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ATCM 2016, Pattaya, ThailandTable of contents
Abstracts for Invited and Plenary PapersABSTRACT FOR 21193Can Technology make a difference to school Mathematics Teaching?AUTHOR: Douglas ButlerAFFILIATION: iCT Training Centre (Oundle, UK), AutographMaths Douglas is in the fortunate position of having the benefit of 30 years teaching, 20 years developing mathematics software, and 20 years promoting TSM training workshops to help teachers make the most effective use of technology. Despite its obvious advantages, and considerable investment from Education Ministries, the majority of mathematics teachers do not allow technology to enliven their teaching. This is mainly through lack of access, but also lack of training. At the same time the software and hardware spectrum is changing rapidly, and many teachers simply fail to keep abreast of all the change. The gradual shift from teachercentric fixed hardware to studentcentric mobile technology is a massive challenge to teachers and to students, and also to those developing appropriate software. This presentation will include some lesson plans that maximise the potential of technology using web resources, spreadsheets and dynamic software, and delivering exciting visualisations and engagement. ABSTRACT FOR 21209Rhombohedra EverywhereAUTHOR: Jenchung ChuanAFFILIATION: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300 A rhombohedron is a 6face polyhedron in which all faces are rhombi. The cube is the bestknown example of the rhombohedron. We intend to show that other lessknown rhombohedra are also abundant. We are to show how the rhombohedra appear in the algorithm of rhombic polyhedral dissections, in designing 3D linkages and in supplying concrete examples in mathematics amusement. ABSTRACT FOR 21256Mathematics, secrets and smartphonesAUTHORS: Jose A Vallejo, Lina Rubí IpiñaAFFILIATION: Universidad Autonoma de San Luis Potosi It is commonplace that Mathematics are everywhere, and we recurrently mention to our students some examples of this occurrence. One of the most used is the mathematics of cryptography. Of course that is true: modern cryptographic methods are strongly mathematicsbased, and there are many excellent texts and web resources explaining at any imaginable level of sophistication their foundations. However, still it is difficult to find resources with a handson approach, in which the student can do more than merely academic computations and examples. Taking advantge of the interplay between mathematics, free software and the computational capacity of current smartphones, we will illustrate how these ingredients can be cooked to build an elementary course on number theory and cryptography with a twist: everything will be done in your (Android) smartphone. ABSTRACT FOR 21271Exploiting Digital Technologies for Learning MathematicsAUTHOR: Celia Hoyles, Richard NossAFFILIATION: UCL Institute of Education, London, UK A key challenge for task design in mathematics education and an organising design principle is to enhance engagement with mathematics. One way to achieve this is to exploit digital technology to reveal more of what mathematics actually is; first, by offering a glimpse of the mathematical models underlying a given (and carefully chosen) phenomenon; and second, by fostering an approach to mathematical tasks that transcends the purely procedural. We describe in this paper how we have attempted to address these challenges. ABSTRACT FOR 21272Outbox Centroid Theorem: An Episode of Dynamic Geometry ExplorationAUTHOR: Weng Kin HoAFFILIATION: National Institute of Education, Singapore An outbox of a given convex quadrilateral is a rectangle such that each vertex of the quadrilateral lies on one side of the rectangle and all the vertices lie on different sides, with all the sides of the rectangle external to the quadrilateral. This paper reports on a new geometrical result concerning outboxes of convex quadrilateral  the Outbox Centroid Theorem, and gives a new proof of an existing result of M. F. Mammana. Interestingly, the investigation that leads to this new result comes from dynamicgeometry explorations. ABSTRACT FOR 21274From One to Infinity: What DGS Has or Could Have Changed in our Teaching and LearningAUTHOR: JeanJacques DahanAFFILIATION: IRES of Toulouse, France The collaborative work enhanced by the communication tools developed in the last decade is perceived by everybody as a progress for teaching and learning. We will see in this paper that this way of working avoids to use all the knowledge developed by experts especially in the use of the technological tools. We will focus our analysis on « dynamic geometry software » and especially on the Cabri environments. We will remind the special role of DGS in a more experimental way of practicing maths (researching, teaching and learning) sustained by the theoretical framework I have developped in my PhD thesis (different stages of an experimental process of discovery, different levels of techniques of investigations known as praxeologies G1, G1 informatique, G2 and G2 Informatique, the heuristic power of dynamic approach of figures.). We will give a lot of examples showing the new tools of exploration or investigation provided by DGS (such as traces, loci, animation, redefinition, macro, sliders.) to understand the difference between a paper and pencil approach or a DGS approach of a problem (that can be not necessarily a geometric problem). In these examples, we will present different techniques that must be taught in order to be used appropriately by the users of DGS. At last we will present my YouTube channel where lots of situations are provided to help teachers and students to use DGS without ignoring all the work of the experts during the last 30 years. ABSTRACT FOR 21279Quadratic and Cubic Polynomials in Applied Problems: Finding Maximum  no Calculus, using CAS (Maple)AUTHOR: Bill BlythAFFILIATION: Australian Scientific & Engineering Solutions, RMIT University, Australia We use CAS to provide a new algebraic approach in some optimization applications where the objective function (to be minimized or maximized) is a quadratic polynomial. These problems can be solved just by knowing properties of quadratics and so give context to why we want to complete the square. Without calculus, to find the max/min of cubics, we introduce a new straightforward algebraic method (no calculus). The use of a