Exact Real Calculator for Everyone

AUTHOR: Weng Kin Ho

AFFILIATIONS: National Institute of Education

Despite its simplicity and versatility, the well-known Floating Point System (FPS) has a serious shortcoming: the finite nature of a computer makes rounding-off inevitable. Because of this, FPS can sometimes lead to serious computational errors, i.e., a small round-off error due to truncation can cause a large deviation in the output in iterations within chaotic systems. This paper bridges the gap between theory and practice of Exact Real Arithmetic (ERA), and reports on the design and implementation of a user-friendly scientific calculator ERCE using Haskell, capable of ERA. With a functional-programming slant, we use ERCE as a channel for the technology of ERA to reach out to a wider community: even a school student can use it.

Let’s TWIST Again

AUTHOR: VLADIMIR NODELMAN

AFFILIATIONS: Holon Institute of Technology

The possibility to study such fundamental notions of modern mathematics as “space” and “spatial transformation” is almost absent in educational software. Instead, such software handles affine transformations of objects lying in 2D or 3D space: specifically, compositions of rotations, translations and scaling, all being applied to geometric shapes.
It is relatively easy to implement affine transformations of the whole space programmatically due to internal nature of computer graphics mechanism. The real challenge is to support nonlinear spatial transformations in a manner that is user-friendly and seamless.
Our noncommercial software “VisuMatica” long ago supports well nonlinear transformations of two-dimensional spaces. As result, the software became a powerful tool which helps to discover the unity of mathematics, to visualize and dynamically explore new mathematical environments and phenomena.

In our lecture we will present 2D- and new, 3D-nonlinear transformational abilities of “VisuMatica”. The spectrum of supported mathematical topics became even wider. In particular, the presentation includes discussion of some applications to vector fields, differential equations, 3D modeling, etc.
From PROMENADE (translations), through the WALTZ (rotations) we advanced to TWIST & SHAKE deformations OF THE WHOLE SPACE.

HOW TO MANAGE ALL THIS CHANGE (PLENARY PRESENTATION)

AUTHOR: Douglas Butler

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

Whatever device you are using, the quality of online material for mathematics teaching contines to evolve and challenge. In addition, the ease with which teachers, students and parents can all now communicate with each other gives us an invigorating new dynamic for learning mathematics.

Dramatic changes in hardware have forced the content providers into new touch-driven environments, and a new wave of writers has emerged who are serving up excitingly fresh ideas.

In this presentation Douglas will cherry-pick from the best of his TSM Resources website. He will remind everyone of the increasing need for continual professional development, and how important it is for the technology not to get in the way of the mathematics.

Construction of a Doubly Ruled Surface

AUTHOR: Jen-chung Chuan

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

A surface is called ruled if through every point there is a straight line that lies on the surface. A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperboloid of one sheet is an example of the doubly ruled surface. A less obvious example is the hyperbolic paraboloid. In this talk we are to demonstrate, using Cabri 3D, how such a doubly ruled surface can be constructed synthetically.

Exploring Metric Spaces Visually with Excel

AUTHOR: Deane Arganbright

AFFILIATIONS: Divine Word Univ., PNG (Emeritus)

This paper provides a novel approach for an introductory exploration of metric spaces, showing ways to use Excel creatively to discover interesting insights into mathematics. We use diverse examples of metrics to provide insights into the concept of distance, and see how it interacts with the areas of geometry, calculus, and other more familiar parts of mathematics. Along the way, we encounter inequalities and other aspects of classical mathematics, and provide new problem solving and teaching techniques, and a means of discovering patterns by employing spreadsheets to enhance the visual interpretation of a thought-provoking part of mathematics.

Incorporating Culture in the Teaching of Mathematics

AUTHOR: Ma. Louise Antonette N. De las Penas

AFFILIATIONS: Ateneo de Manila University

The focus of this paper is to highlight teaching mathematics with the use of technology, incorporating cultural connections.
The first part of the talk focuses on geometric patterns appearing in Philippine artwork that are used as tools in understanding concepts in geometry and algebra. The Philippines is composed of 7,100 islands, home to indigenous communities of varied culture. By bringing into the mathematics classroom works of these communities, the students perceive that mathematics comes from what is done in everyday life, and that it exists in their own culture.
In the second part, we discuss the role of web resources and online geometric software in facilitating a cultural dimension to the mathematics being discussed in the classroom.

Discovering More Mathematics and Applications by Integrating CAS with 3D DGS

AUTHOR: Wei-Chi Yang

AFFILIATIONS: Radford University

It is known that Computer Algebra Systems such as Maple, Mathematica and etc. have assisted us greatly in numeric, algebraic and symbolic computations, which are pivotal for our teaching, learning and research. We have also seen the impacts of 2D Dynamic Geometry Software (DGS) such as Geometers'' SketchPad, Cabri II and etc in mathematics education . In this paper, we use examples to demonstrate, from users'' point of view, how the integration of CAS with a 3D DGS provides us crucial 3D visualizations and theoretical verification needed in teaching and research in mathematics and its applicable fields.

ICT (I see it) in Math education

AUTHOR: Inder Rana

AFFILIATIONS: Department of Mathemaitcs, Indian Institute of Technology Bombay, Mumbai, India

ICT in education has been a buzz word for about 10 years now; still the debate is on the various issues of integrating ICT in education: -what is ICT? –What role it can play? - The level at which it is suitable (primary/middle/secondary/higher education)?-how effective it is and it can be? – Issues like teachers’ orientation?-outcomes versus the cost? - and some on. Each specific country has its own answers to above questions (see [1]). For some of the Indian initiatives and outcomes, one may look at [2]. The aim of this paper is to look at some suggestions for answering first two questions in the context of math education. We will illustrate with examples how ICT tools can help effectively support various pedagogical components in math education at various levels of math education.
References
[1] ICT in Education http://www.unescobkk.org/education/ict/
[2] UNESCO Bangkok http://www.unescobkk.org/education/ict/countries/country-information/india/

Key factors for Successful Integration of Technology into the Classroom: Textbooks and Teachers

AUTHORS: Hee-chan Lew, Seo-Young Jeong

AFFILIATIONS: Department of Mathematics Education, Korea National University of Education, South Korea, Department of Mathematics Education, Korea National University of Education South Korea

The purpose of this paper is to investigate some causes of why technology has not been integrated into mathematics teaching by teachers We considered two aspects to examine these causes in this paper; Korean mathematics textbooks as teaching materials implementing technology, and teachers’ concern on using technology and their levels of its use. First, we analyzed the role of technology in mathematics teaching and learning, especially concentrated on Korean secondary mathematics textbooks. Secondly, we surveyed Korean secondary mathematics teachers’ concerns about integrating technology into their mathematics education and the teachers’ level of its use in the mathematics classroom. We found that mathematics teachers need more proper information and support to integrate technology into teaching mathematics. Additionally, this paper suggests that educational researchers or administrators help teachers move toward more practical use of technology without emotional or physical barriers in mathematics classroom.

