. V. Adeshara, Hardik P. Patel, G. M. Deheri

Affiliations: DEPARTMENT OF MATHEMATICS, GUJARAT COLLEGE, AHMEDABAD - 380 006., GUJARAT, INDIA, VGEC, Ahmedabad, LJ College, Ahmedabad, S P Univ, Anand

This article has been study and analyze the effect of hydromagnetic fluid base squeeze film between rough spongy truncated conical plates by adopting and considering the effect of slip velocity and bearing deformation. By choice the various type of probability density function, the random roughness of the bearing surfaces is characterized by a stochastic random variable with nonzero mean, variance, and skewness. The associated stochastically averaged equation of Reynolds is solved with the help of suitable boundary conditions to obtain the pressure distribution in turn, which results in the calculation of the load-carrying capacity. The graphical and tabular representations indicate the transverse roughness. The graphical representations demonstrate that while the combined effect of bearing deformation and slip is fairly enhanced, the hydromagnetic fluid lubricant saves the situation to a limited extent. At least in the case of the negatively skewed roughness. The slip parameter should be maximized to improve overall bearing system performance. It is found that the semi-vertical angle and magnetization parameter combined effect are relatively better than that of the aspect ratio and porosity combined effect especially when variance (negative) is involved.

Abstract for 21787

DGS and CAS cooperation: doing old things better or doing better things?

Authors: Belen Ariño-Morera, Angelica Martinez-Zarzuelo, Eugenio Roanes-Lozano

Affiliations: Universidad Complutense de Madrid

The most popular educational programs are computer algebra systems (CAS) and dynamic geometry systems (DGS). But there is an implicit dichotomy concerning their educational roles.

On the one hand, CAS are nowadays generally considered a valuable tool, that should be part of the students’ skills, as it helps to perform some routine calculations in a symbolic, formally acceptable, way. Deciding whether it is more convenient finding by hand or by using a CAS the result of 123456 x 78910 or the expansion of the characteristic polynomial of a 5 x 5 matrix, does not seem to yield an educational earthquake. This is probably a consequence of the long experience in teaching with the help of calculators (for performing tedious numerical calculations).

On the other hand, concerning DGS, there are, since long ago, different and serious concerns about the negative influence of the visualization features of dynamic geometry systems, making students confused about the difference between “seeing” and “proving” geometric facts and eliminating their interest in developing any creative geometric thinking for proving rigorously geometric statements. In short: DGS might induce in students a kind of WYSIWYG (the well-known acronym of “What You See Is What You Get”) attitude.

Already back in 2001 the third author detailed in a plenary lecture at ICTMT-5 the need for cooperation between DGS and CAS. In the past twenty years this dream has been achieved in different ways, through external cooperation or by including CAS capabilities in the DGS. The latter is now offered by DGS such as GeoGebra and Geometry Expressions.

"GeoGebra Automated Reasoning Tools" (GG-ART) has gone one step beyond and is able to develop and present mathematically reliable (as CAS operations) automated proving tools for geometric properties (visualized in a DGS style). The educational impact of the dichotomy mentioned above is particularly difficult to deal with in the case of these DGS with CAS features. And this worry especially concerns the use of GG-ART.

In our presentation we will make a call to the education community on the urgency and the need to develop some firm ideas about how to handle this dichotomy. In particular, we will sketch and exemplify our ideas in this respect, summarizing reports on some experiments that have been conducted on different groups of Secondary School math teacher in their initial training, concerning the epistemic impact of handling GG-ART by these young, digital native, future math teachers.

Perhaps, as J. Kaput said long ago, the key point could be planning how to use different levels of technology (CAS & DGS in this case) to do (old) things better (approaching classic geometric statements with the use of GG-ART as an omniscient tutor, answering our partial conjectures and thus helping us to build our own proof), not neglecting, simultaneously, to do better things (formulating different creative geometric tasks that cannot be solved directly by GG-ART).