Computer Algebra System, CAS, such as Maple easily deals with any messy algebra! The key property of a function is that, near a maximum or minimum, the function "looks like a quadratic". This visual idea is combined with some straightforward algebra to find this local quadratic approximation of a cubic near the maximum. Traditional "find the maximum ..." problems are introduced to senior school or first year undergraduate students in their calculus course. With our approach, these applied problems and the Polya method of problem solving can be introduced to precalculus students. We use the CAS, Maple, for algebra and visualization. We use small group collaborative learning in the computer laboratory, so we parameterize the problem and recommend the use of Computer Aided Assessment (such as provided by the package MapleTA). Students engage with the visualization and algebra, are active learners with deep learning of the concept of maximum and have fun doing so. ABSTRACT FOR 21294Challenges in Integrating Technology in Teaching and Learning Mathematics in Basic EducationAUTHOR: Yuriko Yamamoto BaldinAFFILIATION: Universidade Federal de São Carlos, Brazil This paper presents considerations about the role of technology in teaching and learning mathematics from the perspective of teacher education programs that is required to prepare new generation of teachers for the potentialities of diverse uses of technology in the teaching mathematics content on one side, and in the learning new classroom dynamics on other side. The reflections retrieve some insightful initiatives and foresights of pioneering researchers about the educational possibilities of technology tools from late 90´s and 2000´s, bring frameworks from researches in mathematics education, and are illustrated with examples from the author´s work about development of teaching materials for prospective and inservice teachers, regarding the contemporary needs of mathematics education. The paper discusses the concept of experimental mathematics as a core concept that connects the learning of mathematics content, at student level, with the learning by teachers of new methods of teaching, at professional level. The examples, not exhaustive, will be given with CAS, DGS, and Calculators. The challenges to integrate effectively the technology in educational context are commented considering the presence and advantages of information and communication technologies that imply necessarily the rethinking of teacher education. The reflections of this paper take into account the power of technology towards the educational needs of developing countries that strive for a quality education. ABSTRACT FOR 21297Technology: Inquiry based learning, inverse questions, and controlAUTHOR: Matthias KawskiAFFILIATION: Arizona State University New computational tools become available at every faster rates. A fundamental question asks how such tools can help achieve clearly defined learning objectives. This article argues, in a sequence of examples, that computing technologies can much support the implementation of modern pedagogy. The focus is on enhancing a learner centered environment. Of critical importance is that the learner takes the key role of asking further questions, to take ownership of the discovery experience. We highlight the special role of asking inverse questions with examples ranging from math circles to vector calculus. ABSTRACT FOR 21298Technology in Mathematics Education: A Stocktake & CrystalBall GazingAUTHOR: Greg OatesAFFILIATION: The University of Tasmania This paper seeks to conduct a stocktake of the current use of technology in mathematics education, and engage in some crystalball gazing as to how it might be used in the future. First, it briefly discusses the history of the use of digital technologies in mathematics education, focusing primarily on the period of growth from the mid1990's. It will consider some of the theoretical perspectives that have emerged over that period, and using the framework developed by the author [x; x], will attempt to describe the 'current state of play' for the effective integration of technology into the teaching and learning of mathematics. Then using this position and framework as a starting point, the paper postulates what might be some significant challenges ahead for teachers and institutions in the continuing search for effective meaningmaking in mathematics with technology. ABSTRACT FOR 21300Locus, Parametric Equations and Innovative Use of Technological ToolsAUTHOR: WeiChi YangAFFILIATION: In this paper, we discuss two problems found from Chinese college entrance exam practice problems [8]. We see how original problems in 2D, stated in an exam static and somewhat uninspired setting, can be extended to other interesting cases in 2D and more challenging corresponding problems in 3D for students to explore with the help of a Dynamic Geometry Software (DGS) and a Computer Algebra System (CAS). We use a DGS to construct the locus or locus surface geometrically, and use a CAS to verify our locus or locus surface analytically. We shall see with the innovative use of technological tools, mathematics can be made more fun, accessible, challenging and applicable to broader group of students. Finally, we attempt to make these problems relevant to reallife applications, we invite readers to investigate how these problems can be interpreted differently. ABSTRACT FOR 30001Teaching and Learning Mathematics with Mobile TechnologyAUTHOR: Ma.Louise Antonette N.De Las PeñasAFFILIATION: Ateneo de Manila University, Philippines This talk will discuss a current government funded project in the Philippines on the creation of software applications and applets for mobile technology that will enhance the teaching and learning of mathematics. The Department of Education in the Philippines has recently implemented the K to 12 Basic Education program. The K to 12 curriculum recognizes that calculators, computers, including mobile devices such as smartphones and tablets can be appropriate tools in teaching mathematics. These can help learners demonstrate understanding and appreciation of key concepts and principles of mathematics as applied in problem solving, communicating, reasoning, making connections, representations and discussions in real life (Dep Ed, 2012). To fully support the implementation of Mathematics Grade 710, a comprehensive resource has been created to aid teachers develop their competencies