Exploring Space Filling Origami

AUTHOR: Wenwu Chang

AFFLIATIONS: Shanghai Putuo Modern Educational Technology Center, China

Case Studies in Experimental Mathematics

AUTHOR: Shailesh Shirali

AFFILIATIONS: Sahyadri School (KFI), Krishnamurti Foundation India, Rishi Valley School (KFI)

Experimental mathematics is now a well-accepted genre of study. It is a field in which computer-assisted experimentation – the generation of numbers, sequences, graphs and so on, using powerful software – combined with theoretical study can yield a great deal. Though this sounds revolutionary, it is not. Indeed, using numerical and graphical experimentation as a means to arrive at conjectures has been a standard mode of operation used by mathematicians for centuries. The only difference is that today vastly stronger technology is available to us.
In this talk we describe three problems in which substantial progress is accomplished when computer software is used:
1. A problem from number theory, featuring an iteration with an unusual conclusion;
2. A problem dealing with the enumeration of integer-sided triangles; and
3. A problem from geometry, in which we study the variation in a trigonometric function defined on the set of all triangles.
We also give solutions to the three problems.

Developing Students' Mathematical Thinking Through Technology

AUTHOR: Jonaki Ghosh

AFFILIATIONS: Lady Shri Ram College, Delhi University

Research has shown that the appropriate use of technology can transform the traditional mathematics classroom into a dynamic learning environment where the student is actively engaged in constructing mathematical concepts and knowledge. There are a plethora of technological tools which can enable students to explore and discover mathematical concepts. These include Dynamic Geometry Software (DGS), graphics calculators, spreadsheets and Computer Algebra Systems (CAS). Because of these tools, the emphasis in the mathematics classroom has shifted from memorising procedures and techniques to conjecturing, meaningful problem solving and developing mathematical reasoning. These technologies provide numerous advantages. They enable the student to explore mathematical ideas graphically, symbolically and numerically. They can be used as pedagogical tools to extend student¡¦s mathematical thinking and provide possibilities in mathematical modelling activities. Their ability to effectively take over tedious calculations and algorithmic procedures reduces cognitive load on the student and enables her to focus on developing mathematical insight.

This presentation will focus on how an appropriate combination of CAS and graphics calculators along with paper-pencil tasks can be used to develop student¡¦s mathematical thinking. Some examples of technology enabled explorations by students at the higher secondary school level will be used to highlight how such tools can enhance visualization of concepts, give students access to higher level concepts and lead to a rich and motivating environment for exploring mathematical ideas. The presentation will also illustrate students’ explorations of some interesting applications of school mathematics to topics such as cryptography, genetics, estimating ƒà (Buffon’s Needle problem) and fractal patterns in the complex plane. It will be shown that the appropriate use of technology can help students in their investigations giving them control over what they are learning and also help to create a balance between conceptual and procedural knowledge.

Technology Enhanced Problem Based Learning with Applications to Real-World Problems

AUTHORS: Padmanabhan Seshaiyer, Byong Kwon and Thomas Stephens

pseshaiy@gmu.edu, bkwon1@masonlive.gmu.edu, tstephe3@gmu.edu

AFFILIATIONS: Department of Mathematical Sciences, George Mason University, Fairfax, VA 20151, USA

Abstract: In this paper, we consider the application of two diverse software tools to simulate differential equation models developed for disease dynamic models. Specifically, we motivate the SIR disease epidemic model that consists of a system of differential equations that can be solved via numerical algorithms including Euler's method and Runge-Kutta method. We implement these using a MATLAB literate programming approach and show how one can obtain best fit parameters for given data from the real-world and also visualize it using a graphical user interface (GUI). We also present an alternative approach using the AMPL Optimization software to do the same problem. The purpose of introducing the latter software is its capability to handle real-world problems with big data. The results obtained from both methods are comparable yielding similar best-fit parameters for a given set of data and they suggest that the methods proposed herein are reliable and robust for solving real-world applications.

DIFFUSIVE MASS TRANSFER IN AN ECCENTRIC ANNULAR FLOW

AUTHORS: Uma Devi, Bathalapalli Uma Devi, Dinesh P A, Indira Rao

AFFILIATIONS: JSSATE, Bangalore, MSRIT, Bangalore, NMIT,Bangalore, Asst.Professor,Dept. of Mathematics, J.S.S.A.T.E, Bangalore, Associate Professor,,Dept. of Mathematics, MSRIT,Bangalore, HoD & Professor,,Dept. of Mathematics, NMIT,Bangalore

The dispersion in an eccentric annulus region by taking blood as a Newtonian fluid with the investigation of oxygen transfer to the tissue cells in an eccentric catheterized artery is studied. The region bounded by eccentric circles in x-y plane is conformal mapping to concentric circles in plane using a conformal mapping . The resulting governing species equations are analytically solved by using transformation for the concentration. Numerical computations are carried out to understand the simultaneous effects of absorption parameter and eccentricity on the flow with respect to time. The observation through the numerical computations reveal that, as absorption parameter and eccentricity enhances, the solute concentration diminishes.

Klein model of the three-dimensional sphere and dynamic construction of common perpendicular

AUTHORS: yoichi maeda

AFFILIATIONS: Tokai University

In this paper, we introduce gKlein modelh of the three-dimensional sphere derived from the stereographic projection of the sphere. In this model, geodesics look like Euclidean lines instead of Euclidean circles in the stereographic projection. With this model, we study how to make a right angle. For a pair of geodesics in the three-dimensional sphere, there are two common perpendiculars in general. We propose a simple construction of the common perpendiculars. In addition, we mention that Klein model of the three-dimensional sphere has a relation with Klein model of the three-dimensional hyperbolic space.

Mathematics Teaching, Learning and Assessment using Latest ICT tend Social Media

AUTHORS: ENAGANDULA PRASAD, Dr.A.RAMAKRISHNA PRASAD

AFFILIATIONS: VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, Director of UIIC Jawaharlal Nehru Technological University Hyderabad, Andhra Pradesh, India

Abstract: ICT stands for "Information and Communication Technologies." it refers to technologies that provide access to information through telecommunications. It is similar to Information Technology (IT), but focuses primarily on communication technologies. This includes the Internet, wireless networks, cell phones, and other communication mediums. This paper initiates advanced ICT for learning and teaching mathematics through the Social media tools such as Face book, Twitter, YouTube, Geogebra ,Blogs and etc. This paper describes how it works, where it is going, and why it matters in an emerging country-India particularly. It also supports the teaching and learning community in developing ways to gather evidence of the impact of social media tools innovations and current practices on learning mathematics. There is already evidence that teachers are using social media to teach mathematics as part of teaching strategies, with the aim of encouraging students to view social networks as less of a pleasurable distraction. With this paper we are trying to integrate social media into the classroom, and focuses on the need to carefully review existing teaching strategies and understandings of social media before making changes. This paper aims that ‘With today''s computer and Information and Telecommunications technologies, every young person can have a quality and deep understanding of mathematical concepts in education regardless of his or her place of birth or wealth of parents in India.
Keywords: Mathematics, Education, ICT Social Media, Face Book and Geogebra.