Abstract for 21789

Transferring mathematics lessons into their homes through the novel tools of GeoGebra Notes

Authors: Robert Weinhandl, Zsolt Lavicza, Markus Hohenwarter, Melanie Tomaschko

Affiliations: Johannes Kepler Universität, Johannes Kepler Universität, Linz, Österreich

Based on our research and related data collection and analysis of teacher and student feedback, interactive ePortfolio software could be a promising extension of mathematics learning environments. Extending mathematics learning environments in that way could be particularly beneficial in individual or self-learning phases, as was the case with COVID-19 conditional school closures. In our talk, we will present special features, possible implementations and related experiences as well as potentials for further development of GeoGebra Notes. GeoGebra Notes is a specific application of the mathematics software package GeoGebra and was developed initially as a whiteboard-software (Hohenwarter & Hofstätter, 2017). By using GeoGebra Notes, teachers or other users should be able to combine different features of standard whiteboard-software, such as handwriting, with mathematical specific applications like computer algebra systems (CAS) or dynamic geometry software (DGS). Furthermore, GeoGebra Notes enables integrating web pages, audio files or videos to connect presented materials with real-world situations or problems. However, GeoGebra Notes can not only be used as whiteboard-software but also operates in any standard browser, which significantly increases the scope of application of GeoGebra Notes.

Especially in the time of COVID-19-related school closures, the high potential of GeoGebra Notes as a teacher, but also as a student-software became obvious. In our GeoGebra Notes educational study in the school year 2019/2020, which was continued during the COVID-19 school closures, it became apparent that using GeoGebra Notes could improve the teaching and learning of mathematics in general and this applies especially to the time of homeschooling or distance learning. Using GeoGebra Notes as teacher software at the beginning of homeschooling facilitated the abrupt transition from classroom teaching to distance learning for many students in our study. One of the reasons for this facilitation for students was that a familiar blackboard layout, including specific features such as teacher handwriting, could be provided via a browser. In addition to the familiar layout, using GeoGebra Notes also contributed to interactively presenting new mathematical concepts by implementing teacher-developed DGS applications. Implementation of audio or video files created by teachers explained the specifics of the mathematical content as well as how to use GeoGebra Notes. This audio or audio-visual meta-information was highlighted as particularly helpful by the students of our study. However, GeoGebra Notes can not only be used as teacher software but can also be implemented to facilitate students in developing and presenting new mathematical skills. In our study, students developed ePortfolios on different mathematical topics, such as trigonometric functions (see figure). By using GeoGebra Notes, these ePortfolios could be designed dynamically and interactively by the students, and by embedding videos or other web pages directly into the ePortfolio, the mathematical content could be linked to real-world situations. Especially the interactive and dynamic aspect of GeoGebra Notes could contribute to a further development of the ePortfolio concept. According to Carl & Strydom (2017), a distinctive feature of ePortfolios is, among other things, that using photos, videos or other ICT tools should improve the process of creating, presenting and reflecting on learning achievements. The interactivity and dynamics of GeoGebra Notes, for example, that formulas or equations used in a text could also be linked to the CAS or DGS, could contribute to improving reflection on new mathematical concepts and their real-world applications.

Although the current features of GeoGebra Notes already enrich the learning and teaching of mathematics, further development and improvement of the software could bring further opportunities and benefits to both students and teachers. In autumn 2020, GeoGebra Notes will be extended concerning using spreadsheet functions and the associated creation of interactive diagrams. The extension of GeoGebra Notes should also enable users to create mind maps and thus facilitate structuring and presenting ideas or new knowledge. In addition to creating mind maps, the integration of a recording function in GeoGebra Notes could make it easier for teachers or lecturers to present new concepts. Besides, producing learning videos directly with GeoGebra Notes, live streaming of lessons with GeoGebra Notes, or a multi-user functionality of GeoGebra Notes could enrich the teaching and learning of mathematics which is planned for autumn 2020 as well.

References

Carl, A., & Strydom, S. (2017). e-Portfolio as reflection tool during teaching practice: The interplay between contextual and dispositional variables. South African Journal of Education, 37(1).
Hohenwarter, M., & Hofstätter, A. (2017). Entwicklung einer Online Tafelsoftware auf Basis von GeoGebra. In U. Kortenkamp & A. Kuzle (Hrsg.), Beiträge zum Mathematikunterricht (pp. 453–456). WTM-Verlag.

