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  Celebrating Mathematics and Technology  

ATCM 2015, Leshan, China


Table of contents

  1. Abstracts for invited and plenary papers
  2. Abstracts for full papers
  3. Abstracts for presentations with abstract only
  4. Abstracts for poster sessions
  5. Abstracts for workshops

Abstracts for invited and plenary papers


Solve First – Ask Questions Later: discovering geometry using Symbolic Geometry and CAS
AUTHOR: Phillip Todd
Affiliation : Saltire Software

Using symbolic geometry and CAS facilitates a new kind of geometric discovery. Rather than relying on geometric insight to solve a problem, it can be expressed algebraically using the symbolic geometry system then solved in the CAS. The solution can then be examined geometrically in the symbolic geometry system and insight attained after the fact. We illustrate this approach with a number of examples from students’ work over the last decade


See Graphs. Find Equations. Myth or Reality?
AUTHOR: Wei-Chi Yang
Affiliation : Radford University

In this paper, we will discuss challenges and discoveries the author has encountered and explored while using technological tools in teaching and research since the inaugural ATCM in 1995. We know that the graphing capabilities of a computer algebra system
(CAS) and the use of graphing calculators in the generation of plots has revolutionized the teaching, learning, and research of mathematics. We shall use examples to demonstrate generated scattered plots for specific tasks when dynamic geometry system (DGS) is used. The question has become, however, if we, as educators, can inspire students to see a scattered plot, produced from a specific task, and have them readily identify the equation to the corresponding scattered plot? Finding appropriate equations can be an interesting and challenging enough task in two dimensions. It becomes even more of a challenge if we ask students to find equations for what is seen in three dimensions, real-life scenarios. If learners can visualize what is seen with the help of a technological tool, we hope students will be inspired to investigate problems further. We will also reflect on what Professor Wu, Wen-tsun (see [13]) had envisioned in his plenary speech at the first ATCM in 1995 and will explore his predictions and visions as they apply today. 


Catalan Solid and Its Generalization
AUTHOR: Jen-chung Chuan
Affiliation : National Tsing Hua University, Taiwan

A Catalan solid is a dual polyhedron to an Archimedean solid. A list of 13 Catalan solids together with their Archimedean duals can be found in Wikipedia: https://en.wikipedia.org/wiki/Catalan_solid
In this talk, we are to show the most efficient ways to construct 11 dual pairs of polyhedrons among the 13, under the environment provided by the dynamic solid geometry software Cabri 3D. We then proceed to show with animations how each of such dual pairs can be distorted to form other generalized dual-pair polyhedrons families. Here we adopt the notion that two polyhedrons A and B are said to form a generalized dual pair if they have the same number of edges and each edge of A intersects a unique edge of B orthogonally in space. A more complete description of this workshop can be found at the ATCM 2015 Electronic Proceedings: click here.


Computer-aided strategies to shorten the gap between high school and university math courses

AUTHOR: Jose A Vallejo, Antonio Morante
Affiliation : Universidad Autonoma de San Luis Potosi
One of the main problems in most universities is the gap between the knowledge acquired by students in high school and that needed to successfully pass their first university course.
Retention rates around the world show the importance of having a first-semester course dedicated to shortening this gap.
In this paper we offer some selected examples extracted from a transition course designed to help science and engineering students with a weak mathematical background. In the course, basic concepts are first presented in a straightforward way, followed by simplified versions of `real-life'' problems to be solved with the use of these concepts and the aid of a computer. In the process, the student develops both abstract manipulation and technological abilities, getting the feeling that maths are useful (and, hopefully, fun). The course material uses multiplatform free software (explicitly, the CAS Maxima and the DGS GeoGebra).


Stories of Learning Trigonometry from 7th graders-An Experiment of Educational Mathematics
AUTHOR: Jingzhong Zhang, Zengxiang Tong
Affiliation : Chengdu Institute of Computer applications; Otterbein University, USA
This paper reports an innovative three-year mathematics teaching experiment, held in a middle school in Guangzhou, Guangdong, China. Applying a research result in educational mathematics, which rebuilds the logical structure of elementary mathematics, the teacher introduced to the 7th graders the concept of the trigonometric function sinA in a new way, and used it to integrate trigonometry, geometry, and algebra. He first defined sinA as the area of a unit rhombus with an angle A, then, intuitively and rigorously, derived the fundamental properties of the function sinA, showing the equivalence of the new definition and the traditional one. Using area computation method, he guided his students to discover the law of sine and the formula of sin(A + B). Furthermore, he introduced the concept of cosine function using the sine function, and derived the law of cosine using graphic and algebraic method. These trigonometric functions played powerful role in revealing geometric properties of triangles, polygons, and circles. The three-year experiment has greatly enhanced students’ maturity in mathematics, and their ability of problem-solving by combining computation, logical reasoning, and algebraic transforming. These students have performed much better than those studying using traditional textbooks in a variety of standardized tests.


Developing Computational Thinking through Coding

The turn of the 21st Century sees renewed emphasis on STEM (Science, Technology, Engineering and Mathematics). Building a Smart Nation is now a buzzword for many developed countries. Compelled by the advancement of information and communication technology, the ability to code in a programming language is a skill that is now, more than ever, urgently called for. In addition, it is widely believed that coding enhances problem solving abilities. In this paper, by underscoring the disciplinarity of coding, we construct a curricular framework for inculcating computational thinking in authentic classroom situations. Our proposition that computational thinking can only be imparted through doing, and this is supported by episodes of a graduate course, taught by the second author, in which graduate students develop coding competencies in VBA.


Educational Technology in Functional Line of Mathematics AUTHOR: Vladimir Nodelman
Affiliation : Holon Institute of Technology, Israel
The functional line penetrates and closely interlaces with all areas of mathematics at different levels of studies, often determining their content and methods. Starting from familiarity with the concept of function in the secondary school, through precalculus studies, the functional line infiltrates all courses of mathematics: calculus, algebra, geometry, complex analysis, differential equations etc.
An adequate software, which concentrates students’ attention not only and not so much on the demonstration of examples of the concepts being studied, as activates independent creative activity in detection and use of the suitable properties of the studied material and the connections between them, can significantly increase the strength and depth of understanding of the studied matter.
This report presents an approach to development and use of such software and its implementation in the author’s non-profit program VisuMatica. Various examples illustrate the technique of dynamic creation and evolutionary development of generalized models as result of live collaborative analysis of the needs and characteristics of the studied material, its specifics from the point of view the functional line, and proper activities of the students.


Finding best possible constant for a polynomial inequality
AUTHOR: Lu Yang and Ju Zhang
Affiliation : Chengdu Institute of Computer Applications, Chengdu 610041, China; Chongqing Institute of Green and Intelligent Technology
CAS, Chongqing 400714, China

Given a multi-variant polynomial inequality with a parameter, how to find the best possible value of this parameter that satisfies the inequality? For instance, find the biggest number x that satisfies a^3+b^3+c^3+k(a^2*b+b^2*c+c^2*a)-(k+1)(a*b^2+b*c^2+c*a^2)>=0 for all positive real number a; b; c. Analogues problems often appeared in studies of inequalities and were dealt with by various methods. In this paper, a general algorithm is proposed for finding the required best possible constant. The algorithm can be easily implemented by computer algebra tools such as Maple.


New Explorations of Old Mathematics via Spreadsheets
AUTHOR: Deane Arganbright
Affiliation : Divine Word Univ., PNG (Emeritus)
Over the years, many once-common traditional topics and techniques have largely disappeared from the everyday mathematics cosmos. Surprisingly, exploring now-forgotten mathematics through the creative use of spreadsheets can provide new, challenging, and interesting teaching and learning experiences. The projects considered here provide glimpses of historical ideas, while showing the underlying mathematics of algorithms that is now often hidden within powerful computational tools. We present interactive models of such varied topics as counting systems, calculating procedures and devices, graphing techniques, and algorithms that incorporate both animated graphics and effective visual presentations using the spreadsheet display itself. Examples are drawn from such diverse undergraduate areas as geometry, calculus, linear algebra, differential equations, numerical analysis, operations research, group theory, probability, and statistics.


What Have We Done About Mathemaics Experiments With HAWGENT
AUTHOR: Chuan-Bo Zuo
Affiliation : Hawgent Technolgoy Centre in Mathematics, China

In the culture of exam-oriented education, how a mathematics laboratory can be effectively used for serving the daily mathematics teaching after its construction? The topic will introduce what we do on building mathematics laboratories with HAWGENT dynamic mathematics system for K-12 schools in China, and will continue to go into explanations emphasis on developing mathematics experimental curricula.


TED Speech of Calculus: Theory Exists in Case
Affiliation : Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China

What is TED? It is a pattern of speech, where every theory lays in 18 minutes story or case which can show and expose the theory. We can even say that theory exists in case, or theory = case, to some extent.
The process that theory deduces from the case is neither additional complexity nor needing extra proof. In fact decent reward with low cost is the way of educating and thinking.  In the talk, we will apply this methodology to the fundamental university courses, Calculus Theory.
The standard textbooks are too obscure, which is invisible and is only being, to understand and this makes us depressed. Take limitation, epsilon-delta, infinite series, real number or infinite decimal for example. So we¡¡¥d better to state it in another way to change invisibility into visualization and change existence into constructivity. In short, the theory can be stated by 0.999¡


Open source computer systems in mathematics education AUTHOR: Alasdair McAndrew
Affiliation : Victoria University, Melbourne Australia
It is axiomatic in mathematics research that all steps of an argument or proof are open to scrutiny. However, a proof based even in part on commercial software is hard to assess, because the source code - and sometimes even the algorithm used - may not be made available. There is the further problem that a reader of the proof may not be able to verify the author''s work unless the reader has access to the same software.
For this reason open-source software systems have always enjoyed some use by mathematicians, but only recently have systems of sufficient power and depth become available which can compete with - and in some cases even surpass - commercial systems.
Mathematicians and mathematics educators may gravitate to commercial systems partly because such systems are better marketed, but also in the view that they may enjoy some level of support. But this comes at the cost of initial purchase, plus annual licensing fees. The current state of tertiary funding in much of the world means that for all but the very top tier of universities, the expense of such systems is harder to justify.
For educators, a problem is making the system available to students: it is known that students get the most use from a system when they have unrestricted access to it: at home as well as at their institution. Again, the use of an open-source system makes it trivial to provide access.
This article aims to introduce several very powerful and mature systems: the computer algebra systems Sage, Maxima and Axiom; the numerical systems Octave and Scilab; and the assessment system WeBWorK. We will briefly describe these systems: their history, current status, usage, and comparison with commercial systems. We will also indicate ways in which anybody can be involved in their development. The author will describe his own experiences in using these software systems, and his students'' attitudes to them. There will be no assumption of any particular mathematics beyond undergraduate material, so as far as possible mathematical topics discussed will be those with which an educational audience may be expected to be familiar.