MATHEMATICS TEACHING, LEARNING AND ASSESSMENT USING TECHNOLOGY

AUTHORS: NAGANJANEYULU V, NAGANJANEYULU V

AFFILIATIONS: AL HABEEB COLLEGE OF ENGG&TECH, Assistant Professor Al Habeeb college of engg&Tech

Abstract––This paper describes the effects of using Technology as a teaching and learning aid for engineering mathematics. Teachers feel it difficult while teaching 3D graphs to Engineering students and integration of technology into pedagogy which will improve student learning. While many engineering educators have proposed changes the way mathematics is taught to engineers, the focus has often been only on mathematical content knowledge rather than on pedagogy. Work from the mathematics education community across the world suggests that it could be beneficial to consider a broader notion of mathematics: mathematical thinking, the interdisciplinary usage of mathematics content knowledge. We would like engineering students to learn to identify the problems and problem-solving strategies, use of resources, attitudes and practices. Using technology in Teaching and learning will help the students to understand the difficult tasks easily and further technology will engage students in learning process. This article further discusses each of these aspects of mathematical thinking and others examples of mathematical thinking practices based on the authors’ previous empirical studies of engineering students and practitioners uses of Technology in mathematics teaching and learning . This paper offer insights to inform the teaching of mathematics to engineering students using technology.

Computing a Perturbation Bound for Preserving the Number of Common Zeros of a Polynomial System

AUTHORS: Hiroshi Sekigawa, Kiyoshi Shirayanagi

AFFILIATIONS: Tokyo University of Science, Toho University

We propose a method for computing a perturbation bound that preserves the number
of common zeros in T^n of a polynomial system {f_1, ..., f_n}, where T is the
set of nonzero complex numbers and f_j''s are complex coefficient polynomials in
n variables, by using Bernshtein''s theorem, Stetter''s result on the nearest
polynomial with a given zero, and minimization techniques for rational functions
such as sum of squares (SOS) relaxations.

Development of an Item Bank System for the Mathematics e-Learning System STACK

AUTHORS: Yasuyuki Nakamura, Tetsuya Taniguchi, Takahiro Nakahara

AFFILIATIONS: Nagoya University, Kitasato University, Sangensha LLC

System for Teaching and Assessment using a Computer algebra Kernel (STACK) is a computer-aided assessment system for mathematics, and functions as a plug-in for the Learning Management System (LMS) Moodle. With the help of STACK, Moodle can provide questions for online tests. These questions typically require a mathematical expression as a response and the responses are assessed algebraically. STACK is not only able to determine whether a studentfs answer is correct, but can also provide appropriate feedback for various answers. Partial scores can even be assessed for an incomplete answer. However, in order to take advantage of STACKfs rich functionality, questions must be designed carefully. Well-designed questions can be valuable educational resources, especially in an e-learning environment. To promote the sharing of high-quality questions for use in online tests, we developed an Item Bank System for the mathematics e-learning system STACK. Using our system, users can submit authored questions in XML format to STACK along with additional meta data, including subject, difficulty level, targeted grade, and publicity level. Once they are uploaded and stored in the system, all users would be able utilize any questions open to the public. We expect that sharing such questions will further promote the effective use of mathematics e-learning systems.

Computer Algebra Systems as Cognitive Tools

AUTHORS: Tadashi Takahashi, Takeshi Sakai

AFFILIATIONS: Konan University

When computer algebra systems(CAS) were introduced, it was expected that it will
develop to use effectively as a htoolh for mathematics education. In the 2000s, with theevolution of both software and hardware, it has become easy to use CAS in the classroom.However, the proportion of teachers who do so is still quite low. We have to consider their effective use. Humans use strategies to plan solutions, decide procedures, and solve problems. This leads to the cognitive science concept of htool theoryh. We consider the guideline for structuring a class using CAS and show the practice in this paper.

TRANSFORM TECHINQUES FOR CRYPTOGRAPHY

AUTHORS: Anil Hiwarekar

AFFILIATIONS: Vidya Pratishthans college of Engineering Baramati

Laplace transform has many applications in various fields such as Mechanics, Electrical circuit, Beam problems, Heat conduction, Wave equation, Transmission lines, Signals and systems, Control systems, Communication systems, Hydrodynamics, Solar systems. In this paper we discuss its new application to cryptography. Cryptography is used for securing transmission of messages, protection of data which provide privacy and security for the secret information. Applications of cryptography includes in e-commerce; electronic communications such as mobile communications, sending private emails; business transactions; Pay-TV; transmitting financial information; security of ATM cards; computer passwords etc, which touches on many aspects of our daily lives.
In this paper we developed a new method of cryptography, in which we used Laplace transform of suitable function for encrypting the plain text and corresponding inverse Laplace transform for decryption.

Key words: Cryptography, Data encryption, Applications to coding theory and cryptography, Algebraic coding theory; cryptography, Laplace Transforms.
Mathematics Subject classification: [94A60, 68P25, 14G50, 11T71, 44A10]

Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation

AUTHORS: Leslie Chandrakantha

AFFILIATIONS: John Jay College of Criminal Justice of CUNY

Keywords:

Computer simulation methods have been used in upper level statistics classes for many years. Lately, many instructors are adopting computer simulation to introduce the concepts in the introductory level. Students in introductory statistics classes struggle to understand the basic concepts. Research has shown that the use of computer simulation methods as an alternative to traditional methods of books and lecture enhance the understanding of the concepts. Computer simulation using spreadsheets such as Excel allows students to experiment with data and to visualize the results. In this paper, we will describe how to use the simulation using Excel Data Tables facility and standard functions to teach confidence intervals and hypothesis testing in introductory statistics classes. We believe, by using this hands on approach, students get a better feel for these abstract concepts. Our preliminary assessment shows that this approach would enhance the student learning of the concepts.

Exploring numerical methods with CAS calculators

AUTHORS: Alasdair McAndrew

AFFILIATIONS: Victoria University, Melbourne Australia

We describe the use of CAS calculators in a numerical methods mathematics subject offered to third year pre-service teachers. We show that such calculators, although very low-powered compared with standard computer based numerical systems, are quite capable of handling text-book problems, and as such provide a very accessible learning environment. We show how CAS calculators can be used to implement some standard numerical procedures, and we also briefly discuss student satisfaction.

The story of a research about the nets of platonic solids with Cabri 3D: Conjectures related to a special Net Factor - A window for new researches

AUTHORS: Jean-Jacques Dahan

AFFILIATIONS: IREM of Toulouse

In 2007, in the paper presented during ATCM, I showed some very strange results about the maximum of the volume of the convex hull of the folded net of a cube. This result found experimentally with Cabri 3D was validated with the use of the CAS of the Voyage 200 of Texas Instruments. The property states that this maximum is reached when the ratio between the volume of the convex hull and the given cube is 4.0141… We noticed that the angle corresponding to this maximum is given by 40.141…°. We have also proven that only the 5 first digits of these two numbers are the same. Several years later, I came back to this problem, trying to find experimentally some property more interesting about this convex hull. I began to explore a possible link between this ratio and the corresponding ratio between the area of the convex hull and the area of the initial cube when the volume is maximized. Very quickly, I pointed a possible property about the value of the ratio of these ratios that could be Pi/2. It was so unexpected that I wanted to confirm this conjecture. That is the beginning of this research I want to describe. Lots of conjectures will appear experimentally that we will try to corroborate experimentally. We will study this problem analytically in order to increase the accuracy of the special number we want to discover using different CAS software. Even if the conjectures for the cube and other platonic solids are wrong, it opens a window on a more general conjecture about the value of the special factor of a convex polyhedron in relation with the factors of the platonic solids. This last conjecture seems to be a very difficult problem: this is a problem for those who are interested by such properties. Last remark: most of the analytic formula have been validated with Cabri 3D.