Abstract for 21791

Outdoor STEAM integrated framework in elementary schools in Luxemburg using MathCityMap and GeoGebra 3D Calculator

Authors: Ben Haas, Yves Kreis

Affiliations: Johannes Kepler University Linz, University of Luxemburg

In elementary schools in Luxemburg, sciences and mathematics are generally taught in class based essentially on textbooks. However, the findings of multiple studies on understanding and applying skills in STEAM (Science, Technology, Engineering, Arts and Mathematics) report that students need hands-on activities on real-world objects. Furthermore, in times of the COVID-19 pandemic, where numerous restrictions and risks dominate teaching inside the classroom, outdoor learning is safer and offers many opportunities. Hence, we created outdoor mathematical trails with a STEAM integrated approach for elementary schools using the free educational software MathCityMap and the dynamic mathematics software GeoGebra 3D. In these outdoor trails, students used a set of promising technologies, i.e. AR (Augmented Reality) or GPS, to support STEAM education. Based on results from our first study on outdoor mathematical trails in June 2020 (in review), we developed and evaluated a framework on outdoor STEAM integrated teaching. This framework was used for further outdoor task and trail creations in elementary schools, which we investigated by conducting semi-structured interviews with students and teachers. Hence, we will present how this framework was used in elementary schools to create outdoor mathematical trails and describe how it affected the students'' learning.

Abstract for 21792

Use of silent video tasks in the mathematics classroom

Authors: Bjarnheiður Kristinsdóttir, Zsolt Lavicza, Freyja Hreinsdóttir

Affiliations: University of Iceland School of Education, Johannes Kepler University Linz, Austria

Starting with an innovative idea from mathematics teachers and teacher educators in a Nordic-Baltic collaboration project, Bea has designed and developed silent video tasks and their instructional sequence within a design-based research project in Iceland.

Silent videos are ½-2 minutes long animated video clips, showing mathematics dynamically without sound or text. In a silent video task, students get to add their voice-over to a silent video, either by creating a screen recording or by recording a sound file. First, the teacher chooses a silent video displaying some previously studied mathematical ic and shows it to the whole class. Next, students get assigned into pairs to view the video as often as they want whilst they prepare and record their voice-over to the video. Students are free to choose what they include in their voice-over, but one can expect some explanations, descriptions, or narratives. All students’ responses to the task get listened to and reflected on in a whole group discussion. Teachers can highlight some shared knowledge present in students’ responses. Also, topics such as precision in language use and misunderstandings can be addressed and discussed.

Results from the design-based research study indicate that silent video tasks can be used for formative assessment. Teachers can gain insight into students understanding and students get an opportunity to share and become aware of their own knowledge about the mathematical ic shown in the video. Furthermore, it was observed that during implementation of the silent video task, students would participate in the discussion and talk about mathematics with their peers. This was also the case in classrooms where students normally worked silently and individually on problems from their textbooks and were not used to participating in discussions about mathematics.

Abstract for 21798

Training pre-service teachers in real life STEM education

Authors: Piedad Tolmos, Ana Cid, Rocío Guede, Arcadio Sotto

Affiliations: Universidad Rey Juan carlos, Universidad Rey Juan Carlos

Taking contact with the real world is essential in order to have a good mathematical education, as well as a full STEM training. Students need to experiment, to touch, to see with their eyes where are the mathematics around. In order to assure the best learning process for our students, pre-service teachers must have also the best training.

Based on previous studies we present an experience using MathCityMap with the students of the Master in Training Teachers on Secondary Education level. In a way of active learning, are the pre-service teachers themselves who prepare the activity to hypothetical scholars, so that they will be capable to repeat it in the future with their real students.

As part of their training process, pre-service teachers had to develop not only the complete guide to the mathematical trial, but also the mathematical objective of the activity, how they will evaluate the experience, the possible mistakes made by the students and how to help them, and measures of attention to diversity. In addition, with the goal of providing a STEM framework, they were able to include some signs of real problems that children might see along the way.