Technology in the Mathematics Classroom: A Perspective from India
AUTHOR: Jonaki Ghosh
Affiliation : Lady Shri Ram College, Delhi University, India

This paper highlights the role of technology in mathematics education with examples from the Indian context. Mathematics forms the foundation of education in Indian society and is a compulsory subject up to grade 10. The last few years have witnessed extensive use of computer technology in school education. However in the vast majority of Indian classrooms, mathematics is taught in the traditional “chalk and board” manner with hardly any use of technology and the student has little opportunity for visualization and exploration. The National Curriculum Framework of India (NCF, 2005) in its position paper Teaching of Mathematics recommends the use of technology in the form of computer software and calculators. It states “Technology can greatly aid the process of mathematical explorations,….If ordinary calculators can offer such possibilities, the potential of graphing calculators and computers for mathematical exploration is far higher”. The recommendations of the NCF, has been a motivating factor for conducting studies related to the use of technology in the mathematics classroom. In this paper, we shall describe two research studies conducted with students in higher secondary schools where technology in the form of graphics calculators and spreadsheets played a key role in developing their mathematical thinking. Through these studies, we will illustrate that the considered use of technology in a traditional mathematics classroom can help to create a rich and motivating environment for exploring mathematical ideas.


Teaching elementary mathematics with virtual manipulatives: an introduction of Magic Board
AUTHOR: Yuan Yuan
Affiliation : Chung Yuan Christian University, Taiwan

With the development of technology, there has been a reform in math teaching aids during the past ten years. The virtual manipulative has been created, which is a kind of assistive technology device integrating actual teaching aids and computer technology, and is suitable for elementary students in learning mathematics. Based on experience obtained in the development of virtual manipulatives, Magic Board (http://magicboard.cycu.edu.tw) has been created and became a well-known web-based virtual-manipulative environment for teaching elementary mathematics in Taiwan. Magic Board comprises three important components: Magic Board Software, Problem Posing Center, and Instructional Material Center. The Magic Board Software contains a virtual collection of physical manipulatives that elementary teachers can use to teach mathematics. Elementary school teachers can use this on-line virtual environment to pose and organize instructional materials for their students. Website members also have access to a variety of instructional materials that have been posed or organized by other Magic Board members. In this paper, Magic Board will be introduced and its features will be discussed. It is hoped that more teachers will enjoy the use of this resource to integrate technology into mathematics teaching.


Graphics calculators and the school mathematics curriculum: Perspectives and issues from three countries
AUTHOR: Barry Kissane, Wee Leng Ng, G.T. Springer
Affiliation : Murdoch University, Australia; Nanyang Technological University, Singapore; Hewlett-Packard Company, USA
Over the past two decades, graphics calculators have been prominent in many discussions of technology in mathematics education. This paper describes how they have become part of teaching, learning and assessment in school mathematics in each of three different countries: Australia, Singapore and the United States of America, as well as directions for future use. Critical issues associated with effective implementation of graphics calculators into the school mathematics curriculum are highlighted, including the nature of school mathematics, examination practices, Computer Algebra Systems, the support of teachers and students, curriculum change and development, the focus on learning, dealing with inherent limitations of graphics calculators, school and university differences, future technologies.


Creative Thinking in Mathematics with Tangrams and The Geometer’s Sketchpad
AUTHOR: Krongthong Khairiree
Affiliation : International College, Suan Sunandha Rajabhat University Bangkok,  Thailand
The purpose of this paper is to illustrate how Tangrams puzzle can be used to enhance students’ creative thinking in mathematics and to use dynamic geometry software the Geometer’s Sketchpad (GSP) to develop the pictorial representations, and geometrical shapes. In the 2015, action research was conducted in lower secondary school, Bangkok, Thailand. The research findings revealed that the teachers used GSP to construct Tangram puzzle and Egg Tangram. The students explained that they were able to use GSP to drag, rotate and translate the pieces of Tangrams to form the shapes given to them. Creative thinking and problem solving skills were developed while students solved and created tangram puzzles. The students were able to express their geometrical imagination, and their understanding of mathematics concepts by verbal interactions. The students had fun and positive attitudes towards mathematics.


Technology must be transparent and not get in the way of teaching and learning 
AUTHOR: Douglas Butler
Affiliation : iCT Training Centre (Oundle, UK)

Software and hardware solutions for mathematics teaching are evolving all the time, leaving many teachers bewildered by the ever increasing kaleidoscope of possibilities. Douglas will attempt to bring this audience up to date with some exciting lesson plans drawing on a new generation of hardware independent resources, the emphasis always being to let the mathematics shine through.


Smart Education Platform
AUTHOR: Hui Lin, Hongguang Fu, Qingxian Wang
Affiliation : Chengdu Zhunxingyunxue Technology Co. Ltd, 610000, China
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
School of Information and Software engineering, University of Electronic Science and Technology of China, Chengdu 610054, Chin
Smart Education Platform (SEP) is a system designed to serve students, parents, teachers and education administrators. It is an intelligent system powered by the idea of automatic reasoning created by Prof. Jingzhong Zhang, a computer scientist, mathematicians and mathematical educator, as well as the advanced human intelligent technologies supported by the national 863 project. The core ideas of the system including finding problem precisely, checking homework particularly and analyzing problems completely. Using a smart pen, SEP can find the problems in the learning process through children’s writing process, which can help teachers to know students and teach them in accordance with their aptitude, parents to know accuracy children’s learning.


Abstracts for the track of Full Papers


Using Force to Crack Some Geometry Chestnuts

AUTHOR: Phillip Todd
Affiliation : Saltire Software

The symbolic mechanics software “Mechanical Expressions” is capable of expressing static problems where force elements such as springs, masses and actuators interact with geometric elements such as points, lines and circles. It is able to derive symbolic expressions for resultant forces in constraints. Finding an equilibrium for the system involves finding constraint values such that the resultant forces are zero. This can be done in a CAS. In this paper we show how to apply this technique to solve some classic geometry optimization problems.


Visualization of quaternions with Clifford parallelism

AUTHORS: Yoichi Maeda
Affiliation : Tokai University, Japan

In this paper, we try to visualize multiplication of unit quaternions with dynamic geometry software Cabri 3D. The three dimensional sphere S^3is identified with the set of unit quaternions. Multiplication of unit quaternions is deeply related with Clifford parallelism, a special isometry in S^3.


Mobile Learning: impacts on mathematics education

AUTHORS: Maree Skillen
Affiliation : UTS:Insearch

New learning technologies have brought a series of additional challenges to teachers and educators. Whilst some Schools are moving towards implementing 1:1 technology initiatives and Bring Your Own Device (BYOD) programs, others are supporting classroom learning experiences through the purchase of mobile devices including iPads and tablets. Given the original game-based nature of mobile devices they have over time attracted interest from the educational community, and are used to engage learners in tasks that are quite often open-ended, and involve problem-solving. Through the use of mobile devices learning opportunities are becoming more interactive and can promote collaboration between learners in different ways. Cognitive and affective processes are enhanced through the interactive capacities of devices and applications. By using mobile devices as a tool in the Mathematics classroom, new experiences are provided for both the teacher and student. Technology is rapidly changing how we teach, and how we learn. Therefore, teachers need to be familiar and prepared to support traditional methods of teaching mathematics with the integration of appropriate and effective uses of technology, which may include mobile devices and applications (Apps).
Mobile learning and associated technologies are being seen widely as ‘becoming increasingly ubiquitous in society, particularly with youth’. A body of literature exploring mobile technologies and learning in teacher education contexts is now emerging and being described by many as being “a fairly young area of research”.
This paper has emerged from an interest in, and experience with, the use of technology in classrooms. The specific areas of focus to be addressed will centre on summarising developments and terminology; explore emerging practices for learning and teaching; consider possible challenges, limitations and implications for use of mobile learning in classrooms; and, identify possibilities for further research from gaps within the literature. Examples used will relate to the key learning area (KLA) of Mathematics.


The ONAD method for qP-wave equation solving

AUTHORS: Rong Huang, Rong Huang, Yan Yang, Guojie Song
Affiliation : Rong Huang, Rong Huang, Yan Yang, Guojie Song

The forward modeling of qP-wave equation is one of the most important question in seismic exploration, seismology, and so on. Because of its poor stability, the traditional finite difference scheme for qP-wave equation modeling suffer instability easily and numerical dispersion seriously. A novel difference scheme for qP-wave simulation, named ONAD method, is proposed in this paper. The ONAD algorithm can effectively suppress the numerical dispersion under the coarse mesh for acoustic wave and elastic wave field simulation. The numerical results show that, relative to the classical finite difference scheme, like LWC, the ONAD method for qP-wave has obvious advantages. It¡¯s suitable for qP-wave modeling.


Research and Implementation of Determining the Validity of the Mathematical Expression
AUTHORS: Ming Lee, Ju Zhang, Xinyan Li, Lian Chen, Jie Lei
Affiliation : High performance computing application R&D Center Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences Chongqing, China, High performance computing application R&D Center Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications, Chinese Academy of Sciences China, Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications
The effectiveness of mathematical expressions refers to the according of the principles of the mathematical expression and the required logic standard of the mathematical expression, which in turn can correctly. Express certain mathematical meaning. Unless there is a lack of the effectiveness of the mathematical expression in the mathematical teaching software, this will not be able to determine whether the input of the mathematical expression is consistent with the specification requirements of mathematics and mathematical logic, which seriously affects the operational efficiency of the software and users¡¯ experience. Based on the normalization of the matching parentheses, operator priority processing, elementary function identification and constant recognition steps, the effectiveness of expression can be discriminated. Experiments have drawn the conclusion that the effective discrimination of mathematical expressions can significantly improve the efficiency of the teaching software and mapping function, so that it can improve the users¡¯ experience definitely.


Extending Euclidean constructions with dynamic geometry software
AUTHORS: Alasdair McAndrew
Affiliation : Victoria University, Melbourne 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.


Computing the Bell Number by Using Grobner Bases
AUTHOR: Yongbin Li, Andrew Y.Z. Wang
Affiliation : School of Mathematical Sciences, University of Electronic Science and Technology of China, School of Mathematical Sciences, University of Electronic Science and Technology of China

In this paper, we show that the Bell number B(n) counts the total number of zeros of certain polynomial set over the finite field F2. An alternative method for computing B(n) is presented by using Grobner bases. The new method makes a theoretical contribution to discuss the partitions of an n-set in Combinatorics by using Computer Algebra without considering the complexity. Given a zero of the polynomial set, we also give an approach to determine the type of the corresponding partition by computing the characteristic polynomial. Our method is also helpful to enhance the interest of learning Computer Algebra and using computer algebra systems in teaching and studying


Teaching Probability and Statistics with a MOOC by using a Flipped Classroom Model AUTHORS: Stefan Oeyen
Affiliation : University Colleges Leuven-Limburg (Belgium)

This paper describes the steps to transform a traditional model of classroom instruction for teaching “probability and statistics” to a flipped classroom model. “Flipped classroom” is a type of blended learning which reverses the traditional educational set-up. Events which traditionally have taken place inside the classroom now take place outside the classroom and vice versa. A MOOC is used to deliver the content to the students of teacher education before class time. The in-class activity is redefined (in) to micro teaching. This is a big challenge for the students, which demands discipline and commitment. But the results are worthwhile: students are motivated because they can practice the skills they are expected to learn. Class time is dedicated to exploring topics in greater depth in a meaningful way. My role as a lecturer changed from instructor to guide in all the phases of the learning process. I used a manual to develop this new approach of active learning because it’s a real mind shift. The followed steps and the experience are subject of the paper.