in teaching various strands in mathematics and promote critical thinking and problem solving in the classroom. In this talk we present segments of this resource, which includes interactive software for mobile technology together with a framework for the design of teaching guides, arranged according to competencies prescribed by the curriculum. The extent and manner for which technology can be used in the teaching of mathematics depends not only on the availability of resources (software, internet) but on the teacher's ability and disposition to use the devices. The teaching guides are aimed to optimize the use and benefits of technology. Suggested activities for the students are given which promote student centered learning. The mobile apps are designed to support student investigations, promote student centered learning and at the same time enhance teaching practices and student engagement. These cover topics in algebra, geometry and statistics. These include apps for proving in Geometry. Related literature studies show the novelty of these proving applications.
Abstracts for Full PapersABSTRACT FOR 21147Use Technology in Secondary Mathematics Teaching: Preparing Teachers for the FutureAUTHOR: Munindra MazumdarAFFILIATION: MPS College, Guwahati, India Technology is an essential tool for learning mathematics in the 21st century and all Modern school classrooms have access to a range of potential technologies, ranging from calculators and computers to the Internet. This paper examines the use of Information and Communication Technology (ICT) for supporting the teaching and learning of transformations of functions in terms of linear, quadratic, cubic and trigonometry in the secondary school; and identifies some of the ways in which the teaching of functions might be supported by the availability of various forms of technology. An exam was applied and performance comparison between computer and paperandpencil groups. Modern technology provides an excellent mean of exploring many of the concepts associated with functions. This paper suggests some of the avenues for exploration. ABSTRACT FOR 21160Homothetic centers of three circles and their threedimensional applicationsAUTHORS: Yoichi MaedaAFFILIATION: Tokai University, Japan In this paper, we recall the famous Mongef's theorem of three circles. There are several proofs for the theorem. One of the proofs is that of using three similar right cones. Inspired by the proof, we propose a threedimensional problem of the same angles of elevation: For three similar right cones on the ground, find the places from where three angles of elevation are equal to each other. There are at most two places. With dynamic geometry software, we can simply construct the solutions. In addition, the relation between two solutions is cleared. ABSTRACT FOR 21179Two examples on discrepancy potentials of dynamic geometry softwareAUTHORS: Yip Cheung ChanAFFILIATION: Department of Curriculum and Instruction, The Chinese University of Hong Kong It is unavoidable that a computer program has its constraints. In a mathematics pedagogical program such as dynamic geometry software (DGS), the constraints may lead to deviations of mathematical representations from its intended mathematical concepts. If it is used properly, the deviations can open up pedagogical opportunities and hence may be called as discrepancy potentials of the tool. In this paper, examples of developing mathematical discussions by using the discrepancy potentials in two DGS tasks are discussed. It aims at elaborating the idea of discrepancy potentials in the design principles for effective DGSbased tasks. This paper relates to the topic ¡§Mathematics Education using Information Communication Technology. ABSTRACT FOR 21183Connection Between Multiplication and Division of Fraction Using GeoGebraAUTHORS: Boo Jia Yi, Leong Kwan EuAFFILIATION: University of Malaya Several studies had shown that fraction multiplication and division were the most challenging concepts to teach at the primary level. Previous research also found that elementary pupils lacked conceptual understanding when learning fractions. The purpose of this study was to identify Year Six pupils' understanding of the connection between multiplication and division of fraction using GeoGebra. The theoretical framework of this study was based on the radical constructivism theory of integrating mental image, representation, interpretation and problem solving about fraction multiplication and division using GeoGebra. The case study research design was utilized and intended to support pupils building their own understanding among the connection between multiplication and division of fraction. Data for this study includes both verbal and nonverbal behaviors were gathered from seven pupils based on five clinical interview sessions and used to collect data to answer the research questions. The findings revealed that (1) pupils performed better after using mental image with GeoGebra, (2) pupils were able to construct visual representation with GeoGebra to explain its connection between two operations, (3) pupils were able to give meaning about the connection between multiplication and division of fraction after using GeoGebra and (4) pupils faced difficulty in solving problems of multiplication and division with the use of GeoGebra. Interestingly, this study would benefit primary school teachers' teaching and learning methods on the conceptual understanding of multiplication and division of fraction. This study would also further develop pupils' conceptual understanding of fractions using GeoGebra. ABSTRACT FOR 21191The Courselab VLE: Its Effect on the Achievement and Students' Perception Toward Learning AlgebraAUTHOR:<\strong> Carmelita RagasaAFFILIATION: University of the East Manila, National Research Council of the Philippines, MTAPTL, Philippine ELearning Society Courselab, a Virtual Learning Environment was used to design classes in algebra. Its effect on the achievement of the students was tested. Pretest and posttest were given to the experimental and control groups. The findings showed that there was no significant difference in the achievement of students taught with lecture and the use of Courselab. A survey questionnaire showed that majority of the students disagree that they learned better using computer based materials. Seventy two percent agree that they learned better by reading a good textbook and with face to face