Propagation of Love type wave in piezoelectric layer overlying non-homogeneous half-space

AUTHORS: Santanu Manna, Santimoy Kundu, Shishir Gupta

AFFILIATIONS: Indian School of Mines, Dhanbad, Assistant Professor, Department of Applied Mathematics, Indian School of Mines, Dhanbad

The present paper investigates, the mathematical modelling of the existence of Love type waves in a piezoelectric layer overlying a non-homogeneous half-space. Piezoelectric layer is considered for two different cases one is electrical open circuit and another one is electrical short circuit. The general dispersion equation has been derived for both the cases. As a special case dispersion equation has been obtained when the half-space is homogeneous medium. The velocities of Love waves have been calculated numerically as a function of wave number kh. The effect of non-homogeneity and dielectric constant are illustrated by graphs in both electrically open and electrically short circuit cases. All the figures show that phase velocity decreases with the increases of wave number kh. Using MATLAB software, graphical user interface (GUI) has been developed to generalize the effect of parameters discussed. The results can be used to understand the nature of wave propagation in piezoelectric structures.

Integration of Spreadsheet into the Teaching and Learning of Financial Mathematics

AUTHORS: Chee-Keong Chong, Marzita Puteh, Swee-Choo Goh

AFFILIATIONS: UTAR, Sultan Idris Education University, Malaysia

In this paper, we will study the technological integration approach of teaching and learning Financial Mathematics. A sample of 85 undergraduates taking Quantitative Techniques took part in this study. They were taught in Financial Mathematics through the traditional approach in the previous trimester. Pre-test was carried out to find out their performance. Later, they were exposed to spreadsheet approach on the same topic. Then a post-test was administered to assess their performance. Post-test results show significant improvement. A survey was carried out at the same time to determine their perceptions on (i) ease of use in spreadsheet, (ii) the use of spreadsheet template, (iii) awareness on the importance of spreadsheet, and (iv) the urgency in learning spreadsheet. Finally a conceptual model of implementing the integration of spreadsheet into the teaching and learning of Financial Mathematics is proposed.

Interval-symbol method with correct zero rewriting: Reducing exact computations to obtain exact results

AUTHORS: Kiyoshi Shirayanagi, Hiroshi Sekigawa

AFFILIATIONS: Toho University, Tokyo University of Science

We propose an interval-symbol method with correct zero rewriting or ISCZ method for short, which is an extension of the so-called interval method, to obtain exact results while reducing exact computations. Namely, this method uses not only a floating-point interval but also a symbol for each real coefficient of a polynomial. Symbols are used to keep track of the execution path of the original algorithm with exact computations. Moreover, the method has the rule of zero rewriting from stabilization techniques, which rewrites an interval into the zero interval if the interval contains zero. The key point is that at each stage of zero rewriting, one checks to see if the zero rewriting is really correct; namely,
an interval considered to be zero is really zero by exploiting the associated symbol. Therefore, one can expect that it mostly uses floating-point computations; exact computations are only performed at the stage of zero rewriting and in the final evaluation to get the exact coefficients. As another important merit, one does not need to check the correctness of the output.
The results of Maple experiments on convex hull construction indicate that our method is very effective for non-rational coefficients.

GeoGebra in Teaching and Learning Introductory Statistics

AUTHORS: Theodosia Prodromou

AFFILIATIONS: University of New England, Australia

This article discusses the special opportunities for teaching statistics that technology offers teachers who aim to provide rich learning experiences for their students. These opportunities involve automation of many activities such as quickly organising data, computing measures, and generating graphs. By automating the tasks of computing statistics or generating data, technology facilitates students’ ability to visualise abstract concepts, affording an opportunity to focus on conceptual understandings and data analysis. This article also examines how GeoGebra can be integrated into the curriculum and learning process of introductory statistics to engage college students in cycles of investigation including (a) managing data (b) developing students’ knowledge for understanding specific statistical concepts, (c) performing data analysis and inference, and (d) exploring probability models. Recommendations are included for ways mathematics educators can engage college learners in developing their knowledge for exploring data concepts and doing statistics with GeoGebra.

MATHEMATICS TEACHING, LEARNING AND ASSESSMENT USING TECHNOLOGY

AUTHORS: NAGANJANEYULU V

AFFILIATIONS: AL HABEEB COLLEGE OF ENGG&TECH

This paper describes the effects of using Technology as a teaching and learning aid for mathematics. Teachers feel it difficult while teaching mathematics to students using technology and integration of technology into pedagogical content knowledge which will improve student learning. While many educators have proposed changes the way mathematics is taught to students, the focus has often been only on Technological Pedagogical Content Knowledge (TPCK) rather than on pedagogy. Work from the mathematics education community across the world suggests that it could be beneficial to consider a broader notion of mathematics: mathematical thinking, the interdisciplinary usage of mathematics content knowledge. We would like students to learn to identify the problems and problem-solving strategies, use of resources, attitudes and practices. Using technology in Teaching and learning will help the students to understand the difficult tasks easily and further technology will engage students in learning process. This article further discusses each of these aspects of mathematical thinking and others examples of mathematical thinking practices based on the authors’ previous empirical studies of students and practitioners uses of Technology in mathematics teaching and learning .This paper offer insights to inform the teaching of mathematics and incorporate technology in the context of teaching and learning mathematics using technology.

Mathematical study of G-type seismic waves in heterogeneous layer overlying a non-homogeneous half-space

AUTHORS: Santimoy Kundu, Shishir Gupta, Santanu Manna

AFFILIATIONS: Indian School of Mines, Dhanbad, Professor, Department of Applied Mathematics, Indian School of Mines, Dhanbad, Research Scholar, Department of Applied Mathematics, Indian School of Mines, Dhanbad

The propagation of G type seismic waves in heterogeneous layer overlying a non-
homogeneous half space has been studied in this paper. We have considered the rigidity and density in upper layer is in exponential form. Both the rigidity and density in the lower non-homogeneous half-space are varying with depth. Dispersion equations have been obtained in closed form. As a special case when the medium and half-space are homogeneous then the dispersion equation coincides with classical equation of Love wave. Dispersion curves are plotted for different values of inhomogeneity parameters. It is observed that inhomogeneity parameters has dominant effect on the propagation of G type wave. We have seen that the phase velocity decreases with the increases of inhomogeneity
parameters. Variation in group velocity has been shown graphically. We have also drawn surface plots of group velocity with respect to wave number and depth parameter.