Application of TI graphics calculator in the exploration of dynamic changes

Affiliation : Beijing No.80 High School

In recent years, Beijing Senior High School Entrance Examination presented a kind of comprehensive questions named "New Definition", which examine students'' ability of discovering problems, analyzing problems and solving problems with creativity. By graphing calculator we can reproduce the scene of dynamic change. We will deepen students'' thinking and understanding of the problem through students'' autonomous operation and visual feedback, and the activity experience is conducive to improve the ability to analyze problems.20921


Simulating the Spirograph Works by the Geometers Sketchpad
AUTHORS: Xuan Yao, Xinyue Zhang
Affiliation : No.22 middle school Beijing, No.22 middle school Beijing

The spirograph is one of our childhood toys in China. It can help drawing unpredictable and amazing patterns simply by the rotation of the gears. In this article we construct its mathematical model using the Geometer¡¯s Sketchpad. We analyze how the spirograph works and try to simulate the drawing process on the computer. We get some beautiful patterns by applying the idea of iteration, and on this basis, we create a Square Spirograph powered by the Geometers Sketchpad. In this process we feel the charm of mathematics and the practicability of modern techniques.


The use of TI graphics calculator on the circumcircle and inscribed quadrilateral
AUTHORS: Ruiguang Xu
Affiliation : Middle School of Chaoyang District Education Research Center, Beijing

The quadrilateral circumcircle condition is in the student learning after a point, two non collinear three points, triangle and circle and the circle inscribed quadrilateral of a quadrilateral circumcircle and whether there is inscribed circle is the class than exploration circumcircle, the geometric reasoning problems more abstract, students understand there will be a certain degree of difficulty, and graphic calculator is just for students to build a can accurately, image research platform in the inquiry process, experience from the particular to the general mathematical thinking, doing and thinking process to mathematics activity experience accumulation
The author is a teacher of the Affiliated School of Chaoyang District Education Research Center, Beijing


View the World by Equations
AUTHORS: Lai Wei, Hong Li, Yu-Ji Yang
Affiliation : No.22 middle school student, Peking University, mathematics department student
With the progress of modern science and technology, we can translate any equations we can imagine to images with the help of the power of calculate ability by computer. People in the past have been looking forward to using the equations to express the Chinese character image. However as a senior high student to be, I can express any pictures I want, whatever it’s huge like star or tiny like molecular in equations with the help of computers.  In this paper, with the use of HP graphing calculator, based on using equations to write Chinese characters, then we can spread it out to use equations building reality and inspire the innovation of creation. From the point to the surface, I will lead you into the equation world in my eyes step by step. I will show you all my works drown by equations and point out my ideas about them.


The Construction of Mathematics Inquiry Teaching Model in High School under the Technological Environment
AUTHORS: Guo Jiajia
AFFIL IA T ION : Shenyang NO.4 Middle School, China

With the rapid development of science and technology and the avocation for ability, the mathematics inquiry teaching under the technological environment has been paid more attention. This paper follows the qualitative methods and steps of constructing teaching models and constructs “Technology-Inquiry” Teaching Model. Its basic elements contain theoretical basis, teaching objectives, implementation conditions and operating sequences. This study extends the theory of technology and inquiry teaching, and plays an active role in constructing reasonable integration and inquiry system.


Investigation and Thoughts on Using Graphing Calculator to Promote Junior High Students’ Understanding of the Mathematics Essence
AUTHORS: zhihong zheng, xiang fang

This paper summarizes the effects of using graphing calculator to promote junior high students¡¯ understanding of the mathematics essence via the analysis of the questionnaire and interview data and the Exam score differences in pre and post-test and it then illustrates the students’ achievements in the application of graphic calculator in verifying£¬ exploring operative and critical mathematical experiment with specific cases. Finally, this paper puts forward some helpful thoughts on the use of graphing calculators in mathematics teaching.


The Advantages of Ti calculator’s Operating Techniques in Math Teaching
AUTHORS: Jiang ping, zhang xin
Affiliation : Northeast Yucai School Hunnan New District in Shenyang Century Road No.41, Northeast Yucai School Hunnan New District in Shenyang Century Road No.41

The paper describes the teaching effects of educational technology in math teaching and the desired technology operating mode. With the aid of TI calculator, some effective teaching cases are presented, hoping to achieve the efficient combination of educational technology and teaching demands.


The Construction of Uniform Polyhedron with the aid of GeoGebra
AUTHORS: Jiang Ping, qiu fawen
Affiliation : Northeast Yucai School Hunnan New District in Shenyang Century Road No.41

The paper deals with various constructive methods of Uniform Polyhedron with the aid of Geogebra and explores the connections among them, summarizing some feasible methods of the construction of polyhedrons. The functions and features of Geogebra are well utilized and fully realized especially with the customized function to construct star polyhedron.


Affiliation : Northeast Yucai School

With the popularity of Khan Academy, flipped classroom and online micro-video lectures are becoming effective tools and facilitators in education, changing the way of both teaching and learning. Graphing calculator is widely applied in math class as well, serving as an innovative tool for students to further their learning and exploration. What will happen if we combine online micro-video lectures and graphing calculator together in everyday learning? Last semester, I made a micro-video to explain the problem of constant in conic section by using TI-nspire graphing calculator. With the aid of graphing calculator, students dived deep into a series of problems and discussions, drawing more conclusions than expected through cooperation and exploration. Their passion and curiosity for learning are enormously aroused, leading to efficient learning and discussion in class. Therefore, the class is successfully flipped. This paper provides a typical teaching case study of how online micro-video lectures and graphing calculator can be combined to improve everyday learning mode, thus offering practical help to the schools experimenting with flipped classroom.


The Application of Information Technology in the Formation of the Concept of Functions
AUTHORS: Hong Li, Peixin Li, Hao Ding
Affiliation : No.22 high School of Beijing, Student

This paper takes a practical problem as the starting point to make students understand the meaning of variables and constants. By analyzing the particular problem, students investigated the changing process of functions, identified the relationship between two variables and approached the pattern of the changes. Students were encouraged to use graph calculators in the research. The relevant software in the graph calculators enabled students to tabulate and observe the pattern of data. It also enabled students to plot the set of data in order to identify the changing process. The combination of tables, images and formulas helped students to have a better understanding of the concept of functions. When analyzing the characters of functions, information technology provided different methods of researching according to the preferences of each student. It also motivated the passion of students and showed their intelligence, as well as the beauty of Mathematics.


Information Technology and Geometric Transformation -research on the set which be made up of geometric transformation through information technology
AUTHORS: Yubing Leng
Affiliation : No. 22 middle school, Beijing, China

Put a square as an example, research on the relationship between its various transformations. The basic question we study is: study the nature of the set that be made up of eight transformations of the square by defining a new arithmetic. After the preliminary study, we have a basic achievement of research and harvest: from the symmetry of square to preliminary understanding of the "group". In this process, technology played a big role, it made us have a more intuitive understanding to "transform" and "relationship between transformations". In addition, our preliminary research conclusion is this set meet closure, commutative law, single variable law, the associative law, etc.


The Role of Generalization in the Discovery, Proof and Visualization of a Theorem about Cubics with the Help of CAS and DGS (TI-Nspire and Cabri
AUTHORS: Jean-Jacques Dahan
Affiliation : IRES of Toulouse

Researchers know the important role of generalisation during their work because they know when it is appropriate to use it. Teachers who are not researchers, most of the time, need to convince their students that generalisation is a tool that can and must be used. But they often do not show their students examples where this process could be or is successful. Last year, while thinking about a property of cubics we had known for a long time, we wondered if it could be the particular case of a more general one. Here we give the result we got when we tried successfully to generalize the known property of polynomial of third degree defined on R by another one about polynomial of third degree defined on C replacing tangent lines to the curves of real functions by tangent planes to surfaces defined on C (considered as R2). This paper aims to show the discovery of this brand new property and its proof using particularly the CAS (computer algebra system) of TI N’Spire. It aims also to show the power of dynamic geometry in studying and visualising such a problem. I think that the final theorem presented in this paper has neither been discovered nor proved before. We also tried (unsuccessfully) to define a group on the points of a complex cubic in order to generalize the result known on a real cubic. Nevertheless, we think it is interesting to show when and why some directions of research are not successful and especially in using the power of visualisation of DGS (dynamic geometry software), here Cabri 2 Plus.


Detecting unnecessary assumptions of elementary geometry problems by CAS
AUTHORS: Yosuke Sato, Ryoya Fukasaku
Affiliation : Tokyo University of Science, Student

A geometry problem given for high school students in a place such as a competition of International Mathematical Olympiad or an entrance examination for a university often contains unnecessary assumptions. Such assumptions sometimes undermine the quality of the problem.
In this paper we introduce a method to check whether a given assumption is essentially necessary for solving the problem. It also computes necessary and sufficient assumptions for getting a solution.
Our method uses three tools of computer algebra, Grobner bases computation, quantifier elimination over complex numbers and quantifier elimination over real numbers. Anyone can use our method with a minimum basic knowledge of computer algebra using any CAS with these tools.


An efficient implementation of Boolean Grobner Bases of a power set algebra
Affiliation : Tokyo University of Science

An implementation method of Boolean Grobner bases of a powerset algebra introduced in [14] is optimized for developing a software in the computer algebra system SageMath using the PolyBoRi library. Our software achieves tremendous speed-up comparing to our previous implementation in the computer algebra system Risa/Asir. It enables us to have a first-ever real time symbolic computation Sudoku solver by Grobner bases. It also leads us to correct errors on the data of a mathematical hierarchy of Sudoku puzzles reported in [15].


Ti Calculator Reshaping Teachers and Students¡¯ Roles from the Perspective of Effective Learning
AUTHORS: Yibo Fu, Liping Wang, Xiaoyu Wang, Xiujun Zhang
Affiliation : 13478291043, 13897912411, teacher

This thesis is a study on Ti calculator reshaping teachers and students¡¯ roles from the perspective of effective learning. We discuss the evaluation criterion of teaching effect realized by educational technology and attempt to explore effective technical operation mode in mathematics teaching. Education system the development of education is of primary importance in china. Using Ti calculator fit the needs of education and social development and develop in advance appropriately. Since the calculator is used in mathematics teaching, a strong demand often indicates that the students¡¯ learning need is expanding. Thus Ti calculator deconstructs the definition of teachers and students'' roles in learning and indicates the direction of education development in the future.


A Case of Monitoring and Analysis on Inquiry Learning Process under the Technical Support
AUTHORS: Zheng Yan
Affiliation : Beijing No.80 high school

With the development of network techniques, graphing calculator is no longer simply as a learning tool used by individual students to explore mathematics, it¡¯s also a teaching management tool by teachers to monitor students¡¯ exploring and learning process. This paper takes "Linear Equation in Two Unknowns under the Rectangular Plane Coordinate System" as a teaching case that the author had been implemented, and it also illustrates the effects of graphing calculator, electronic lattice pen and other techniques used in specific teaching processes upon mathematics teaching and education, from the perspective of monitoring the students¡¯ exploring and learning process by teachers


The application of the Logo language in junior high school geometry teaching-Talking from the polygon exterior Angle and proved
Affiliation : Beijing No22 High School, Beijing,China

Coding has just been introduced into some junior high schools. Turtle graphics is a one of the popular ways for introducing programming to students. This paper reports that a series of activities have been developed to guide students to explore geometry with LOGO "turtle graphics", such as the properties of polygon. A few examples are described to show the students could better understand (and predict and reason about) the ideas such as the exterior angles of any polygon add up to 360 degrees with programming the turtle's motion ext. While the idea of computing thinking is also discussed.