discussion. Seventy seven percent agree that they learned better by listening and by reading and rereading materials. The perception of the students on the effectiveness of Courselab in learning college algebra was not favorable. Fifty seven percent disagree that it was clear how Courselab modules fitted into learning algebra and that they also disagree that the scoring system in Courselab was useful for students in preparing their subject's test. On the other hand, half of the students think that they can easily understand and deal with the interface and more than half think that the platform tools were easy for students to use. This means that Courselab was not the problem but it was learning algebra in Courselab where the difficulty was. ABSTRACT FOR 21192Introducing MATLAB into High School MathematicsAUTHORS: Ian Allan ThomsonAFFILIATION: Ormiston College, Australia In order to solve cubic equations by Euclidean means, the standard ruler and compass construction tools are insufficient, as was demonstrated by Pierre Wantzel iin the 19th century. However, the ancient Greek mathematicians also used another construction method, the "neusis", which was a straightedge with two marked points. We show in this article how a neusis construction can be implemented using dynamic geometry software, and give some examples of its use. ABSTRACT FOR 21196Using Dynamic Geometry Software to Enhance Student Understanding of the Concept of SpeedAUTHOR: Wee Leng Ng, Foo Him HoAFFILIATION: National Institute of Education, Nanyang Technological University, Ministry of Education, Singapore The authors of this paper have conceptualized and constructed a tool, using dynamic geometry software, to simulate scenarios of word problems involving speed, and used it to help students acquire the concept of speed and solve speed problems involving two objects moving toward each other. This paper demonstrates how such a tool can be created using GeoGebra, and describes how the use of this tool had improved understanding of speed concept, and ability to solve speed problems for a class of sixth grade students in Singapore. ABSTRACT FOR 21198On Simple Representation of Locally Closed SetsAUTHORS: Yosuke Sato, Ryoya Fukasaku, Katsusuke NabeshimaAFFILIATION: Tokyo University of Science, Tokushima University A locally closed set of an affine space is defined as a difference of two varieties. Simple representation of locally closed sets is of great importance in many areas of computational mathematics. We presents a practical simplification algorithm of locally closed sets. Our algorithm consists only of computations of Groebner bases, it does not use any heavy computation of polynomial ideals such as a primary decomposition. ABSTRACT FOR 21201Finding the signature matrix of minimizing the Cayley transform by using Computer AlgebraAUTHORS: Dexuan Zhang, Yongbin Li, Haocheng ZhouAFFILIATION: School of Mathematical Sciences, University of Electronic Science and Technology of China, School of Mathematical Sciences, University of Electronic Science and Technology of China Given an orthogonal matrix Q, we can choose a diagonal matrix D with diagonal entries such that I+QD is nonsingular and then that the Cayley transform (QD)=(I+QD)(IQD)^(1) is well defined. Evan O''Dorney has proven the existence of the diagonal matrix $D$ with diagonal entries plus or minus 1 (called a signature matrix) to make sure every entry of QD is less than or equal to 1 in absolute value. The remaining question is how to compute D directly. In this paper, we present a method for computing the signature matrix D based upon Grobner basis and RealRootClassification in the case of $n=2$. Our approach is helpful to develop the interest of learning computer algebra and using computer algebra systems in researching. ABSTRACT FOR 21202Impact of multimedia in Teaching MathematicsAUTHORS: Haftamu Menker Gebreyohannes, Abdul Hadi BhattiAFFILIATION: Middle East College, Oman In this paper, we are going to examine issues within the new frontier of integrating technology into mathematics education. We present an approach on how to teach mathematics courses by integrating meaningful multimedia technology to foster the learning process. Specifically, this paper focuses on how the integration of multimedia based teaching approach into a Calculus and Numerical Methods module impact on student's performance and their attitudes toward educational technology. Empirical data will be collected from controlled and experimental group students enrolled into this mathematics module which include students' engagement using traditional and multimedia technology teaching and learning process. ABSTRACT FOR 21203Mathematical Regression Modeling For Smart Environmental Weather forecastingAUTHOR: Haftamu Menker GebreyohannesAFFILIATION: Middle East College, Oman Environmental weather forecasts have been increase the city's ability to be selfsustaining and lowering environmental impact as well as metrological support for critical decisions as climate change brings more extreme weather events. To predict weather meteorologists form models based on the land's geography and starting weather conditions and they can calculate future forecast by entering it into a computer to be processed. In this paper we will describe a survey of Mathematical techniques and Practices used to model weather forecasting today.. ABSTRACT FOR 21204HexagrammumsAUTHORS: Vladimir ShelomovskiiAFFILIATION: University of TechnologyPapua New Guinea, DeomaRussia In this paper we consider hexagrammums, plane geometric configurations based on six points. Pairs of given points form straight lines. Points of intersection of these lines form the new daughterly points. We get the net configuration of points and lines. The work is based on firstly, delightful drawings of Hirotaka Ebisui [1], and secondly, the GInMA software [2], which makes it easy to explore the geometric configurations and exercise their conversions. Typically the only one unusual point found by Ebisui has served the source for the study. As a result, the net has been found. In each case, the method of barycentric coordinates has been used for the formal proof. The evident solutions have been found in many cases with the use of collineations. This may introduce solutions of problems into standard courses of geometry. All the pictures in the paper are interactive. So they come to life, install on your computer GInMA software from the website [2]. Free basic version will allow you to get acquainted with all the materials, to conduct a study, to create your file, but not to keep it. See the video How to convert pictures from the text in interactive drawings. ABSTRACT FOR 21205Enhancement of Plotting Environment of STACK with GnuplotAUTHORS: Kenji Fukazawa, Yasuyuki NakamuraAFFILIATION: National Institute of Technology, Kure College, Graduate School of Information Science, Nagoya University, Japan In this paper, we explain our approach to building an enhanced plotting environment in which, for example, graphs of implicit functions and surfaces described by functions containing two variables could be visualized. This enhancement is achieved by creating Maxima functions, which produce the appropriate scripts of gnuplot, which is then called with these scripts. This approach enables us to make full use of the power of gnuplot, and can be applied to any plotting software other than gnuplot, such as matplotlib, and Pyxplot. Several examples of questions with enhanced plots are presented. ABSTRACT FOR 21206A Study of gamification on GeoGebra for remedial pupils in primary mathematicsAUTHORS: KAI CEAT LIM, KWAN EU LEONGAFFILIATION: FACULTY EDUCATION, UNIVERSITY MALAYA Remedial pupils are often more engaged in their learning when the content delivered uses gamesbasedactivities. This study integrated gamification using technology in learning mathematics which is one of the 21st century learning approaches. In this paper we report the results of a study on lessons using 2 learning games based on GeoGebra with reference to remedial pupils' motivation in learning primary mathematics. The respondents consisted of 4 remedial pupils from a primary school in Selangor, Malaysia. Data were obtained through observation on lessons and questionnaire on students' perception in gamification on GeoGebra. Observation by using video recording indicated that the sample showed high motivation in learning mathematics. Questionnaire result also showed students' positive interest in using gamification on GeoGebra. In conclusion, this study found that using gamification on GeoGebra is highly effective in helping remedial pupils to learn primary mathematics besides increasing their motivation in learning. This study strongly recommends the implementation of gamification on GeoGebra to facilitate mathematics learning at the primary level especially in geometry. ABSTRACT FOR 21210IMPACT OF USING TINKERPLOTS IN STATISTICAL REASONINGAUTHORS: Leong Kwan Eu, Pavethira SelorajiAFFILIATION: Tenby Schools Setia Eco Park, Universiti Malaya In this 21st century of learning, students are not only required to know how to do the calculation procedures but more importantly they must be able to justify their solutions by reasoning. This is particularly important in the teaching and learning of statistics in schools. This study aims at investigating the impact of using TinkerPlots in statistical reasoning among Year Five pupils. The research was conducted in an international school. The research utilized the quasi experimental research design. Two intact classrooms were selected with one classroom as the control group while the other was the experimental group. The experimental group went through intervention using TinkerPlots whereas the control group went through the traditional method. The research conducted pre test and posttest for both the groups. The findings show that a significant difference existed between pretest and posttest for the experimental group. In conclusion, the students' statistical reasoning results improved using TinkerPlots. The study implies that using TinkerPlots enhances students' reasoning skills. Implementing teaching and learning statistics using TinkerPlots would help students explore data, concepts and test their conjectures. This would support the studentcentered learning where teachers facilitate the students to develop their ideas and knowledge. ABSTRACT FOR 21211Exploring generalizations of a result about cubic polynomialsAUTHORS: Alasdair McAndrewAFFILIATION: Victoria University, Melbourne Australia For a real cubic function with three distinct roots, the tangent at the mean of any two of them passes through the third. This elegant and elementary result seems to have first surfaced as an investigation for students studying the International Baccalaureate. There are number of ways for generalizing this result; in this article we look at two of them: higher degree polynomials, and polynomials over the complex numbers, and the quaternions. Thus we show how the result can be defined in considerable generality over general domains. This may be considered as a case study in the use of a CAS to generalize a simple result. ABSTRACT FOR 21216Are Mathematics Students' Learning Styles Related to Their Preferred Method of Learning How to Use Advanced Calculators?AUTHORS: Hazel TanAFFILIATION: Monash University, Australia One of the learning styles models used for investigating students' preferences is based on the Visual, Aural, ReadWrite or Kinesthetic (VARK) modalities for receiving information. This paper presents the research findings of a survey study on Singaporean and Australian students, contrasting students' VARK preferences with their instructional learning preferences when using graphing calculators and calculators with computer algebra systems (advanced calculators). Students filled in an adapted 7item instrument about their VARK preferences, and were also asked to indicate their most preferred instructional method of learning how to use the calculators to solve mathematics problems. It was found that students generally preferred visual and kinesthetic instructional methods when learning how to use calculators, regardless of their VARK preferences. Results also show that there were regional differences in students' VARK preferences. Overall, the results suggest that students adapt their learning preferences to different contexts, and that advanced calculators lend themselves to visual and kinesthetic modalities of learning. ABSTRACT FOR 21217Teaching methodology for smart students with lessdeveloped abstract thinking skillsAUTHORS: Vladimir ShelomovskiiAFFILIATION: University of Technology, Deoma The author has been teaching statistics to students in Papua New Guinea for three semesters. These students are smart but their mathematical knowledge and abstract thinking skills require considerable development. The