Finally, both to prepare the activity previously in the classroom, and for subsequent mathematical work, Geogebra will be used.

This experience is part of a set of activities developed by our research group Gie STEM with the objective of improving the training in STEM education of pre-service teachers, both in the master''s studies, the degree in primary education, and the degree in early childhood education.

Abstract for 21811

PROMOTING LEARNER ENGAGEMENT IN A MATHEMATICS CLASSROOM

Authors: Matshidiso Moleko, Prof Percy Sepeng

Affiliations: University of the Free State, SACE, Central university of Technology, SACE, AMESA

Engaging learners in the learning process increases their attention, motivates them to practice higher-level critical thinking skills, and promotes meaningful learning experiences. Using the learner engagement theory, the study sought to explore how learner engagement could be promoted in a mathematics classroom. Teaching that is not centred around learner engagement principles makes it hard for learners to develop conceptual understanding and to demonstrate an in-depth understanding of the mathematical concepts. Six mathematics teachers participated in this study. Data in this qualitative case study were collected using open-ended questionnaires, free attitude interview and later analysed through thematic analysis technique. In response to the research question: how can learner engagement in a mathematics classroom be promoted? four approaches were considered investigated: i) removing unnecessary learning barriers, ii) tapping into learners' prior knowledge, iii) integrating modern technology and vi) providing authentic, specific, and frequent feedback. The study shows that successful learner engagement depends on the removal of learning barriers, eliciting prior knowledge, integrating technology into the teaching of mathematics as well as providing frequent feedback. The study thus suggests the need for teachers to consider these approaches in order to strive to promote learner engagement so to provide meaningful learning experiences.

Keywords: learner engagement, mathematics classroom, meaningful learning experience

Abstract for 21818

Discovering Architecture for Mathematics Learning through Digital Fabrication and GeoGebra

Authors: Kristof Fenyvesi, Kyeongsik Choi, Natalija Budinski, Shereen El Bedewy, Eva Ulbrich, Julia Handl, Zsolt Lavicza

Affiliations: University of Jyväskylä, Sejong Academy of Science and Arts, Petro Kuzmjak school, Serbia, Johannes Kepler University, Linz

Architecture is among those topics, which has a multitude of connections to both mathematics and culture. In this presentation, we introduce innovative mathematics education practices, focusing on different mathematical connections in architecture, and employing digital fabrication to create tangible tools for mathematics learning. Digital fabrication in the mathematics classroom has opened new perspectives for providing engaging, collaborative, and creative problem-solving activities based on real life. Connecting 3D-printing, physical manipulatives (e.g., building blocks), and GeoGebra in mathematics learning offer several opportunities to promote creativity, critical thinking, teamwork, ICT skills as part of transversal competence development. Digital fabrication can efficiently support introducing the STEAM approach in the mathematics class by connecting mathematics learning to applications in various fields, such as technology, engineering, arts, and design. Implementing these complex links in mathematics education can get a new impulse by employing both digital and physical modeling in the learning process. The presentation will include examples of mathematics classroom practices designed for students in different age groups.

Abstract for 21819

Web-browser based STEM learning activities with JSXGraph

Authors: Pekka Alestalo, Roman Hašek, Marc Bernat Martinez, Igor Pesek, Alfred Wassermann

Affiliations: University of Bayreuth, Aalto University, Finland, University of South Bohemia in ÄŒeské BudÄ›jovice, Czech Republic, BonNouEdu. La Vila Joiosa, Spain, University of Maribor, Slovenia

We will present examples for STEM learning activities for High School and higher education based on the open source JavaScript library JSXGraph (https://jsxgraph.org) and the moodle plug-ins Formulas and STACK.

These examples are developed in the European ERASMUS+ project ITEMS (Improving tools for E-assessment in Maths and Science, https://itemspro.eu).

JSXGraph offers a wide variety of mathematical visualizations, including interactive geometry, function plotting, symbolic derivatives, splines, various curve types and animations, see https://jsxgraph.org/wiki for examples.