Evaluating Importance of Information Elements in Graphical Content Using Gaze Points

AUTHORS: Ryoji Fukuda, Junki Iwagami, Takeshi Saitoh

AFFILIATIONS: Faculty of Engineering Oita University, Kyushu Institute of Technology Japan

In this study, we evaluate the importance of information elements using gaze points of a person with normal vision. There are many information elements in a mathematical figure. It is necessary to identify important information elements in order to prevent information overload. We focus on elementary geometric figures and express them using directed graphs. non-visual communication analyze the potential of gaze points to express subconscious intentions.

Graphic Input System in Elementary Geometry for Non-visual Communication

AUTHORS: Ryoji Fukuda, Masato Kojo

AFFILIATIONS: Faculty of Engineering Oita University, Faculty of Engineering, Oita University Japan

In this study we developed a graphical input system of elementary geometry for non-visual communication. In this field, figures contain various information elements, that are expressed by delicate positional relations between various element pairs. These communications are done subconsciously among sighted persons using, for example, handwritten figures. We analyze these tasks and recognized their intentions based on the hand-written curves.

Activities for Cultivating Creativity in Statistics course

AUTHORS: Kyoko KAKIHANA, Mr.Takumi MAKINODAN, Miss. Atsumi Kimura

AFFILIATIONS: Tsukuba Gakuin University, Teshirogi Junior Highschool, ahij21@tkb.ed.jp

During the past ten years, the internet has spread widely and quickly into our lives. In that period of time, we have had numerous chances to extract meaningful data from massive amounts of information and make decisions or create new ideas with these data. Additionally, it has become important to know how this data, through analysis and calculation, is to be characterized. For these activities, it is necessary to develop students’ statistical literacy. In math education, statistics education is one facet that is focused upon. In Japan ,“Utilization of Data” at the junior high school level and “Data Aanalysis” at the high school level have been included in the new Courses of Study by MEXT (the Ministry of Education, Sports, Science, and Technology). Also, in Principles and Standards for School Mathematics (the National Council of Teachers of Mathematics, the U.S.) it has been stated that “Students need to know about data analysis and related aspects of probability in order to reason statistically—skills necessary to becoming informed citizens and intelligent consumers.” However, many teachers appear to be at a loss as to how to teach statistics in math courses. One possible reason is that they have been taught statistics by basic statistical expression and calculation without the use of concrete examples by paper and pencil. Therefore it is difficult for teachers to teach statistical literacy and for students to understand statistical thinking. In this paper, a new type of educational activities to cultivate statistical literacy through the collection and analysis of data are shown; through these activities students seemed to use mobile data terminals effectively.

THE MOVEMENT FROM BEHAVORISTIC ORIENTATION ‘COMPUTER ASSISTED INSTRUCTION’ TO CONSTRUCTIVISTIC ORIENTATION ‘STUDENT PROGRAMMING’ IN MATHEMATICS EDUCATION

AUTHORS: Mamdouh Soliman

AFFILIATIONS: Professor, Mathematics Education, College of Education, Kuwait University

This study presents a historical background and attempts to describe the shift in the use of computers in mathematics education from behavioristic oriented CAI movement towards constructivist based on student programming movement. The purpose of this paper is to review the changes that computers have on mathematics education, and their applications on teaching and learning of mathematics. There are three broad categories of the applications of computers in that field: computer assisted instruction (CAI), student programming, and general purpose educational tools such as spreadsheets, databases and computer algebra systems (CAS).
To achieve the purpose of the paper we describe how that behaviorism is considered to be the theory underlying CAI. According to that we considered the most types used in CAI programs: drill and practice, computers as tutors, simulations, gaming. The paper also clarified the effects of CAI programs on learning and teaching mathematics. The second step is to clarify student programming and its effectiveness on teaching and learning mathematics which started from the strong connections between students own computer programs in mathematics and their thinking processes. We reviewed tow traditions: the first one is the BASIC-PASCAL tradition. The other tradition, LOGO which is rooted from the artificial intelligence and supported by Piagt’s cognitive development theory. There are different uses of LOGO across mathematics curriculum. There are many examples to show the signicance use of LOGO such as : the concept of ratio, the idea of measurement: distance on a floor can be described in terms of units of natural number concepts which can be developed through guessing the number. The early findings indicated that LOGO had an effect in improving cognitive and problem solving skills more efficient than CAI in various measures of cognition, such as reflectivity and divergent thinking.
By using spreadsheets in the mathematical curriculum we can: drawing graphs comparing the graphs of y=x2 and y=x3 - finding the second and thirds roots of numbers through iteration. Finding for instance, length of the inside edge of cubicle box given the volume numerically - calculating the area under a curve - introducing the function concept. For example, a set of numbers in one column and another set of numbers in another column can be represented by the symbols x and y. The function can be defined as relation between two sets of data.
By the end of our paper we introduce Computer Algebra Systems (CAS) are digital devices used to manipulate symbols. The current survey indicated that various computer applications in mathematics education contributed greatly to classroom practices.

Conceptual development and the modern scientific calculator: Using a forgotten technology

AUTHORS: Barry Kissane, Marian Kemp

AFFILIATIONS: Murdoch University

Calculators have frequently been regarded only as devices to perform calculations and thus often regarded with disapproval by mathematics teachers. With the availability of sophisticated technologies in many settings, it seems that the potential for scientific calculators has been neglected recently, and developments in this technology not adequately exploited. This is of particular significance in developing countries, where resources are limited. In this analytic paper, we highlight some opportunities created for conceptual development with regular access to a modern scientific calculator. The focus is on the development and deep understanding of mathematical concepts, widely recognized as of prime importance to student learning. The analysis is illustrated with examples related to the multiple representation of concepts and to the use of an advanced scientific calculator to provide numerical experience of important mathematical concepts.

A Comparison of Polytechnic Students’ Attitudes toward Advanced Scientific Calculators

AUTHORS: Wei Ching Quek, Chew Pheng Kok-Mak

AFFILIATIONS: Singapore Polytechnic

Students from Singapore Polytechnics have wide range of mathematics background. Most of them continue with their polytechnic education with calculators approved for the primary school leaving examination. During their course of studies, they may be introduced to some functions such as SOLVE, MATRIX, VECTORS, COMPLEX that are useful for engineering mathematics, but these functions may not be available in their calculators. No previous studies had examined how students'' mathematical backgrounds influenced their choice of calculators in engineering mathematics instruction. Two groups of students are selected and introduced to advanced scientific calculators in their engineering mathematics modules. The study sought to determine whether there was a difference in student’s attitude towards advanced scientific calculators in engineering mathematics instructions. Do student''s attitudes towards advanced scientific calculators use in mathematics instruction differ in terms of mathematical ability level? Do student''s attitudes towards advanced scientific calculators use in mathematics instruction differ in terms of price range of the calculator? Do they concern about being over dependent on the calculators? Data collected from questionnaire and exam scores was analysed using both descriptive and inferential statistics. The results indicate that a significant difference in attitudes towards the use of advanced scientific calculators. The findings of this study are useful to module coordinators and module developers.