author is forced to build teaching on the basis of binding mathematical concepts with objects of the real world. The subject of the paper are examples of realizing this idea. ABSTRACT FOR 21219Parallel and Distributed Boolean Grobner Bases Computation in SageMathAUTHORS: Akira NAGAI, Yosuke SATOAFFILIATION: Tokyo University of Science, NTT Secure Platform Laboratories, Japan We introduce a parallel and distributed computation method of Boolean Grobner bases, which are implemented in the computer algebra system SageMath using the PolyBoRi library. We present an easy way to parallelize Boolean Grobner bases computation using a decorator for parallel computation supported in SageMath, we also present a way of distributed computation using a multiprocessing module in Python. Our software achieves satisfactory speedup comparing to our sequential implementation in SageMath. ABSTRACT FOR 21222Exploring Derivative Functions using HP PrimeAUTHORS: Betty, Wan Niu Voon, Ling Shing WongAFFILIATION: Universiti Tenaga Nasional, Faculty of Health and Life Sciences, INTI International University, Persiaran Perdana BBN, Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia Derivative is one of the essential topics in calculus, which is an important basic skill should be mastered before integration comes in. Learning derivative in higher education can be achieved by using interesting graphingcalculator based learning. In this paper, activities using HP Prime to explore derivative function are outlined. The usage of Function and Statistics 2Var applets are emphasized and used in these activities. Through these activities, students are able to learn how to sketch the graph of a derivative from its original function, through observation on the changes of slopes and tangent lines in HP Prime. ABSTRACT FOR 21227Teaching and Learning of Geometry in Primary School Using GeoGebraAUTHORS: Boo Jia Yi, Leong Kwan EuAFFILIATION: University of Malaya, University Malaya The purpose of this article is to discuss how GeoGebra can be used to teach the concept of angle in Geometry in elementary level. This result is obtained after 2 weeks of lesson exploration. Teachers used GeoGebra as a teaching tool to make the lesson more creative and innovative in order to show how geometrical shapes relate with different angles in different polygons. For students, they can use GeoGebra to construct, drag or apply the actual shape instead of drawing on a piece of paper. Besides that, all the works created by students can be saved as documents for future reference. At the end of two weeks' exploration, pupils were asked to answer survey question regarding their experience with using GeoGebra. Analysis of the survey showed that pupils are able to express their geometric imagination and understanding of mathematical concepts before and after the exploration. Hence, using GeoGebra can make the classroom lesson more enjoyable and interesting. ABSTRACT FOR 21261Solving Sudoku Puzzle by Evolutionary AlgorithmAUTHORS: Kedar Nath Das, Sumit Bhatia, Shubhin Puri, Kusum DeepAFFILIATION: Assistant Professor, Department of Mathematics, NIT Silchar, Assam, India, Department of Computer Science and Engineering, The Pennsylvania State University, USA, Department of Chemical Engineering, IIT Roorkee, India "Sudoku" means "Single number". "Sudoku Puzzle" is an interesting and popular Japanese game, where the nongivens need to be filled by a single number (from 1 to 9) provided no repetition occur in the corresponding rows, columns and subsquares. Solving a Sudoku puzzle is challenging due to its easy rules and difficult inherent phenomenon. Although a number of approaches exist for solving a given Sudoku puzzle, it becomes a challenge among the researchers to solve it by using evolutionary algorithms. In this paper, a Retrievable Genetic Algorithm is proposed to solve a given Sudoku puzzle. A new fitness function is designed with puzzlecharacterdependent constraints. The Genetic Algorithm is made "Retrievable", since the population is reinitialized after a certain number of generations in order to escape from the premature convergence or from being trapped in the local minima. A set of 9 sample puzzles of different difficulty label have been considered for comparison. The superiority of RetGA is ensured from the comparative results and discussions.
Papers with Abstract OnlyABSTRACT FOR 21153Modeling with NetlogoAUTHOR: Crista ArangalaAFFILIATION: Elon University, USA Netlogo is a free software in which can be used to learn agent based modeling. In addition, there is a package for importing data from Netlogo into Mathematica so students can then explore the similarities and differences between agent based models and traditional differential equation models. This presentation will give an overview of how to introduce Netlogo programming in the classroom, examples of predator prey and SIR agent based models developed by students, and how this technology inspires further study in applied mathematics. ABSTRACT FOR 21154THE COMBINED EFFECT OF OUTCOMEBASED EDUCATION (OBE) AND BLENDED LEARNING ON THE STUDENTS PERFORMANCE IN GENERAL MATHEMATICSAUTHOR: Restituto RodelasAFFILIATION: Andres Bonifacio Integrated School, Philippines The need to improve student learning in response to the increasing demands of globalization prompted studies on and pilot testing of alternatives to the traditional approach to delivering education. This study evaluated the effectiveness of the combined use of blended learning and outcomesbased education in Grade 11 General Mathematics classes at Andres Bonifacio Integrated School in the first semester of AY 2016  2017. Each consisting of two classes, the control group was handled using blended learning while the experimental group was handled using blended learning and outcomesbased education. Blended learning consisted of 4 facetoface classes and one online module per week. With outcomesbased education, various instructional strategies, class requirements, and assessments were used to ensure that the students were able to do the learning outcomes. The same test was given as pretest and posttest and the posttestpretest score difference was used to measure the student learning. All results were statistically significant at a significance level of 0.05. The groups were equal in prior knowledge on the topics. There was positive learning in each group, but both classes in the experimental group had greater score difference