Multivariate Pade approximation using Quantifier Elimination
AUTHORS: Takuya Kitamoto
Affiliation : Yamaguchi University

Pade approximation is a well-known technique and has a lot of applications in various fields of science and engineering. Given an analytic function, the technique approximates the function by a rational function in a such way that power series of the rational function agrees with the power series of the given function. When given function is univariate, the computation of Pade approximation is fairly simple. However, if given function is multivariate, the computation is rather complex.
Besides, in the multivariate case, the rational function approximation often have poles (zeros of the denominator of the rational function) near the expansion point, which make applications of the Pade approximation difficult. In this paper, we propose a multivariate Pade approximation that utilizes Quantifier Elimination to avoid poles near the expansion point. Quantifier Elimination is a new technique in Computer Algebra, and currently being investigated by many researchers. Given a mathematical formula with quantifiers, Quantifier Elimination, in short, computes a quantifier free mathematical formula that is equivalent to the original mathematical formula.
In our algorithms, we first set up free parameters in the multivariate Pade approximation, then we use the parameters and Quantifier Elimination to exclude poles near the expansion point. Some numerical examples are given to show effectiveness of our algorithms.


Area Type Judgment of Mathematical Document Using Movements of Gaze Point
AUTHORS: Ryoji Fukuda, Yuki ogino, Kenji Kawata, Takeshi Saitoh
Affiliation : Faculty of Engineering Oita University, Graduate School of Engineering, Oita University, Kyushu Institute of Technology

In this study we attempt to determine the area of a mathematical document on which a person is concentrating, using the movements of their eyes. Training data using this analysis were created using a gaze point extraction method. There are thousands of image files generated by a movie. We also developed a software tool to determine an adequate area for each image file. Our result will valid for the analysis human intention when a person reads a mathematical document.


Text-Based Communication Tool for Mathematical Documents for Visually Handicapped
AUTHORS: Ryoji Fukuda, Yuki Toyosaka
Affiliation : Faculty of Information Science, Kyushu Sangyo University, Faculty of Engineering, Oita University

In this study, we consider the expression methods of mathematical documents, for which the receiver is visually impaired, and the supplier is his/her support. The structure of an information graph is an important factor for the accessibility of the documents in this situation. We developed a software tool to express this structure for the support and also developed a tool to access this document for the visually handicapped. Moreover, we consider the information element for which we need some extra explanations.


An Example-Based Illustration of Using Graphing Calculators in Function Teaching
AUTHORS: Luan Dequan
Affiliation : Shenyang, China

As graphing calculators become widely accepted by elementary and secondary school teachers and extensively used in fundamental math education, some teachers insist that traditional teaching style has its own advantages which make it stand the test of time. However, in this information age coming along with students’ confusions, teachers are supposed to focus on advancing students’ academic skills while fostering their creativity, team-work spirits and perseverance in scientific explorations. Appropriate utilization of graphing calculators in math instruction directly serves this purpose, while improving students’ sense of symbolic-graphic combination and deepening their understanding of textbook knowledge. This process is not contradicted to the preparation of College Entrance Examination (Gaokao). “Function”, as one of the core concepts in high school math, is crucial to the development of students’ mathematical thinking. This article demonstrates the use of graphing calculators in function teaching by investigating the intersection positions of two inverse functions (using exponential and logarithmic functions as an example) and provides an inquiry-based approach to the conclusion that “there exists an intersection point of two inverse functions which is not on line y=x”.


Comparison of Chinese and Australian attitudes to CAS in education
AUTHORS: Alasdair McAndrew, Xiangzhao Li
Affiliation : Victoria University, Melbourne Australia, Department of Mathematics Shanghai Maritime University No.1550 Hai Gang Rd., Lin Gang New City Pu Dong Shanghai, P.R. China Zip 201306

Various articles in both academic journals and the popular press over the past decade have attempted to uncover the reasons for Chinese success in school mathematics. As ranked by PISA, Chinese students consistently do better than their Western counterparts. Reasons which have been proposed (in the West) include more time for mathematics in schools, greater knowledge of mathematics (as well as ability) by the teachers, greater involvement by parents in their child’s education, and an over-riding ethos that every child can succeed. It is notable that Chinese mathematics (prior to university) puts a high emphasis on technical skills in algebra and geometry (and in some provinces, calculus), and is very focused on success in examinations. The Chinese approach has its critics, but there is no doubt that whereas mathematical standards, as measured by international tests, seem to be slipping in the West, those standards remain very high in China. The Chinese approach however seems to provide little space for experimentation in mathematics, and in particular for the use of technology. Educators in the West are slowly realizing that using computer algebra systems can greatly enhance learning of, and interest in, mathematics, and that the use of such systems seems not to impair technical skills. This article is an initial investigation into the use of CAS in the context of the Chinese education system, and how attitudes differ from those in the West.


Figure Drawing using KETCindy and its Application to Mathematics Education
AUTHORS: Hideyo Makishita
Affiliation : Shibaura Institute of Technology

Figure drawing normally means generation of a figure suited for given conditions using rulers and a pair of compasses only for a finite number of times. Hereinafter, this is referred to simply as figure drawing. This paper presents a discussion of, in addition to figure drawing, the practice of drawing figures by adding mathematical contents. When mathematical material is added to figure drawing using rulers and compasses, the use of dynamic geometry (DG) software is one option, whereas KETCindy is used for this study because KETCindy is equipped with DG Cinderella as GUI and can be used for drawing figures by Script as CUI. Therefore, mathematically precise figures can be drawn with ease, producing beautiful results. This paper explains figure drawing while the quadratic curve concept is added to figure drawing. The author considers that figure drawing by Script is extremely useful for mathematics education from the viewpoints of application of mathematics to mathematics. This point will be discussed hereinafter.


Teaching Mathematics using Augmented Reality (AR)
AUTHOR: Janchai Yingprayoon
Affiliation : International College, Suan Sunandha Rajabhat University

Information technology enables us to develop innovative learning/teaching tools for mathematics education both in the classroom and out-of-school activities. This paper shows a brief potential and challenges of using Augmented Reality (AR) in mathematics education. The learners can view geometrical objects in 3-dimention having better understanding of the structures. Mobile phones or computer tablets can be used to view the 3D geometrical objects using special application software. Autodesk Maya software is used to draw geometrical objects and some AR viewing software can be used to view the objects in 3D. This paper will describe how to develop a simple AR system for the improvement of abilities of learning mathematics. Sample AR materials used for mathematics education at high school as well as


Papers with abstract only


Reduce Math Anxiety And Help Students Become Independent Learners Using “Flipped Classroom” Method
AUTHOR: Premjit Singh
Affiliation : Dept. of Mathematics, Ohio University

This presentation discusses how a “Flipped Classroom” inverts traditional teaching methods.
Course materials and lectures are sent to students through Power Points ahead of class so
that students go through the material before class and spend class time in answering
students’ questions and dealing with their difficulties. As a result, students participate in
problem solving and focus on mathematical concepts and processes to improve student
engagement and mathematical understanding. 
This method aids in reducing math anxiety and helping students become independent learners, 
aka “Math Selfies.” The technique is named “Flipped Classroom” because what used to be homework is now done in class and delivery of content through Power Points is facilitated by students at home.


Blended learning on Engineering Mathematics with powerful Web 2.0 tools
AUTHOR: Wei Ching Quek
Affiliation : Singapore Polytechnic

The purpose of this paper is to investigate the effectiveness of blended learning for adult students studying engineering mathematics in polytechnic. The author will present the various changes during the implementation of blending as technologies evolved, and look into the future trend of blending learning experience.
Although blended learning literature abounds, there are not many research papers about blended learning in the Asian and Polytechnic Mathematics context. The issue is made more complicated as the concept of blended learning is not well defined.
The model of blended learning follows the instructor led content blended with self-study e-learning. Students enrolled in Engineering Mathematics module at PACE (Professional and Adult Continuing Education Academy) have 11 lessons conducted face-to-face and 4 lessons on-line, using some powerful Web 2.0 tools.
After five years of implementation of e-learning weeks, it is timely to review the contents/presentations of e-learning. Students were surveyed to evaluate effectiveness of resources for blended learning of engineering mathematics. In additions, the tests and examination scores of four batches of PACE students are also analysed.


Submariner – A Taste of Real-World Application of Trigonometry Through the Use of Heumi


In the game known as Submariner played on 46-inches Heumi multi-touch platform, students took on the roles of navel officers to protect Singapore’s waters. Working in groups of four, each student assumed one of the following roles: commander, navigator, sailor and weapon specialist. Trigonometrical concepts such as bearings and angles of elevation were applied to destroy invading ships. The game was played after the students had completed classroom teaching on trigonometry, with the aim of letting students better appreciate the application of mathematics in the real-world. A survey (n = 87) was administered after the game. Students said that the game (i) was interesting and fun, (ii) enhanced their understanding of trigonometry, (ii) allowed them to better appreciate the application of trigonometry in real-life, and (iv) made them more interested to learn mathematics. Details of the survey findings and their implications for future studies will be shared in the presentation.


The Iteration Procedure and the Pythagoras Tree
AUTHOR: Leyi Zhang
Affiliation : NO.22 middle school, Beijing Y

As a junior school student, I have been taught the methods to verify the Pythagorean Theorem.
One of the methods is to use each side of a right triangle as the side of a cube respectively and to demonstrate that the square of the hypotenuse equals to the sum of the other two sides. Thanks to the inspiration of our teacher, we managed to draw the beautiful Pythagoras Tree. However, the similarity between each right triangle could not be guaranteed if they were drawn by hand. As a result, we considered whether it was possible to use modern technology to draw the Pythagoras Tree. We used the iteration function in Geometric Sketchpad and found that by changing the length of two legs in a right triangle, there was a particular situation where the Pythagoras Tree could be complete symmetric. In the end, we found that iteration procedure could largely reduce the repetitions in our research and by using this application, we were able to draw more colorful and beautiful patterns.


Integrating the External and Internal Beauty of Mathematics
AUTHORS: Ruijia Liu
Affiliation : NO.9 senior high school, shijingshan district, Beijing city, China

In the past few years, increasing application of hand-held technology in classrooms has triggered many teachers¡¯ thoughts about how to truly integrate technology with course contents. Through analysis, comments and reflections over a sample lesson ¡°Gymnastics of Mind, beauty of graphs in heart¡±, this article illustrates how to effectively incorporate technology into math teaching. First, prepare course contents according to students¡¯ performance, making sure that teaching goals match with students¡¯ level of comprehension. Second, in class, encourage students to use graphing calculators to explore the process of geometry construction, allowing students to absorb new knowledge into their cognitive structure by ¡°creating¡± knowledge by themselves. This process promotes students¡¯ learning, thinking methods and dedication side by side. Finally, integrate the external beauty of mathematics (graphs) with its internal beauty (reasoning). The entire lesson provides students with simple but useful, flexible and extendable mathematical thoughts. The ultimate purpose of this lesson is to help students learn thinking via learning mathematics.