From a technical point of view, JSXGraph merely takes 160 kByte to load and offers a tight integration into web pages. It is used in a wide variety of elearning platforms, like moodle, ilias, WIMS to name a few. The JSXGraph filter for the popular elearning platform moodle (https://moodle.org) allows inclusion of JSXGraph material into moodle learning activities. Together with the plug-ins Formulas or STACK, randomized questions are possible. The project Abacus (https://abacus.aalto.fi/) is a huge source for STACK material, including many JSXGraph based questions.

The new handbook on programming JSXGraph (https://ipesek.github.io/jsxgraphbook/) enables a gentle introduction to creating JXGraph applications.

Abstract for 21828

Teaching Math Remotely

Authors: Karishma Punwani

Affiliations: Maplesoft

Teachers and students around the world have been suddenly faced with the need to teach and learn math without a classroom. This is a challenging task, but Maplesoft can help. Maplesoft offers a variety of tools and services that support remote learning of math and math-based courses. Learn how the Maple Calculator, Maple Learn and Maple work together to help students solve and visualize math problems, check their homework, and explore mathematical concepts. In this presentation you will see how these tools work together and the resources that are available to support learning.

Abstract for 21831

Simple Augmented Reality (AR) for Elementary School Mathematics

Authors: Dee Jean Ong

Affiliations: International College, Suan Sunandha Rajabhat University, Thailand

Augmented Reality in education is relatively new but developing rapidly. AR is a live direct or indirect view of a physical, real-world environment whose elements are augmented (or supplemented) by computer-generated sensory input. This work shows how AR is used for the development of a simple Mathematic concept for elementary school children. These activities can arouse curiosity as well as develop interest and better understanding of the concept of Mathematics. The AR materials are in the form of flash cards. The users have to use application software “Augment” to scan the flash cards to view the numbers appearing in 3D from the flash cards.

Abstract for 21837

An accurate time measurement of short interval using an electronic RC-charging circuit

Authors: Janchai Yingprayoon

Affiliations: International College, Suan Sunandha Rajabhat University, Thailand

Some experiments need to do in a short span of time. It is not possible to measure the time manually using a normal swatch. Some can be done by using a highspeed photography. There is another way of a measurement of short time accurately by the help of an electronic RC-charging circuit. The time measurement starts by charging a capacitor C through a resistor R. The voltage across a capacitor, Vc is an exponential function of time t with the constant values of R, C and a constant voltage supply Vs of the circuit. The voltage across a capacitor C can be measured by using a datalogger with high sampling rate. The voltage charging across capacitor Vc is very fast and the charging time t can be calculated from the equation Vc = Vs. (1-exp(-t/RC). This time measurement can be applied to a freefalling object experiment in order to calculate the acceleration due to gravity, g.

Abstract for 21839

THE EFFECTS OF INQUIRY-BASED LEARNING ON STUDENTS’ ACHIEVEMENT AND MATH ANXIETY

Authors: Nutcharun Yanakit

Affiliations: International College, Suan Sunandha Rajabhat University

This study was classroom action research. The purposes of this research were: 1) to enhance students’ achievement by using inquiry-based learning and 2) to investigate the effect of inquiry-based learning on levels of students’ math anxiety. This classroom action research used Stringer’s model: look, think, act. The participants were thirty-one grade 12 students who enrolled in the first semester of the academic year 2019 at a secondary school in Bangkok, Thailand. Research instruments consisted of eight lesson plans for twelve periods in the ‘Limits and continuity of functions’ ic, pretest, posttest, and student’s math anxiety questionnaire. Data were collected regarding students’ pretest and posttest scores and students’ responses in math anxiety questionnaire.

The results of this action research indicated that: 1) the effectiveness concerning for students’ achievement after being instructed had an Effectiveness Index (E.I.) score of 0.7689 which means that the students can be developed 76.89% from the beginning and 2) student opinions towards the instruction that affect their math anxiety in learning mathematics were at ‘Very high anxiety (6.45%), ‘High anxiety’ (25.81%), ‘Low anxiety’ (48.39%) and ‘Very low anxiety’ (19.35%).