than those in the control group. Based on this, the combined blended learning and outcomesbased education had positive impact on student learning. ABSTRACT 21166Exploring Mathematics with TechnologyAUTHOR: Maree SkillenAFFILIATION: UTS:Insearch, Australia Technology has been referred to as having an integral role in the reform of mathematics education, and is rapidly changing how we teach and how we learn. Educationalists are required to support changes in mathematical content and instructional methods, as well as incorporating and supporting changes in technology. A new approach to instructional design is needed to combine and integrate these changes so that technology can be utilised to allow students to explore and discover mathematical concepts through appropriate computer applications. Recent trends emphasise the importance of learning with technology, rather than learning about technology. Computers should be viewed as a cognitive tool to enhance student learning of content material, rather than a tool which allows an individual to acquire isolated skills in basic applications or specific programming languages. This presentation will consider how the use of technology provides a paradigmatic shift in the instructional focus of specific computer applications, to more sophisticated uses of general purpose software. Educational uses of technology will be examined as exemplars for a discussion of alternative modes of teaching to engage students. ABSTRACT 21168Enriching the Teaching and Learning of Linear and Nonlinear Systems of Equations through Developing a Module using HP Prime Graphing CalculatorAUTHOR: Loreto Delizo, Joanne OlosAFFILIATION: Saint Pedro Poveda College, HP Calculators, Saint Pedro Poveda College HP Calculators In response to the needs of the 21st century learners, efforts have been made to integrate technology in the High School Mathematics classroom. Various ways of teaching and learning linear and nonlinear systems of equations have been done, which can be further deepened with the aid of graphing calculators. This paper explores the development of a module on linear and nonlinear systems of equations, which aims to enhance the teachinglearning experience using the HP Prime. The teachermade module intends to develop students' better understanding of the concepts involved in the given systems in order to solve reallife applications. This presentation will consider how the use of technology provides a paradigmatic shift in the instructional focus of specific computer applications, to more sophisticated uses of general purpose software. Educational uses of technology will be examined as exemplars for a discussion of alternative modes of teaching to engage students. ABSTRACT FOR 21169The Occurrence of Passive Intermodulation and Troubleshooting in Thailand Mobile IndustryAUTHOR: Mr.Aditep Chaisang, Mr.Sinchai AnantapreechaAFFILIATION: Faculty of Industrial Technology, Rambhai Barni Rajabhat University, TEST & MEASUREMENT CO. , LTD, Thailand This paper describes the problem of the passive intermodulation (PIM) in mobile communications. We focus the problem occur between the transmitter and antennas. The paper start from the theory of intermodulation, mathematics concept and effect in mobile channels. The problem occurs when two or more signals frequencies are transmitted at the same time in the same passive device. The nonlinear behavior produces spurious signals where frequencies are linear combinations of the frequencies of the original signals. Then we measure PIM level and find the problem solving methods. Finally, we got the PIM level that can be acceptable due to IEC 62037 standard. ABSTRACT FOR 21176Improving Primary Mathematics Teaching and Learning with ORIGO Stepping Stones Online ProgramAUTHOR: Korakot ChonvichitAFFILIATION: Dara Academy, Thaialnd This study investigated the impact of ORIGO Stepping Stones online program on the teaching and learning of mathematics at Dara Academy Chiang Mai, Thailand. The targeted population consisted of 400 students and 12 teachers in grade 2. To assess the effects of the intervention, a mix of classroom observation; semistructured interviews with the mathematics teacher; and students' artifacts were used. The tenmonth intervention of ORIGO Stepping Stones consisted of Lesson Study activities, and Mathematics Professional Leaning workshops. Even though this study was limited in duration and scope, the outcomes clearly support earlier research on positive effects of ORIGO Stepping Stones on teachers' mathematical content knowledge and student motivation. The study revealed that the students had positive attitudes toward Stepping Stones online program with increases in motivational intensity as well as their desire to learn the mathematics. The outcomes also showed some obstacles in implementing electronic and online program in Thai school with reference to both the teacher and the students. Based on these findings, some recommendations for better outcomes are discussed and a suggestion is included for future research. ABSTRACT FOR 21213On the Visualizing Activities of Analytic Expressions of Lines and Circles via DGSAUTHOR: Minshik Cho, Minji KimAFFILIATION: Department of Mathematics, Korea National University of Education The equations of straight line and circle are one of the most important contents of Korean high school mathematics courses. They are expressed analytically as the solutions of equations in the coordinate plane. Hence students mostly learn the topic only practicing and calculating equations. Some topics include parameters meaning pencil of lines like kx+k+y=0. Since they do not mention the geometric meaning of parameters of straight line and circle equations in Korean textbooks, many students don¡¯t understand involved geometric meanings in analytic problems. The purpose of this study is to investigate, through case study, how to apply DGS(Dynamic Geometry Software) and to find out effective methods for learning equations of straight line and circle with technological assistance. We developed some problems in order to investigate students'' level about connecting algebra with geometry. Only a few students could solve those problems analytically. Many students could not even understand written solutions. One of the reason is that the lack of understanding on the relation between analytic expression and its geometric meaning. Learning worksheets including DGS activities were designed