Utilizing Graphing Calculators to Develop Students’ Mathematical Thinking Quality
AUTHORS: Kang Shen
Affiliation :

According to the basic concepts of ¡°Mathematics Curriculum Standard¡±, one of the fundamental principles of math education is to improve students¡¯ mathematical thinking skills. The application of graphing calculators plays an important role in enriching students¡¯ math activity experience and fostering students¡¯ mathematical thinking. By demonstrating the teaching-learning process of a sample lesson ¡°Midpoint Quadrilateral¡± and further investigating several in-class problems, this article briefly illustrates how to effectively use graphing calculators in normal middle-school math lectures and utilizing graphing calculators to develop students¡¯ mathematical thinking quality.


New Technology, New Ideas

AUTHORS: Min Jiang
Affiliation : ChangZhou No.5 High School China

The introduction of new technology is the development and enrichment of the traditional mathematics teaching methods. It is the direction we want to practice that how to integrate the new technology into our daily teaching, and play a greater role. This paper research on student''s mathematics learning, thinking and exploring, highlight the "do" practice, diversity and exploration, make students improve the ability to solve the problem, feel mathematics charm through self-exploration using HP prime graphing calculator, combined with the specific case column, namely: function application, fixed point locus, series model.


Using or not using graphing calculator is different¡ª¡ªThe depth integration of approaches and strategies of information technology and mathematics teaching
AUTHORS: Zhiyong Zhang
Affiliation : ChangZhou No.5 High School
The most of value of mathematics education can¡¯t be achieved without the deep integration of technology and Mathematics. This article explore the way of integration from three directions that is the situation creation, inquiry experiment and process reconstruction. This paper tell us Prime graphing calculator¡¯s visual function could make students understand the essence of mathematics deeply and improve thinking level, change students learning style. Through derivative calculation, composite functions, and other teaching cases, the article explain Prime graphing calculator has it uniquely value. It is becoming powerful tool of studying and solving mathematical problem because it¡¯s hand-held, has the advantages of symbolic computing and wireless environment construction. In addition, the paper explore the teaching strategy of integration between technology and teaching from students¡¯ actively exploring learning, teachers¡¯ grasping the knowledge venation and advancing design activities, mining techniques and developing curriculum resources course..


HP graphing calculator application in statistical testing "researched on the relation between vision and writing horizon"
AUTHORS: Xiaoguang Gu
Affiliation : Beijing No.9 Middle School

Using handheld technology could provide convenient for students to learn statistics and deal with too cumbersome data computing. According to the study by the typical cases of problem solving and statistical thinking, this paper reports a high school math e-mathematics laboratory activities. Students use HP Prime graphing calculator, explore the correlation between vision and writing stadia, and experience the whole process of problem solving. On the one hand, the student shows the distribution of visual acuity and the visual range of the students through frequency distribution histogram of the sample. On the other hand, the student make a scatter plot with vision and sight distance as variable, image with functions fitting function, and analyze the relationship between the stadia and vision. Eventually students and teacher sum up good writing habits could help student maintain good eyesight. The use of statistical App could make students spend more time actively for reasoning analysis higher cognitive activity, make students further understand statistical thinking.


The Programming Button of HAWGENT Dynamic Mathematics System
AUTHOR: Chuan-Bo ZUO, Chu-Biao LIN
Affiliation : Hawgent Technology Centre in Mathematics, South China Normal University

HAWGENT is another dynamic mathematics system developed in China recently. The topic will introduce some feathers of HAWGENT especially its programming button on designing and developing interactive learning materials.


AUTHOR: Chuan-Bo ZUO, Mei-Ju LI
Affiliation : Hawgent Technology Centre in Mathematics, South China Normal University

信息技术的发展日新月异,服务于数学教学的工具和 资源也层出不穷,但是教师的数学教学质量、学生的 数学学习成绩并没有明显的提升. 原因何在呢?我们从教师、教学和技术三方面分析了技术运用于数学教学现状,并进一步提出技术支持下的数学教学设计原则,然后再展示基于这种原则指导下的几个教学设计案例.


Using Information Technology Enhancing Mathematics Ability £­The Summary of the Application of CASIO fx-82ES series Calculators to Mathematics Teaching and Learning in the Stage of Compulsory Education of China
AUTHORS: Jiyan Wang

Affiliation : East China Normal University

What is mathematics£¿What should be mathematics become?
Mathematics is a lively and interesting subject which has rich culture glamour, it is never mixed object simply by many form of symbols, digits and figures.
Modern information technology, for example CASIO fx-82ES series Calculators has become the useful tool and powerful assistant for students learning mathematics concepts and solving mathematics problems.  CASIO fx-82ES series Calculators make mathematics: Succinct, not long and wordy. In the operation of numbers and expressions, the students can use the calculators to solve the complex problems rapidly.  Real, not false. In solving the real problems the students can use the calculators to establish mathematics models with real data. Interesting not uninteresting. For many mathematics problems the students can apply the inducing and reasoning methods by use of the calculators.
Simple not tedious. The students can use the calculators to make the problems of recurrence sequences simply and rapidly. CASIO fx-82ES series calculators can enhance students mathematics ability, make mathematics be significant and fun£¡


Multiple representations cases in linear algebra course bases on APOS and Three world of mathematics theory

AUTHORS: Yanyan Shan, Qin'an Huang
Affiliation : Inner Mongolia University of Technology, Shaanxi Normal University

The development of sociology of mathematical knowledge, has established the important position of new forms of mathematical knowledge in education. As the brief representation, tacit knowledge is embedded in met-before, which promote deeper development of mathematical cognition. Crystalline concepts are, frequently appeared in form of explicit knowledge, on behalf of higher development level of three world of mathematics theory. Integrating APOS theory and three world of mathematics theory in mathematics classroom, is an effective approach to keep balance of the relationship. As the behalf of abstract and formal knowledge in college courses, linear algebra is the important field to research coordinating of multiple representations, different components of teachers¡¯ professional knowledge and developing of teaching cases. In the mutual dialectical process among social, historical, natural and logical construction, keeping balance of mathematical structure and cognitive development, is an unconscious choice and endeavor direction of mathematical learning theory.


The introduction of enigmatic number e with Casio fx-cg20
AUTHORS: Hailian Zou
Affiliation : Hangzhou Foreign Languages School

The irrational number e is considered to be one of the most important numbers in mathematics. However, there are little introductions about how this number has been found in both Chinese and A-Level math curriculum, instead, this number is given directly. This article is intended to derive the number of e step by step by using the real-life example of trying to find the maximum compound interest for different options with the help of graphic calculator¡ªCasio fx-cg20. The various models in relation to exponential growth and decay will be introduced as well.


Creating Tablet based constructivist learning environments for learning mathematics in developing countries – a South African perspective
AUTHOR: Werner Olivier
Affiliation : Nelson Mandela Metropolitan University, FirstRand Chair in Maths Education
Access to quality curriculum-aligned digital material to support the delivery of mathematics syllabi in schools poses a major challenge in many developing countries. In South Africa for example, a lack of ICT infra-structure in many schools and inadequate content and technology skills amongst teachers are some of the major impediments in the way of achievement in mathematics and learner progression. The advent of Tablet technology over the past five years opened up exciting possibilities to create constructivist learning environments for mathematics that are not dependent the internet or school ICT networks. In this talk an offline techno-blended model and a supporting digital resource package for the teaching and learning of mathematics at secondary schools will be described. Visualization and multi-representation of mathematical objects, results and relations were integrated in an innovative way to create a digital T&L support package, called TouchTutor. The design of the package is device agnostic and runs off-line on Android Tablets to represent a flexible and user-friendly platform to create modern constructivist learning environments. A range of critical support functions that support and compliment the core content delivery of school curricula was built in as part of the TouchTutor Package. These include interactive self-assessment with feedback, career guidance and interactive language support. The development and implementations of such a model to incubate mathematics learners in South Africa for successful access to higher education will be discussed with reference to the impact that the techno-blended model for mathematics had on self-directed learning.


The Application and Analysis of the Function Calculator FX-991ESPLUS
Affiliation : Jianping High School

My report is intended to introduce the application of the new calculator in Function, Sequences, Complex number, Statistics, Equation and its function in such aspects as verification, exploration and assumption, which is of practical value when teachers instruct students to use the calculator in exams.


Application of Casio-CP400 in the mathematics teaching
AUTHOR: Bao Zhu, Zhiqiang Wang, Ziying Wei
Affiliation : High School Attached to Northwest Normal University

The new curriculum standards for senior high school mathematics encourage the combination of both the traditional teaching methods and the modern information technology. Casio cp400 Graphing Calculator has several features such as function plotting, statistic and program, providing an interactive studying conduction which has prompt feedback and clear photo illustrations, and thus provokes students¡¯ initiative and creativity. This passage shows the applications of the graphing calculators in our high-school mathematics and AP calculus classes through several specific examples..


Pascals Triangle - An alternate approach
AUTHOR: Christopher Longhurst
Affiliation : Hewlett Packard

In this presentation I intend to show how Pascals triangle can be investigated in a number of different ways using technology, Worksheets and some interesting thinking outside the square activities that will enhance the students understanding and use of the patterns involved in Pascals triangle. I will use a graphing calculator and calculators will be available for participants to explore the activities presented.


Lesson Design Using Technology to Engage Students in Mathematics Learning
AUTHOR: Thomas Yeo
Affiliation : Texas Instruments

How can mathematics teachers design a lesson well? In the modern world where our students are born digital-natives, lesson packages need to be engaging and fun for the students to participate actively and be engaged in learning. Using the TI-Nspire as a teaching and learning tool, we are able to create interesting yet brain-stimulating activities to achieve that goal. Concepts can be taught through activities and exploration of concepts. It can even be self-directed, at the student’s own pace. This hands-on approach encourages student participation in class and promotes critical thinking. The multi-representation and cross-apps capabilities of the TI-Nspire also facilitates students to make the connections between different concepts they have learned.


Researches on the Application of Graphing Calculator to Senior One Students on Learning Functions
AUTHOR: Xiaoshu Chen
Affiliation : Xi’An Middle School of Shaanxi Province

As the writer finds in her teaching experiences for a Chinese senior one student, one major challenge in learning math is regarding functions. Many students have great difficulty in understanding the definition of function, the basic elementary functions and the application of function. Graphing calculator, a portable and affordable technology, is a good helper in solving the problem. Therefore, the writer tries to carry out the teaching practice based on CASIO fx-CG20 so that she can improve the students¡¯ ways to learn and apply function and make the students manage to learn function well.
Methods: The study involves 68 senior one students in Xi¡¯an Middle School of Shaanxi Province. Firstly the writer teaches them the basic concept of function and several elementary functions. Then the writer divides the students into 23groups. Each group has two or three students. Those groups work together and study 12 research subjects in four months, during which the writer conducts the teaching procedures with the aid of graphing calculator and makes adjustments when necessary. In this way, the writer can evaluate the effects of learning function with the help of graphing calculator. In this report, the writer will mainly share her three study cases: 1) Comparison among power, exponential, logarithmic function¡¯s growth; 2) heart-shaped line; 3) Learning about ¡°folding paper¡± activities.
Conclusion: The Practice and literature research show that graphing calculators assist high school students in learning function, which can effectively promote active learning, and play a positive vole in students¡¯ study. This method can produce a human-computer interaction with pictures and letters, quickly present the knowledge from various perspectives and enhance students'' understanding of learning function. This method allows students to do some difficult experiments on their own so that their application awareness can be improved. All in all, this method can effectively stimulate students¡¯ interest in learning. Such an interactive way for the teaching process is meaningful, highlighting the important role of students in teaching and Studies, as well as building innovation and collaboration awareness of students.