Abstract for 21842

Exploring the successfulness of a blended online training program to promote math teachers to create online lessons

Authors: Chaweewan Kaewsaiha, Pongrapee Kaewsaiha

Affiliations: Digital International Business Program, SSRU, Associate Professor in Mathematics Education Program, SSRUIC

This study aims to explore the success of a blended online training program to promote math teachers to create online lessons. This study used the design-based research method. The sample consisted of 156 junior high school math teachers from 10 educational districts in Thailand using stratified sampling. The training consists of 3 phases, starting from designing the lessons that meet online learning requirements following the instructions from the manuals and resources provided on the website. The next step is introductory and preliminary feedback regarding the Pedagogy, Content, and Knowledge (PCK) given via live streaming and Technological Knowledge (TK) given via videoconference. In the third phase, participants joined the on-site workshops for additional training. In the end, qualified lessons have been published on the Massive Open Online Course (MOOC) platform created for this project. Gathering information related to PCK and TK showed that teachers created online lessons using different techniques. The lessons are accurately presented and are engaging. Moreover, interviews and satisfaction questionnaires revealed that the produced online lessons are useful in real-world situations, such as teaching and learning during the COVID-19 epidemic. However, the lessons produced did not cover all the topics specified in the Basic Education Core Curriculum in mathematics.

Abstract for 21845

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

Authors: Chalongrat Khaoloek

Affiliations: International college, Suan Sunandha Rajabhat University

The objectives of this classroom action research were to enhance 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 secondary school in Bangkok, Thailand. The ic used in this study was Vectors in Three Dimensions. The instruments were 7 lesson plans using flipped classroom. Before class, students studied online learning through video clips, work sheets, exercises, and tests. During class, students discussed the contents that they had studied from home, solved harder problems, and getting individual help from teacher. Learning lasted 14 periods with 50 minutes in each period. There were three cycles of action plan. Data were collected from pretest, posttest, and satisfaction survey. Data were analyzed by using Effectiveness Index (E.I.), mean, percentage, mode, and standard deviation. The results showed that: 1) the Effectiveness Index (E.I.) of the class was 0.8017 which revealed that students’ scores were increased 80.17 percent from the beginning and 2) students’ satisfactions towards understanding, learning management, and learning atmosphere by using flipped classroom were at very satisfied, satisfied, and satisfied, respectively.

Abstract for 21846

Online Learning and Augmented Reality: Enhancing Students Learn Transformation Geometry During the Covid-19 Pandemic

Authors: Krongthong Khairiree

Affiliations: International College, Suan Sunandha Rajabhat University

The purpose of this study aims to explore the students’ perceptions of online learning self-study on Transformation Geometry using augmented reality, via smartphone. In the 2020, action research was conducted in Bangkok, Thailand. The total of 20 Lower Secondary students participated in this study. The duration of the action research was about two months from June to July 2020 during the Covid-19 pandemic in Thailand. The students had self-study through online learning lesson and used smart phone to scan QR Code Reader to explore Transformation Geometry: Translation, Reflection and Rotation animations and activities. Based on the students’ interviews they revealed that they studied through online learning incorporated with augmented reality they were able to visualize contents in a textbook. Augmented reality animated content of Transformation Geometry and it made the concepts easier to learn and retain. However, more than 50% of the students revealed that they wanted to study in the normal classroom and used augmented reality in mathematics class.