so that student's understanding of the straight lines and circles can be improved. During the class with DGS activities, students could correct their misconceptions and understand the geometric meanings of parameters of straight line and circle equations. Analysis of data including worksheets, DGS activities, and interviews showed effects of geometric understanding as a result of utilizing DGS. During the students had personally composed problem situations on their own through DGS, they had intuitively recognized beneath geometric meaning. ABSTRACT FOR 21218Fostering a Teaching Culture with Technology in MathematicsAUTHOR: Maree SkillenAFFILIATION: UTS:Insearch, Australia With education increasingly moving towards technology enhanced delivery we need to identify and use alternative approaches to teaching and learning to support our students. To sustain the engagement of students in mathematics classrooms, teachers are employing a pedagogical design capacity. This involves the mobilisation of mathematics and embedding of realtime assessments to transform the learning and application of concepts by students. Performance levels in Mathematics subjects have improved, and teachers have noted increased participation and commitment to learning by students. This presentation will provide examples of teaching and learning approaches where technology has been incorporated to ensure that studentcentred technologyenabled learning is occurring at UTS: INSEARCH, a pathways provider preparing students from diverse language and learning backgrounds for study in Australia. ABSTRACT FOR 21220Development Students'' Understanding the Formula of the Surface Area of Sphere through the SAK handson ActivityAUTHOR: Cherdsak PakdeevirochAFFILIATION: King's College, Samphran, Nakhon Pathom, Thailand, Institute for Innovative Learning, Mahidol University, Thailand Sphere is a threedimensional geometric shape of which its formula of a surface area is difficult for students to understand. In this study, students in grade 9 were allowed to participate with the Surface Area Kit (SAK) as a handson activity integrating the POE strategy. The dynamic mathematics software GeoGebra was applied as learning tool and representative of the concrete entities. The results showed that student' developed understanding about the meaning of the surface area of the sphere formula and there are significantly different understanding between the students who did and did not study with SAK handson activity. Moreover, the three processes about the students' understanding gains were also identified and discussed. ABSTRACT FOR 21221Project Based Learning in Science with Graphing Calculator Coupled Portable SensorsAUTHOR: Wong Ling Shing, Voon Betty Wan NiuAFFILIATION: INTI International University, Malaysia, Universiti Tenaga National, Malaysia Project based learning allows students to participate in the learning process, by allowing them to construct questions, draw hypotheses, find explanations, and discuss their idea collaboratively, which all together polish the students' thinking competency. Through simple graphing calculator coupled portable sensors, project based learning can be carried out in teaching biology related topics. In this paper, an example of project based learning in biology is reported. The students were given a few portable sensors, including light, temperature, pressure, and pH sensors which could be coupled with graphing calculator to collect data on a life culture of living algae. The possible designs from of the experiment, and the benefit of conducting the project for students are highlighted. ABSTRACT FOR 21223Preservice Teachers'' Designing of Mathematics Activities Integrated the Use of the Geometer's Sketchpad SoftwareAUTHOR: Sasiwan Maluangnont, Pilaluck Thongtip, Teerawit Tinprapa, Poonyapon ChanfoyAFFILIATION: The Institute for the Promotion of Teaching Science and Technology, Suan Sunandha Rajabhat University The purpose of this study is to investigate how preservice mathematics teachers could design activities that used the Geometer's Sketchpad software to teach mathematics. This study was conducted with a group of 20 preservice mathematics teachers who enrolled in a mathematics teacher preparation program in Thailand. This mathematics preparation program provided a course for preservice teachers to experience the use of technology, including the Geometer's Sketchpad, in mathematics classroom teaching. As preservice mathematics teachers learned to use the Geometer's Sketchpad software, they were provided opportunities to experience a set of mathematics activities that used the Geometer's Sketchpad software to enhance mathematical learning. At the end of the intervention, preservice mathematics teachers had to design mathematics activities that integrated the use of the Geometer's Sketchpad. Results of this study showed that preservice mathematics teachers, who learned to use the Geometer's Sketchpad software and experienced the mathematics activities that integrated the use of the Geometer's Sketchpad software, were able to design mathematics activities that used the Geometer's Sketchpad software to enhance students' mathematical learning. Besides the activities in geometry, the preservice mathematics teachers were able to design mathematics activities in other mathematical areas such as numbers and algebra. ABSTRACT FOR 21229STEM in MathematicsAUTHOR: Thomas YeoAFFILIATION: Texas Instruments With the increasing popularity of STEM education around the world, educators are now more interested in how a STEM activity or lesson looks like. In this session, participants will hear the perspective of a Math educator implementing a STEM activity and how can STEM education help teach Math more effectively. ABSTRACT FOR 21253The Art of Using Modern Communication Technologies in Mathematics TeachingLearning Process: Facebook and TextMessagingAUTHOR: Rodulfo T. Aunzo, Jr.AFFILIATION: Faculty, USC Cebu Philippines Communication is vital tool towards progress. Nowadays, varied mode of communications have surfaced even in the educational arena. A lot ot educators have already been utilizing facebook and textmessaging in facilitating teachinglearning process. In this paper, techniques and strategies were developed and tested in Mathematics teachinglearning process. Results of the investigations will be presented in this paper. ABSTRACT FOR 21270Multiple Language Converter
AUTHOR: Joe Marlou Opella 