Can I get better marks using a Graphing Calculator?
AUTHOR: Christopher Longhurst
Affiliation : Hewlett Packard

Graphing calculators are a very handy tool in answering exam questions. They are also a very god tool to investigate and understand concepts in maths.
In this presentation, I will take some questions form Australian exams for year 12 including the VCE and WACE exams and show how using this technology can help the students answer the questions and maximize marks.


Integrating Casio-CP400 in teaching high school math curriculum -The practical role of technology from teaching and learning perspectives
AUTHOR: Zhisong Lian, Jeffrey Wong
Affiliation : Maple Leaf International School-Dalian, Maple Leaf International School- Dalian

Technology has played vital roles in Mathematical teaching and learning since the last century. This article is intended to give a brief introduction from a teaching and learning perspective on how the Casio-CP400 can be integrated into daily lessons in high school math classes such as Geometry, Algebra, and Calculus.


Harnessing the Power of Graphing Calculator in Teaching and Learning High School Mathematics
AUTHOR: Helma Mesa, Lovely Mei Pescador
Affiliation : Saint Pedro Poveda College, HP Calculators, Saint Pedro Poveda College, Calculators
Saint Pedro Poveda College in the Philippines has answered the global call for more advanced and interactive technology integration in teaching Mathematics in the Secondary level, partnering with HP Calculators, through the use of the power of the HP technology. The paper will describe the teaching practices and strategies of Poveda High School Math Area to reinforce and enhance teaching practices by exploring how Math concepts may be learned by high school students, including Math topics in the STEM (Science, Technology, Engineering, and Mathematics) track of the K-12 Senior High Program and in the Advanced Placement programs for Calculus AB and Statistics, through investigative/exploratory approach with the aid of the features/functions and the power of graphing calculators. Examples of modules/worksheets and exploratory activities with this technology will be presented to show how the teaching-learning process is enhanced and to give the possible users the opportunity to harness the graphing calculator technology and bring classroom to life in Mathematics.


The Impact of Using Cabri 3D on Achievement and Skills in Initial Geometry
AUTHOR: Rika Yanti
Affiliation : Singaperbangsa University of Karawang (UNSIKA), Indonesian mathematics society (IndoMs)

This paper describes classroom experiment on use any software to optimalize the spatial ability from 180 students in this college. One-shot case study was selected in this research in order to know and analyze the role of using Cabri 3D in college students on subject matter “Kapita Selekta Geometri”. Intelligent quotient test is one of the instrument was used in this case, but on the other hand we use performance test which gifted as a project, and in the end of the lectures they should face a posttest about their skills in initial geometry. The result show that there is a correlation between performances and conceptual understandings. Besides that, this research showing the positive impact of using Cabri 3D especially in domain of point, line, shape distance or angle in geometry 3 dimension to spatial ability. Yet, from IQ test there was something special about the spatial ability, the results show that 38% our students’ colleges have score below the value of mean. But their performance showing some raising, although for one or more case need special treatment and peer teaching or something like learning tutorial. The need of some books or tutorial program which were used at home also important to help them solve any projects. Another thing is the limited access to the internet in our laboratories caused by the bad internet connection in this city only available for forty students, and there is only one server in our room. Generally the value of mean which show an achievement in spatial ability is more than fifty percent.


Effects of Flipped Instruction on the Performance and Attitude of DMMMSU-MLUC High School Students in Mathematics IV
AUTHOR: Remalyn Casem
Affiliation : Don Mariano Marcos Memorial State University, Mathematics Teachers Association in the Philippines

This study aimed to determine the effects of flipped instruction on the performance and attitude of high school students in Mathematics IV of DMMMSU-MLUC, SY 2014-2015. The study made use of the true experimental design, specifically the pretest-posttest control group design. Descriptive-correlational research methods were also utilized to determine the level of performance and attitudes of the participants toward mathematics, as well as the extent of relationship between the two variables. There were two instruments used to gather data, the 25-item pretest-posttest which was subjected to validity and reliability tests and the Modified Fennema-Sherman Attitudes Scale which had four subscales, namely, confidence in learning mathematics, attitude toward success in mathematics, mathematics anxiety and perception of teacher’s attitudes which were twelve items each. The study revealed that flipped instruction improved the Mathematics performance of the participants but had no significant effect on their attitude toward the subject.


The Impact of Using MMPL Models with Contextual Approach on Grade 8 Students’ Skills in Spatial Ability
AUTHOR: Hanifah Nurus Sopiany
Affiliation : Singaperbangsa University of Karawang (UNSIKA), Indonesian mathematics society (IndoMs)

This research aims to figure out the effect of the contextual MMP learning model towards the students’ competence in spatial mathematics. This quasi-experimental research featuring non-equivalent control group involved sixty four students of grade eleven at one of the secondary junior schools in Karawang. The research instrument used was tests including a pre-test and a post-test, which were then analyzed using a statistical tool of t-test. In addition, it also employed observational sheets of contextual MMP learning. The analysis resulted in several points as follows: 1) in general, implementing the contextual MMP learning model improved the students’ competence in spatial mathematics; 2) the improvement of the students’ competence in spatial mathematics of which learning implemented the contextual MMP learning model was significantly better than that of which learning implemented contextual learning model; 3) there was a different improvement in terms of the students’ competence in spatial mathematics between those who were taught using contextual MMP learning model and those who were taught using merely contextual learning viewed from the lower-average category of students’ mathematical competence on the outset. However, there was no different improvement found in both middle- and upper-average students’ category; 4) the improvement of the students’ competence in the lower-average category taught using the contextual MMP learning and contextual learning was better than that in the middle- and upper-average; 5) there was no interaction identified between learning and mathematical knowledge on the outset regarding the improvement of spatial mathematics; 6) there was a significant difference of the students’ mathematical self-esteem between the students who were taught using the contextual MMP learning model and those who were taught using merely contextual learning model; 7) there was a significant correlation, as indicated in high-and-positive category of co-relational coefficient value, between mathematical self-esteem and spatial mathematics competence after being treated using the contextual MMP learning model..


AUTHOR: Restituto Rodelas, Eleonora Claricia
Affiliation : Jose Rizal University

The effectiveness of remediation plus extensive students and teachers utilization of numeracy tool (R+ESTUNT) in improving the performance of students in College Algebra was investigated. Two Algebra classes of Jose Rizal University (JRU) in the first semester of AY 2015 – 2016 were the subjects with 40 students in the experimental class and 48 students in the control class.
Pre-test and post-test on one-variable linear equation and its application were administered prior to and after conducting remediation. With the use of ten numeracy tools, the experimental group was given remediation on the sub-topics discussed after every class. The students had to answer each numeracy tool repeatedly until the level of numeracy attained is ‘approaching proficiency.’ Remediation involved working on parallel problems, group discussion, and peer tutoring.
Using right-tailed t-test for dependent samples, significant difference was found between the post-test and pre-test scores of both groups. A right-tailed independent samples t-test of the means of score differences indicated a significant difference between the experimental and control groups. This provides sufficient evidence that the mean score difference of the experimental group is greater than that of the control group. Thus, the use of R+ESTUNT is effective in improving the mathematics achievement of Algebra students..


AUTHOR: Hanifah Nurus Sopiany
Affiliation : Singaperbangsa University of Karawang (UNSIKA), Indonesian mathematics society (IndoMs)

The study was motivated by the findings in the field that there are mathematical operation type ordinal scale, in addition to the error in processing the data on ordinal scale. The first case is about the observation sheet that uses ordinal scale, in its concluding observations using the average assessment of the scale. To describe it should use the minimum, maximum, median, frequency tables, percentages, or graphs. The second case is about data processing from scoring rubric, should Spearman correlation rank test to test its validity, instead of using the Pearson product moment test.


AUTHOR: Ramlah Hasanah, Rika Yanti
Affiliation : Singaperbangsa University of Karawang (UNSIKA), Indonesian mathematics society (IndoMs)

This research aims to find out improving students’ mathematics logic thinking skill through Means-Ends Analysis (MEA) method and students’ mathematics logic thinking skill through conventional method. It is parallel with the problem; it is still low of students’ mathematics logic thinking skill through Means-Ends Analysis (MEA) method of Senior High School.
This quasi-experimental research takes the population all of students at tenth grade of State Senior High School in Kutawaluya – Karawang. There are two classes of tenth grade as the sample of the research; the first class is experiment class using Means-Ends Analysis (MEA) method and the second class is control class using conventional method. Each classes consist of 40 students. Both of classes is given pre-test and post-test about skill of mathematic logic thinking with the same question.
Data analysis quantitative research uses SPSS 21 for windows. The result of the research showed that the improvement students’ mathematics logic thinking skill through Means-Ends Analysis (MEA) method is better than the result of students’ mathematics logic thinking skill through conventional method.


Creative Mathematics Activities in the Classroom
AUTHOR: Janchai Yingprayoon
Affiliation : International College, Suan Sunandha Rajabhat University

Children are curious and they love to have fun with exciting things around them. Appropriate activities can be found to stimulate them to have fun and love to learn Mathematics. The ways to develop creativity in Mathematics and Technology Education are introduced to increase intellectual curiosity, to develop problem solving and thinking skills, to promote discovery as well as to unleash creativity. This workshop will show how to make Mathematics lessons more meaningful, effective and interesting, how to cultivate intrinsic motivation for learning Mathematics, and how to develop thinking abilities, problem-solving skills and creativity. Creative hands-on activities will also be demonstrated as follow:
- Projectile motion
- Digital Sundial
- Magic Dice
- Fun with measurements
- Mathematics from Bamboo
- Mathematics of Robot arms
Every participant will receive a fun and creative activity pack.


On the Application of Calculator in Solving Limits Involving Indeterminate Forms
AUTHOR: Maria Ailynn Diansuy
Affiliation : Pamantasan ng Lungsod ng Maynila, Mathematics Teachers Association of the Philippines-Tertiary Level

The paper discusses on the application of technology, particularly CASIO calculator (model 991ESPlus), to solutions of Limits involving indeterminate forms. The paper begins with a discussion of the theoretical aspect of solution in solving limits involving indeterminate forms, the L’Hospital’s Rule. It then delineates to the application of calculator based solutions in solving indeterminate forms. Based on students’ outputs, it then concludes with a discussion on the implications of the calculator based solutions to the teaching and learning of limits involving indeterminate forms.