Improving Students'' Conceptual Understanding Through the Use of Interactive Smart Boards and Virtual Manipulatives

AUTHORS: Beverly Ferrucci

AFFILIATIONS: Keene State College

To encourage students to develop research skills, institutions often initiate programs of faculty-student research. This presentation reports on one of several recent faculty-sponsored projects that merge mathematics education research and technology. Groups of prospective elementary school teachers received instruction in spatial visualization using either concrete 3-D tangram blocks or virtual analogues on Smart Boards. Analogues were programmed in Sketch Up by the student, who also delivered the instruction; instructional and research design were a joint, student-faculty component of the project. Results showed (1) significant gains only for the technology group; and (2) increasing student-reported levels of comfort with virtual blocks that showed evidence of approaching their comfort with the concrete blocks.

A benchmarking approach of quality assessment for e- and blended learning

AUTHORS: Stefan Oeyen

AFFILIATIONS: University College Limburg associated Catholic University Leuven

The increasing use of Information and Communication Technology (ICT) has a major and important influence on the education of mathematics around the world.
This evolution makes us think about the choice of media, the software usable for the set objectives, digital didactics and pedagogy… In this fascinating world of e- and blended learning it is a great opportunity to ensure and improve the quality of mathematics education.
Reflecting (self and with peers) about this subject is absolutely nescessary. This presentation provides tools for quality assessment in e-and blended learning. The focus will be on “course design”, one of the six areas which can be assessed (strategic management, curriculum design, course design, course delivery, staff support and student support).
By focussing on specific benchmarks and criteria, teachers or multidisciplinary teams will be able to develop performance indicators which are fit for purpose in their own context. This method might form the basis for a self-evaluation about the quality of a personal course.

WHAT’S NEW AND EXCITING ON THE WEB FOR MATHEMATICS TEACHERS

AUTHORS: Douglas Butler

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

Bring your own device to this session and explore Douglas'' TSM Resources website (Technology for Secondary Mathematics):
- tools for the busy teacher
- ideas for using Google Earth
- selection of great iPad apps for mathematics
- interesting images to fit graphs to
- interesting data to analyse
www.tsm-resources.com

Virtual Manipulatives as a Tool for Discourse in Teaching Children Mathematics

AUTHORS: William Speer

AFFILIATIONS: Director, Mathematics Learning Center, University of Nevada Las Vegas

For children, in fact, for all, learning mathematics is best evidenced when the ability to transfer and the ability to make connections are present. When choosing a virtual manipulative students should not be able to quickly complete a designated activity without making connections to the underlying mathematics. One of the best ways to judge the attainment of these abilities is to engage the student in discourse. This leads to technology as a tool to further student learning, not replace or hinder it.

OPTIMIZATION APPROACHES IN IMRT PLANNING

AUTHORS: KISHORE S P, NARASIMHAM N V S L, RAMAKRISHNA PRASAD A

AFFILIATIONS: VARDHAMAN COLLEGE OF ENGINEERING

Keywords-intensity modulated radiotherapy (IMRT); Dose volume histogram (DVH); beam angle optimization (BAO); linear programming problem; nonlinear programming problem.
Radiation is one of the most common treatments for cancer and is often a part of the main treatment for specific types of cancer, such as, lung, head and neck, Hodgkin disease. The main challenge is to quantify optimization techniques in radiation therapy. In the formation of a model a lot of emphasis is given on testing various objective functions with constraints. The challenge in therapy planning is to determine a treatment plan which would involve finding irradiation directions, beam parameters and optimize intensity profiles. In recent years IMRT has helped in the realization of conformal therapy. The main objective of conformal therapy is to deliver a lethal dose of radiation to the tumor while sparing the OARs (organs at risk).Radiation oncologists often use cumulative dose volume histogram to determine the quality of treatment plan. In this paper an attempt has been made to study radiation treatment planning using linear and nonlinear programming approaches.

Exploring Taxicab Geometry with Excel

AUTHORS: Maryanne Bagore, Jeffrey Ambelye, Deane Arganbright

AFFILIATIONS: Divine Word Univ., PNG (Emeritus), Dept. of Information Systems Divine Word University Madang, Papua New Guinea, Dept. of Mathematics and Computing Science Divine Word University Madang, Papua New Guinea

In this interactive presentation we use Microsoft Excel to investigate the geometry of the real plane that is generated by the taxicab metric d((x1,y1),(x2,y2)) = |x1 –x2| + |y1-y2|. In the process we compare and contrast this geometry with Euclidean geometry, finding both similarities and many surprising differences. We use a wide range of the features of Excel not only to display our results, but also as a way for students to discover patterns, as we generalize many of the results of standard analytic geometry. We use both spreadsheet charts and the basic spreadsheet display itself to visualize illustrate our results and applications, and provide some creative Excel animations. Our material has been developed in teaching the concepts to students in both standard and online classes.

Bias Reduction Method Applied to Regression: Modelling Count Data

AUTHORS: Ashwini Joshi, Vidyagouri Prayag, Pralay Senchaudhuri

AFFILIATIONS: Cytel Statistical Software & services Pvt. Ltd., Cytel Statistical Software & Services Pvt. Ltd., Cytel Inc.

Abstract: This paper deals with the bias reduction method for computing estimates of parameters maximizing the likelihood of Poisson regression. The method is implemented for count data such as lesions in multiple sclerosis, MRI trials etc which arise in clinical trials quite often. The penalization of likelihood is required in order to reduce bias as suggested by Firth (1993, Bias reduction of maximum likelihood estimates. Biometrika, 80, 27-38). Using the set up of Generalized Linear Models (GLM) Poisson regression is dealt with by computing point as well as interval estimates of parameters. Important aspects of these biased reduced estimates such as shorter confidence intervals, existence in case of degeneracy, separation or quasi separation in the data are studied. We illustrate the methodology with the help of few examples.

Interactive Videos: Engaging Students in and out of the Classroom

AUTHORS: Haitham Solh

AFFILIATIONS: American University in Dubai, Louisiana State University, University of Southern Mississippi

In a technology-oriented world, numerous tools provide help for students studying Mathematics, but few are as engaging as interactive video lessons. This paper provides a theoretical background for this approach, focusing on the differences between procedures and concepts in Mathematics. Then, the “interactive video” approach is explained in detail. Finally, advantages of this approach are highlighted in comparison with current online teaching videos.

Animated Teaching Materials for Statistics Education in Beginner-level University Classes

AUTHORS: Shunji Ouchi, Setsuo Takato

AFFILIATIONS: Shimonoseki City University, Toho University

We will consider how animated teaching materials created with KETPic and R help novice learners understand statistical concepts and effect their visualization of statistical chance (stochastic) phenomena. KETpic is a macro package used to embed high-quality graphics in LaTex documents which can be implemented in different Computer Algebra Systems including R. R is a popular open-source software tool used in statistical analysis and for graphic output. It provides a wide variety of statistical and graphical techniques, and is highly extensible. Through careful utilization of both these systems, it is possible to develop animated teaching materials that contribute positive effects to statistics education. In this report, we will introduce and demonstrate the animated teaching materials (in PDF format) we have created, including graphics based on simulated data sets generated by R.

HANKEL DETERMINANT FOR A NEW CLASS OF CONVEX STARLIKE ANALYTIC FUNCTIONS

AUTHORS: Gurmeet Singh

AFFILIATIONS: Khalsa College, Patiala

ABSTRACT: We introduce a new class of Convex Starlike analytic functions and its subclasses and obtain sharp upper bounds of the functional |a_2 a_4-a_3^2 | for the analytic function f(z)= z+ ¢²_(n=2)^¡Ä¢Æa_n z^n,|z|<1 belonging to these classes.