Abstract for 21849

PROMOTE ENHANCEMENT ON NUMERICAL COMPETENCE AND INTELLIGENCE OF LEARNERS (PENCIL) IN MATHEMATICS

Authors: Mailyn Tumanan

Affiliations: Andres Bonifacio Integrated School

Mathematics is a subject that students often dislike and dread enough to get to real difficulties in learning. Poor mathematical competencies are common among students and result in low academic achievement and arithmetic difficulties seen to be a problem in day to day activities. The teaching of Mathematics does not depend solely on varied instruction. There are cases of rampant absences in which the teachers are faced with the problem of how to assist the students in their learning difficulties. As many researchers have already pointed out, the majority of evaluations of remedial education have serious methodological flaws (Grubb, 2001; Bailey & Alfonso, 2005). Some remedial programs were contented merely with the completion of teaching the subject matter rather than the outcome of that teaching. The study Promote Enhancement on Numerical Competence and Intelligence of Learners (PENCIL) in Mathematics focusing on the possibility of reducing the number of Junior High School learners with learning difficulties in Mathematics of Andres Bonifacio Integrated School from 4% to 1.0% at the end of the second semester of School Year 2019 – 2020. This study aims that by structured, early interventions supporting numeracy-related learning, the problems might be reduced or even solved by providing at-risk student optimal opportunities to improve their knowledge and skills, preventing them to failed in Mathematics. The participants of this study were selected from One hundred twelve (112) students or 4% of the 1730 junior high school students of Andres Bonifacio Integrated School S.Y 2019-2020 However, the study PENCIL implementer was the mathematics teachers of this school who are committed and competent was tapped to address this problem of learning difficulties in mathematics among Junior High School learners. The intervention teaching materials in each session was carefully designed which used in remediation to the student-respondents was modified in each sessions were found effective in the enhancement of mathematical skills of the students. In particular, number activities such as Measurements in Grade 7, Linear Inequalities in Two Variables in Grade 8, Variation and Radicals in Grade 9 and Polynomial Functions in Grade 10 Mathematics were specifically taught in a six Saturdays instructional program. This study looked to measure mathematical competence and resulted a positive effect in terms of the mean percentage score of the students from 43.7% and expect a fifty percent 50% mean percentage score or 7% improvement on mathematical skills on the second quarter assessment. Moreover, as evidenced by a follow-up assessment conducted in one month after the end of the enhancement activities, the effect of the mathematical training was maintained during class hours in Math. In conclusion, the implementation of this study aimed in improving numerical mathematical knowledge seems to be a crucial resource to promote learning in Junior High School.

Abstract for 21852

CASIO FX-9800GII GRAPHING CALCULATOR AS A TEACHING TOOL IN STATISTICS AND PROBABILITY FOR GRADE 11

Authors: KARL GADWIN DELA CRUZ

Affiliations: Jose Rizal University, Ilaya Barangka Integrated School

The purpose of this study is to examine the effectiveness of Casio FX-9800GII graphing calculator as a teaching tool in solving real-life problems in different disciplines involving normal distribution in Statistics and Probability for grade 11 students.

The sample of the study involved two selected groups from four classes in Ilaya Barangka Integrated School, Division of Mandaluyong. Students in the experimental group received an instruction using graphing calculator while the control group students underwent the traditional chalk and talk method without the graphing technology. Instrument was used in this study is the real-life problems in different disciplines involving normal distribution with 25-item test. Findings of this study show existence of a significant difference in the mean scores between the two groups; students who used graphing calculator performed better compared to students without access to graphing calculator. This study is pertinent as it investigates a different approach in teaching real-life problems in different disciplines involving normal distribution while integrating the latest graphing calculator technology in the lessons.

Abstract for 30005

3D Dynamic Geometry and Parametrizations in Neotrie VR

Authors: José L. Rodríguez

Affiliations: Departamento de Matemáticas, CITE III, Universidad de Almería, La Cañada de San Urbano, Almería, Spain

We present a new 3d Graphing Calculator in Neotrie VR to generate parameterized curves and surfaces. It works like other existing software in virtual reality, but with the added advantage that we can later edit the geometric elements with the dynamic geometry tools available in the game. This allows us, for example, to propose exercises to students where they represent parameterized curves and surfaces, and study their symmetries (translations, rotations or reflections). All this in a totally immersive environment, where one manipulates the elements of the objects as if they were real. There will also be a quick introduction to the implemented dynamic geometry tools and how to use them with concrete examples. Different scenarios of how Neotrie has been used in real math classrooms will be shown. This is a joint work by Diego Cangas and Carmen Sánchez from the University of Almería.