Two different "environment" of the junior high school function Inspiration from the students using handheld technology to explore the two function
Affiliation : Chaoyang Branch of Beijing Institute of Education Affiliated School

This paper mainly talks about the study of the two functions of the image properties of y=ax^2 in two different environments. Through comparative study, I found that using computer aided study in the experimental class, students' interest in learning more high, to solve the problem, students according to the individual chose different ways, such as excellent students will directly use properties to solve the problem, students with learning difficulties is the calculator ocular auxiliary function; in the experimental class is more prominent in the key content of this lesson, that is, using the quadratic function image to explore the nature of quadratic function. While in the contrast class, because of the complexity of the process of painting images, the students' learning difficulties are obviously negative, and the emphasis of classroom teaching is not outstanding. Through the comparative study, I think using the computer aided teaching, did reach mentioned in the curriculum of the modern information technology as a student learning mathematics and solve the problem of powerful tools dedicated to change students' learning style, make students happ


Hands-on workshops


Introduction to ANOVA with CASIO fx9860
AUTHOR: Wei Ching Quek
Affiliation : Singapore Polytechnic

For comparing the means of two independent groups, we often employ hypothesis testing to investigate if there is a significant difference between the means. However, if there are more than two groups, Analysis of Variance is the statistical test for comparing the means. This practical workshop focuses around ANOVA with CASIO fx9860 and includes:
This workshop is consists of three activities:
1. Getting Started
Getting started with the CASIO fx9860a a popular graphing calculator with a comprehensive statistics functions. The workshop will explore essential features of the CASIO fx9860 in order to get the workshop started. No previous experience with CASIO fx9860 is required.
2. Quick review on Theories of Hypothesis Testing and ANOVA
A quick review of basics of one way and two way ANOVA as well as how to interpret the output.
3. Demonstration and Practice
Demonstrate how to implement one way and two way ANOVA with CASIO fx 9860. Examples are drawn from application in business and engineering. Participants will explore the problem numerically and graphically to gain further insights to the problem.


From Inductive Reasoning to Mathematical Induction with Geometry Expressions
AUTHOR: Phillip Todd
Affiliation : Saltire Software

Dynamic Geometry systems facilitate inductive reasoning, as the student makes conjectures from the interactive diagram. Such conjectures are either left unproved or proved by conventional means. Symbolic Geometry systems such as Geometry Expressions allow the student both to make more elaborate conjectures and to prove them.
In this beginner level workshop we will learn how to use constraints in Geometry Expressions to specify a model symbolically and how to extract algebra to make and prove a conjecture about Pappus Chains.


Making Math Apps with Geometry Expressions
AUTHORS: Phillip Todd
AFFI L IA T ION S : Saltire Software

In this beginner level workshop, you will learn how to create a stand-alone browser app from a Geometry Expressions model. The app you generate will use JavaScript and html5, but you won’t need to do anything other than press a button in Geometry Expressions. We will touch on ways to publish your app: on the Web, embedded in an iBook, or turned into a mobile app and sold on an app store


Steiner Porism and Its 3D Generalizations
AUTHORS: Jen-chung Chuan
Affiliation : Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to the first, the circles are said to form a Steiner chain.
Steiner Porism states that if a Steiner chain is formed from one starting circle, then a Steiner chain is formed from any other starting circle.
In this Tutorial, the participants are guided to construct an animation displaying two fixed circles in space, not having the same axis, while a Steiner chain move "between" the two.
We then proceed to show that such a Steiner system can be inverted through a sphere so that the inverted system enjoys the property that any two disjoint circles before the inversion can be assigned stationary.


Construction of Dual Patterns of Circles on a Sphere
AUTHOR: Jen-chung Chuan
Affiliation : Department of Mathematics, National Tsing Hua University,
Hsinchu, Taiwan 300

Throughout this tutorial we perform the construction on a sphere in space provided by Cabri 3D. We shall focus on patterns formed by circles only with the property that each meets any other members of the same family at most one point. Two such families A and B are said to form dual patters if each member A meets member of B orthogonally at their points of intersection.
A straightforward construction of the dual patterns is to construct the incircles of the Archimedian solid and its dual, known as the Catalan solid. Each particular pair of dual patterns is to be used to further generate many others by means of inversion with respect to an arbitrary sphere in space.


Code for Fun with Scratch

AUTHORS: Lee Choo Mooi
Affiliation : Ministry of Education, Singapore

This hands-on coding workshop introduces the Scratch software (http://scratch.mit.edu) and how it can be used to enhance learning and application of mathematics in problem solving. Participants are required to bring their own laptops installed with the software (ver 1.4) downloadable from the website. Workshop materials will be provided


Enhancing the Teaching and Learning of Mathematics Through Handheld Technology
AUTHORS: Wee Leng Ng
Affiliation : National Institute of Education, Nanyang Technological University

Handheld graphing technology, if used appropriately in the mathematics classroom, has the potential to enhance the teaching and learning of mathematics by empowering students to learn across different visual representations of mathematical concepts. With the aid of such technology, teachers have the means to help students develop a deeper understanding of abstract mathematical concepts and sharpen their critical thinking skills.  In this workshop, participants will explore the use of the TI-Nspire CAS CX handheld in helping students develop relational understanding of concepts in calculus and statistics at upper secondary and pre-university levels.


Mathematical Problem Solving with a Graphing Calculator
AUTHOR: Wee Leng Ng
Affiliation : National Institute of Education, Nanyang Technological University
Enabling students to acquire and apply the necessary mathematical concepts and skills to solve problems in a wide range of situations is one of the primary aims of mathematics education. On the other hand, empowering students to make effective use of a variety of mathematical tools, including technological tools, in the learning and application of mathematics is identified as an important objective of many school mathematics curricula. Problem solving activities involving the use of technological tools have the potential to contribute to meeting the two aforementioned goals of mathematics education.
In this workshop, participants will engage in activities which explore effective uses of the TI-84 Plus graphing calculator, at different stages of the problem-solving process, in solving a collection of mathematical problems suitable for upper secondary students.


Pre­calculus (and beyond) with wxMaxima and GeoGebra
AUTHOR: Antonio Morante, Jose Antonio Vallejo
Affiliation : Universidad Autonoma de San Luis Potosi

This is a hands­-on workshop companion of the invited talk by Dr. José Antonio Vallejo. It is oriented to beginner users of free multi­platform computer algebra system wxMaxima and dynamical geometry software GeoGebra. In the first session we introduce the software basics. Then we drive some selected computer lab practices inspired in simplified real life problems related to subjects such as RSA cryptosystem, Information Theory, reflection properties of Cassegrain antennas and Reed­Solomon correcting code method.


KETCindy -- linkage between dynamic geometry and TeX graphics
AUTHOR: Masataka Kaneko, Hideyo Makishita, Satoshi Yamashita, Kiyoshi Kitahara, Setsuo Takato
Affiliation : Toho University, Kiasarazu National College of Technology, Kogakuin University
TEX has become most major tool to edit teaching materials in collegiate mathematics education because it provides high quality output of mathematical expressions and automates most aspects of publishing features. However, it is not so easy for teachers to generate high quality “graphics” in final output of TEX. We have developed KETpic which is a macro package of Computer Algebra System (CAS) to convert the graphical output of CAS into TEX readable code (http://ketpic.com). Though it has turned out that using precise graphics generated with KETpic is extremely effective for students to connect their intuitive observation and deductive reasoning [1, 2], its linkage to the interactive presentation of graphics has not been sufficient. Therefore, we recently developed KETCindy.
It is a plugin of Cinderella, one of the most popular Dynamic Geometry Software (DGS), to generate graphical data for interactive presentation on Cinderella screen and export the corresponding KETpic code simultaneously. A more complete description of this workshop can be found at the ATCM 2015 Electronic Proceedings, click here.


AUTHORS: Chuan-Bo Zuo
Affiliation : Hawgent Company, China



Enhancing Understanding of Parameters Using Technology
AUTHOR: Yew Fook Chan
Affiliation : School of the Arts Singapore
Parameters is an important concept often not emphasized by educators in the classroom. However, it is crucial for deeper understanding of functions and graphs. In this session, we will discuss how we can use technology to facilitate the learning of functions and graphs and parameters using handheld technology. Lesson examples will be shared.


Million Dollar Golf Hole
AUTHORS: Ian Sheppard
Affiliation : Wesley College, Shriro, Hewlett Packard

In this session participants will workshop a Year 12 investigation in which technology plays a significant role. The mathematics is primarily based on an iterative numerical method for solving differential equations. The task is scaffolded with an activity written for the HP Prime which participants will begin before working on the investigation. Through this process, the presenter will model his classroom practice and discuss aspects that support students to engage in creative and complex problem solving.


The Art of Parabolic Functions
AUTHORS: Ian Sheppard
Affiliation : Wesley College, Shriro, Hewlett Packard

Our approach at Wesley College to teaching this Year 10 (15-16 year old students) unit involves backward planning, using technology to focus on broader concepts and culminates in a project where students use symbolic representation of functions and Relations to create their own art work or drawing. In this session, the planning process will be described, participants will have the opportunity to use relevant technology such as a graphic calculator or (Desmos on an internet connected device) to trial some of the learning activities from this unit and see some examples of student work. HP Prime devices will be available for participants to use while trialing activities.


Cabri 3D to check if enlightened black objects are seen as black objects
AUTHORS: Jean-Jacques Dahan, Jean-Marie Laborde
AFFIL IA T IONS: IRES of Toulouse, Cabrilog Grenoble France

In this workshop, we will represent 3D animated black objects with the tools of Cabri 3D and observe that what we can see is not black at all : we obtain a range of grey colours between white and black. In doing so, we will understand the principle of « Outrenoir » (« Black but not black ») created by the famous French painter Pierre Soulages and related to the vibratory nature of light. We will go further in modelling this principle with other colours. The secondary aim of this workshop is to show the possibility of an artistic and motivating approach of 3D geometry with Cabri 3D.


Dandelin’s theorem: dynamic visualization with Cabri 3D
AUTHORS: Jean-Jacques Dahan, Jean-Marie Laborde
AFFIL IA T IONS: IRES of Toulouse, Cabrilog Grenoble France

In this workshop we will construct maximal spheres inscribed in the space limited by a cone and a plane. They are called after the name of the Belgian mathematician Dandelin who introduced them in 1822. Actually in the case of the plane cutting the cone along an ellipse, Dandelin''s theorem states that the contact points of the 2 maximal sphere are the foci of this ellipse. Using the figure constructed with Cabri 3D we will search for a proof of that theorem without any assumption on the nature of the intersection of the cone by the plane. So we will demonstrate that the famous Dandelin’s theorem holds also in the case of hyperbolas and parabolas


Creating Authentic Mathematical Modelling Activities Using Technology
AUTHORS: Thomas Yeo
AFFIL IA T IONS: Texas Instruments

In this workshop, participants will learn how to use handheld technology to create meaningful and authentic lesson activities using real world problems. These activities will be used to teach mathematical modelling in the classroom and allow students to learn and apply concepts. The ideas and design process behind this approach will be shared as well.


Unveiling Classwiz FX-991EX : Maximizing its Application in Mathematics Classes
AUTHORS: Maria Ailynn Diansuy
AFFIL IA T IONS: Pamantasan ng Lungsod ng Maynila, Mathematics Teachers Association of the Philippines-Tertiary Level

This workshop presents features of Classwiz FX-991EX and its application to solving mathematics problems. However, it unveils the features through calculator techniques which facilitates problem solving process easier. It focuses on problems involving algebra, geometry, calculus and statistics. This workshop showcases the powerful functions of Classwiz FX-991EX in mathematics education.