On the Effects of Visualizing Activities of Quadratic Curve Problems using GeoGebra

AUTHORS: Minshik Cho, Sang-Je Cho, Kwang-Sang Lee

AFFILIATIONS: Department of Mathematics, Korea National University of Education, Graduate School, Korea National University of Education, Korea Institute for Curriculum and Evaluation

The quadratic curves are one of the most important contents of Korean high school mathematics courses. They are defined analytically as the locus satisfying some geometric properties. Hence students mostly learn the topic only practicing and calculating equations in the coordinate plane. Since they do not mention how quadratic curves are connected with cross section of cone in Korean textbooks, many students don¡¯t understand involved geometric meanings in analytic problems.

The purpose of this study is to investigate, through case study, how to apply Geogebra and to find out effective methods for learning quadratic curves with technological assistance. We adopted some difficult test problems from College Entrance Exam, so called - CSAT(College Scholastic Ability Test). Only a few students could solve those problems analytically. Many students could not even understand written solutions. One of the reason is that the lack of understanding on the relation between analytic expression and its geometric meaning.

Learning worksheets including GeoGebra activities were designed so that student''s understanding of the quadratic curves can be improved. During the class with GeoGebra activities, students could correct their misconceptions and understand the reason why the shape of construction are quadratic curves.

Analysis of data including worksheets, Geogebra activities, and interviews showed effects of geometric understanding as a result of utilizing Geogebra. During the students had personally composed problem situations on their own through Geogebra, they had intuitively recognized beneath geometric meaning. Moreover, they could understand geometric behavior and related concepts through the process of manipulating worksheets using some functions of GeoGebra, especially coordinate indicating function, drawing graph, dragging graph, and slider emerged.

The use of dynamic tools to develop students’ understanding of the fundamental ideas of calculus

AUTHORS: Debbie Verzosa, Angela Fatima Guzon, Ma. Louise Antonette De las Penas

AFFILIATIONS: Ateneo de Manila University

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this presentation, we describe lesson sequences utilising dynamic tools for teaching the epsilon-delta definition of the limit and the Fundamental Theorem of Calculus. The lessons were designed on the basis of observed student difficulties and the existing scholarly literature. We first discuss students’ initial understanding of the formal definitions in calculus as well as some of their initial proof constructions. We then present ways by which teachers can design guide questions to accompany the dynamic tools so as to facilitate students’ reconstruction of these calculus ideas.

PILOT STUDY USING CASIO MATHS TEACHING AND LEARNING TOOLS AT HIGHER SECONDAY STAGE IN DELHI NCR REGION

AUTHORS: P. K. Chaurasia

AFFILIATIONS: National Council of Educational Research and Training, CASIO

With believe that use of ICT foregrounds the ways in which teaching learning community can match in school the opportunities for learning more qualitatively. The role of ICT in the mathematics curriculum is much more than simply a technical skill or as a means of improving learning effectiveness. It shows way for transforming the goals and processes of education. It provides a real opportunity for teachers of all phases and subjects to rethink fundamental pedagogical issues alongside the approaches to learning that students need to apply in classrooms. To taste our believe that when students learn with Casio technology of teaching and learning Mathematics, they may use it as a cognitive tool that helps them to construct meaning based on their prior knowledge and conceptual framework, we planned to conduct this pilot study.
In fact, the mathematics education community is engaged in a constant quest to find out how children best learn mathematics. Due to coherence property of Mathematics, it is an enormous and constantly expanding network of interrelated facts and ideas like the fields of cognitive development and the psychology of learning. A large proportion of teachers these days try to base much of their teaching practice on constructivist ideas – that is, on the belief that the teacher’s role is to create opportunities for children to build their own understandings of concepts. However, if only we could discover precisely how the child best learns mathematics then we could work out exactly how to teach the child the subject in the most effective way. Based on these pedagogical processes of teaching and learning Mathematics, in this pilot study we will try to discover how the Casio''s digital technologies will help students to best learn with.
Even though technology can influence what is taught, teachers need to be mindful of designing instruction and environments that promote these content and learning framework. To test our beliefs that Casio tools support learning requirements when it is used “as a tool for processing the concepts with investigations and problem solving”, we selected fifteen CBSE based schools in Delhi NCR region. The research team has designed instructions for five selected chapters of higher secondary Mathematics curriculum. The study is still in process. In the initial interaction of teachers in their classroom, we started with the experience that these Casio based digital technologies can be seen as catalysts for a paradigm shift. In recent years, the emerging information and communication technologies (ICTs), has shifted our views on effective teaching and learning even further. Emphasis is now placed on equipping students with effective inquiry skills, including the ability to find and process new methods. The question was- up-to what extent the use of digital technologies like Casio''s Mathematics teaching and learning tools supports these different learning dimensions? Can Casio digital technology create an environment, rather than just a tool, for learning and teaching? The study is still in process with a group of Mathematics teachers in 15 schools of Delhi NCR region. The initial reflections are very important and also guiding the further movement with the study.

Analysis of Utilizing GSP Processes in Solving Geometry Problems by the Gifted

AUTHORS: Jaehak Lee, In Suk Choi

AFFILIATIONS: Korea National University of Education, Ulsan Science High School, Korea

The purpose of this study is to analyze the process of utilizing the GSP software program in solving geometry problems by the mathematically gifted. This study aims to provide information pertaining to the demands of teachers and students using GSP, and to find the most practical, efficient application in the geometry class. For these purposes, two research tasks were set up as follows: 1. How do the gifted utilize GSP in solving geometry problems?
2. what do the gifted think about utilizing GSP in solving geometry problems?

In order to solve these research issues, I studied the characteristics of the gifted, and I developed geometry-related teaching and learning materials for the gifted. I designed a task that required students to find original images of anamorphic images by anamorphic systems such as the mirror shape of a right circular cone and cylinder.
I observed the following results from this study. First, the gifted students utilized GSP to devise a plan for solving their problem, or to correct mistakes they had made in their solution plan. They were not satisfied with only finding a solution; they also wanted to discover the reasoning behind their solution. Using GPS, they were able to consider all of the conditions of solving the problem. Some students used all of the conditions, and others used only a few. They wanted to modify the problem using GSP. They used the software to save time and effort after using their energy to develop the larger concepts. Secondly, the gifted used the GSP program as a tool for exploring new solutions to problems. They felt that it was a great achievement to be able to visualize the problem as a mathematical modeling of their ideas. However, they didn't use GSP to develop their solution.
We can determine the following conclusions from the results of this study. First, the gifted are able to both model and justify mathematical problems using GSP. Because the students I observed are particularly talented in mathematics, they were able to make progress toward solution strategies without the normal regressions that one would expect from another group. Secondly, these students have a strong desire not only to see a concrete representation of their ideas, but also to create formal justification for their solutions. They were quite pleased that the GPS software enabled them to do those.