AP Calculus Problems with HP Prime
AUTHORS: GT Springer
AFFIL IA T IONS: Hewlett-Packard

In this hands-on workshop, participants will explore a number of problems in AP Calculus using the HP Prime graphing calculator. First, we will look at a problem involving implicit differentiation using the CAS and the Advanced Graphing app. Then we will examine the concept of a slope function using the Geometry app. As time permits, we will look at 1 or 2 other problems. A more complete description of this workshop can be found at the ATCM 2015 Electronic Proceedings: http://atcm.mathandtech.org/EP2015/20986/20986.pdf.


Origami as a low-tech empowered by high-tech hand-held Calculator
AUTHORS: Chang Wenwu
AFFIL IA T IONS: Shanghai Putuo Modern Educational Technology Center, Master teacher of Intel TTF & TEO Program

This 60 minutes workshop will focus on one or two hand-on origami activities which allow the audiences have a wonderful experience of mathematics learning by doing. The involved origami activities, one is western Fifteen puzzle another is Chinese Hua Rong Dao game, requiters no previous knowledge or skill on this way. A calculator program will also introduced to ensure the randomized setting is solvable.


Cyclic and Bicentric Quadrilaterals
AUTHORS: GT Springer
AFFIL IA T IONS: Hewlett Packard

In this hands-on workshop, participants will use the HP Prime graphing calculator and its dynamic geometry app to explore some of the many properties of cyclic and bicentric quadrilaterals. The workshop will start with a brief introduction to the HP Prime and an overview of its features to get novice participants oriented. Participants will then use ready-to-hand constructions of cyclic and bicentric quadrilaterals to explore. A more complete description of this workshop can be found at the ATCM 2015 Electronic Proceedings: http://atcm.mathandtech.org/EP2015/21004/21004.pdf.


Formal Proof of Validity Automated Theorem Proving System Using Rules of Inference and Rules of Replacement

AUTHOR: Lea Marissa Domingo, Mon Cristopher Micosa, Arjay Rasco, Joe Marlou Opella
Affiliation : Cavite State University Carmona Campus, Cavite State University Carmona Campus, Philippines

Automated Theorem Proving (ATP) systems are powerful computer programs capable of solving immensely difficult problems. ATP systems have been successfully used in logic, mathematics, computer science, engineering, and social science. It is a technology very suited to situations where a clear thinking domain expert can interact with a powerful tool, to solve interesting and deep problems.
An ATP system has expansive use in logic and one of the areas is propositional logic specifically creating formal proof of validity. The formal proof of validity is a propositional logic tool that allows arguments to be proven valid.
This study was conducted to develop an automated theorem proving system using Formal Proof of Validity anchored on the Rules of Inference and Rules of Replacement. This computer program shows that a statement (the conjecture) is a logical consequence of a set of statements (the axioms/hypotheses). Unlike first-order and higher-order logic that engage mostly compound arguments and mathematical theorems, the propositional logic engages on entailment of sentences, such that, the validity of an argument is based on the validity of the sentences in the argument.
The validity of proof constructed by the system is determined by the steps in creating the proof, such that the steps are composed of sentences that are the result of the application of the rules of inference and rules of replacement. The system has two main features: an interactive way of proving argument (construct proof) and an automated proof of argument (auto proof). Moreover, the system has the following sub-features: an automated translator of written argument into symbols (symbolic proof) and a comparison of construct proof and auto proof.
The system was developed using Python 3.4 as its programming language and the Modified Waterfall Model as the software development model. It received a very satisfactory rating when evaluated using a questionnaire adopted from the International Organization for Standardization (ISO) 9126.


On Subordination of Harmonic Univalent Functions associated with Wright''s generalized hypergeometric functions

Affiliation :  Birla Institute of Technology and Science, Pilani, INDIA

In Recent years one of the fields that the evolving and improving technology serves is Education and Tuition. The developments in computer and communication field caused changes in education understanding and brought along the new techniques and methods that are used in today’s education. The objective of this study is to develop a Web Based Application That Improves Permanency and Facilitates Learning in Mathematics Education.


Autograph Workshop for teachers
AUTHORS: Douglas Butler
AFFILIATION: iCT Training Centre (Oundle, UK), Autograph-Maths

In this workshop a number of lesson plans will be presented that have been shown to improve student understand and engagement. Topics will cover pure mathematics (in 2D and 3D) and key concepts in Probability and Statistics. Statistics is often regarded as a tricky subject to teach, but this session will harness the power of visualisations to make light work of large data sets, and clarify some of the basic principles that can so easily elude students. Delegates are invited to bring their laptops and Autograph will be installed

Poster sessions


Obstacles and Solutions for Using Computer in Saudi Mathematics Education

AUTHORS: Zafer Alshehri
Affiliation : King Khalid University
Computer technology has become the life line of the present generations and an important part of most educational organizations and institutions. This type of technology has had the potential to be influential in improving the quality of teaching and learning mathematics. Thus, the current study aimed at investigating the obstacles and solutions for using computer in Saudi mathematics education. For attaining that, the researcher used the descriptive method-questionnaire of a random sample consisted of 152 mathematics teachers at the southern region of Kingdom of Saudi Arabia. The study experiment took place during the academic year 2014/2015. The results of the study showed that there is a lack of using computer applications among mathematics teachers and they showed different sources of obstacles in using computer. In light of the results, the study presented some solutions for overcoming obstacles facing the use of computer applications in mathematics education. In addition, some recommendations and suggestions for further research were discussed.


An Online journey using Moodle for assessment of large groups: Mathematics Students Experiences

AUTHORS: Pragashni Padayachee
Affiliation : Nelson Mandela Metropolitan University

Higher education is experiencing rapid growth in South Africa and student numbers have grown considerably in many undergraduate courses. Teaching and learning in large groups seems to have become the norm at many higher education institutions. Teaching, learning and assessments of these large groups remain challenges facing many educators. To enhance student learning consideration should be given to effective teaching and learning and efficient assessment and effective feedback of these assessments. In response, many educators are considering online teaching, learning and assessment within a blended learning environment.
This three year action research study describes the experiences of three cohorts of students taking the mathematics for accounting course at the Nelson Mandela Metropolitan University in the Eastern Cape of South Africa. This course was redesigned for delivery in a blended learning environment and in addition to face to face learning incorporated Moodle technology. In particular online assessment was developed to be used as learning. Through this practice, it is hoped that, to some degree the question of students’ learning with regard to mathematics could be successfully addressed.
Preliminary analysis of the data revealed that students maintained that Moodle provided a supportive learning environment in which to learn mathematics. Students indicated that assessments were more effective and efficient, providing immediate feedback and that this approach to assessment impacted favourably on their mathematics learning.
Knowledge gained from this study may contribute to an improvement of the course delivery of the MACC101 course by presenting its pitfalls and successes.


A Geometrical Approach for Some Properties of Geodesics on Some Flat Surface of Revolution

AUTHOR: Pakkinee Chitsakul
Affiliation : King MongKut's Institute of Technology Ladkrabang

In any geometry setting, it is interesting to study the distance between points, the most important curves are geodesics. In this work, we present some properties of geodesics extension via some flat surfaces of revolution such as a flat cylinder and a flat cone.


AUTHOR: Rika Yanti
Affiliation : Singaperbangsa University of Karawang (UNSIKA), Indonesian mathematics society (IndoMs)

This research is motivated by the achievements of students in math in Indonesia are generally low. This is apparent from the information for International Students Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS), that Indonesia follow TIMSS in 1999, 2003 and 2007, 2011 and PISA 2000, 2003, 2006, and 2009 with results do not show much change at any participation. In the PISA 2009 Indonesia only ranks 61 out of 65 participants. Meanwhile, Indonesian student achievement in TIMSS continues to decline. In the TIMSS (2011) Indonesian students was ranked 38 out of 42 with a score of 386 on the average score of 500 and a standard deviation of 100. One reason for this is that students seized with anxiety when faced with a test or a race.
Based on the facts and attributed to ideal conditions that may be achieved by students in the learning which has been described previously, it takes the efforts of teachers and observers teaching and learning of mathematics to design learning that can improve the ability of mathematical representation. Because mathematical representation is an ability that positively impacts student achievement (Yudhanegara and Lestari, 2014). One that includes cooperative learning in it is an open problem-based learning, because learning is applying mathematical representation skills.
The approach used in this study is quantitative and the method used is experiment using a quasi-experimental research design in the form of nonequivalent posttest only control group design. The experimental class, given open problem-based learning, while the control group was given direct instruction. The population in this study, all eighth grade students of MTs Nihayatul Amal Purwasari Indonesia. Instruments used in the form of mathematical representation tests, for non-test questionnaire student anxiety. Based on the analysis and discussion of research, obtained the conclusion that: (1) the level of anxiety of students were given a open problem-based learning lower than students gain direct instruction, (2) the ability of the mathematical representation of students were given a open problem-based learning higher than the capability mathematical representation of students who are given direct instruction, (3) there is a strong negative correlation between student anxiety with ability of representation given open problem-based learning.


Numerical Solution for the Kaup-Kupershmidt Equation by Spectral Collocation Method
AUTHORS: Abdur Rashid
Affiliation : Gomal University, USM, Penang

In this article we solve the Kaup-Kupershmidt equation (K-KE) by using spectral collocation method. We use the finite difference method along time direction and spectral collocation method in space direction. The stability and convergence of the spectral method are proved by energy estimation method. Numerical results of the proposed method are presented.


A Web-based Application in Teaching Mathematics to Secondary School Students

AUTHOR: Bulent Yaytanli, bulent gaytanli
Affiliation :  Anadolu University,Turkey

In Recent years one of the fields that the evolving and improving technology serves is Education and Tuition. The developments in computer and communication field caused changes in education understanding and brought along the new techniques and methods that are used in today’s education. The objective of this study is to develop a Web Based Application That Improves Permanency and Facilitates Learning in Mathematics Education.


Malmquist Productivity Index with Fuzzy Data by Possibility Theory
AUTHOR: Shivi Agarwal
Affiliation : BITS PILANI

This paper proposes the method to estimate the productivity change with fuzzy data by possibility theory. Productivity change has been widely studied with crisp inputs and outputs but, in some cases, input and output data of decision making units (DMUs) can’t be precisely measured. Thus, the uncertain theory has played an important role in productivity change. In these cases, the data can be represented as linguistic variable characterized by fuzzy numbers. Malmquist productivity index (MPI) is widely used to estimate the productivity change by calculating the relative performance of a DMU for different time periods using data envelopment analysis (DEA). The fuzzy DEA (FDEA) model is solved using the concept of chance-constrained programming and possibility theory. The results of FDEA is used to estimate MPI with fuzzy data. Finally, numerical examples are presented to illustrate the proposed method to estimate MPI with fuzzy data.


Web-based teaching of quadratic functions
Affiliation : Education Faculty , Anadolu University , 26470, Eskisehir TURKEY

There has been an extremely important development in the 21st century on computer technology. These developments have made it necessary to use these technologies in education and training. One of these technologies is a web-based teaching. In this study, Quadratic functions for a web-based learning material was designed. Students' success in learning the functions via the web-based instructional materials have been evaluated with traditional education. The results were interpreted.