GeoGebra for tablets and on other devices

AUTHORS: Zsolt Lavicza, Balazs Koren

AFFILIATIONS: University of Cambridge, Eotvos Lorand University, Budapest

The development of the GeoGebra software has been accelerated during the past years. GeoGebra 4.0 was released in September 2011 with many new functionalities, among others extended statistical features and one-click upload to GeoGebraTube. GeoGebra 4.2 has been available since September 2012, which includes the long awaited feature the Computer Algebra System (CAS) view. Meanwhile the GeoGebra Community has shared more than 40,000 examples on GeoGebraTube in less than two years.

In parallel with the improvement of the Java based GeoGebra software, the GeoGebra Team has started to develop an HTML5 version of the software to make it available on many different devices. The first step was to release GeoGebra in the Chrome WebStore and make it available running in any web browser. However, touch devices needed rethinking of the user interface as well as allowed introducing new functionalities. In September 2013, Tablet Apps for Windows 8, Android and iOS are to be released making GeoGebra available for even more students and teachers. In our talk, we will show functionalities of the new GeoGebra Tablet Apps, give an overview of software development on 3D, Statistics, STEM, GeoGebraTube and show some examples of GeoGebra use in different countries and learning environments.

On the development of an uber-modern techno-blended teaching and learning model for mathematics in South Africa

AUTHORS: Werner Olivier

AFFILIATIONS: Nelson Mandela Metropolitan UNiversity, FirstRand Chair in Maths Education

In this talk we describe the advent of a teaching and learning model that was developed with the aim of addressing the dire mathematics education crisis in South Africa. A description will be given of innovative approaches to harness some of the latest ICT options for flexible teaching and learning support for secondary school learners and teachers. Included in the talk will be a demonstration of curriculum aligned content support for learners via Android Tablets and mobile phones. Recent implementations of a techno-blended model in learner incubation projects and skills development programmes for teachers will be also be discussed with reference to successes and challenges that were experienced.

MathDisk: An Interactive Learning Environment

AUTHORS: Mohamed Jaffarali, Ajit Kumar

AFFILIATIONS: Mathdisk Technologies, Department of Mathematics Institute of Chemical Technology Matunga, Mumbai 400 019

In this article we look at new advances in technology for interactive teaching and learning through "MathDisk" for School and College Mathematics. MathDisk, which is designed exclusively for educational purposes, can help students and teachers to experiment and explore mathematics using web. What distinguishes MathDisk from the numerous other dynamic geometry tools currently available is its approach and philosophy. In almost all the Math tools, trying to do anything beyond graphing a simple 2D function requires writing code using the tool''s native programming language. MathDisk on the other hand allows the users to express equations as they see it in their textbooks using "Natural Math Notations". The equal emphasis to both the symbolic and visual representations of Mathematics makes MathDisk an ideal tool to create online interactive mathematics textbooks. MathDisk also uses "Integrated Rigid Body Dynamics" which can help students understand the abstract nature of mathematical structures using simulated physical models. Users of MathDisk can use scripting based on the syntax of popular "processing" language to produce amazing math and physics models. "Sequencer" module of MathDisk allows users to deconstruct a given mathematical model by showing how individual steps are transformed and assembled to produce the final output. Unlike desktop based applications, MathDisk allows users to share their individual resources and their entire working space over web, a key feature in todays interconnected world.

Effects of Hall Current on MHD Natural Convection Flow with Heat and Mass Transfer of a Chemically Reacting, Heat Absorbing and Radiating Fluid past an Accelerated Moving Vertical Plate with Ramped Temperature through a Porous Medium

AUTHORS: Syed Modassir Hussain, Gauri Shanker Seth

AFFILIATIONS: O. P. Jindal Institute of Technology, Indian School of Mines, Dhanbad, Jharkhand

Effects of Hall current on unsteady hydromagnetic natural convection flow with heat and mass transfer of an electrically conducting, viscous, incompressible, chemically reacting, heat absorbing and radiating fluid past an accelerated moving vertical plate with ramped temperature through a porous medium in the presence of thermal and mass diffusions is studied. The exact solutions of momentum, energy and concentration equations, under the Boussinesq approximation, are obtained in closed form by Laplace Transform technique. The expressions for skin friction, Nusselt number and Sherwood number are also derived. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically whereas numerical values of skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of pertinent flow parameters.

Keywords: Hydromagnetic natural convection, ramped temperature, chemical reaction, heat absorption, Nusselt number, Sherwood number.

Activity Theory: what does it have to offer to research and practice with mathematics and technology?

AUTHORS: Kate Mackrell

AFFILIATIONS: University of London

Activity Theory, originating from Marx, Vygotsky, Leontiev and Engestrom, is a theoretical framework in which the fundamental unit of analysis is that of purposeful activity in a cultural-historical context. This paper will introduce and critique the basic concepts of Activity Theory and the ways in which it has been applied in research and practice in interaction design (which includes HCI) and mathematics education using technology.

Technology enhances classroom control and improves students’ performance

AUTHORS: Bikash Jain

AFFILIATIONS: Future Learning, Educomp Solutions Ltd

Education without proper assessment and gap-filling process is futile
Sharing your knowledge without understanding your audience is not effective
Concept sharing without dynamic, engaging and multiple representations is not modern

Education today has changed its shape – it has oriented itself with multi facet aspect and technology. Explanation involves multi-dimensions: Text, pictures, video, animation, technology, and rehearsal. Pupils are from different culture/background; educators have to understand them and their understanding level before speaking the first bits of curriculum. Concept teaching and deliberation should have exploration suitable to everyone. And then there has to be a proper/quick assessment followed by remedial system in place. All this revolves around two critical persons: Educator and student. Both are under tremendous pressure to achieve excellence.
Use a UNIQUE bundle of technology, off-setting the pain area and supplementing education.
Won’t it be interesting to enquire which quadrilateral shape would cover the maximum area with constant perimeter, taking a check on prerequisite knowledge, dynamic exploration and then quick assessment, and to close it with remedial note, if any.
Analysis points:
1. What is the magnitude of the effects of technology on schooling outcomes concerning mathematics education?
My conclusions touch on the need for a proper technology-integration, for effective strategies to stimulate deep learning, for goal-directed assessments, for addressing the needs of a would-be mathematically literate. The evolution of students’ understanding after having gone through this kind of procedure is unmatchable.

Role of Technology within Teaching and Studying-“Connect”

AUTHORS: Mujo Mesanovic, Madhu Ashok Bathija

AFFILIATIONS: American University of Sharjah

Almost all universities in the world use some kind of online learning product to support and enhance learning. In the field of mathematics there are many products such as Pearson''s web based learning product, McGraw-Hill have Connect and Alex and there are many others. We would like to present our experience about McGraw-Hill product called Connect. In this paper we would like to describe firsthand experience using this educational tool for enhancement of learning and teaching of mathematics at university level. We are describing three different approaches to the Connect from faculty side, students’ side and administrators’ side. We show beneficial factors of the product as well as some difficulties that may happen while using Connect. At the end we present some significant results from the case study that we conducted while using the product in the pre-calculus class for architects at the American University of Sharjah.

Developing New Models Using Percentage Time Series

AUTHORS: Shou Hsing Shih

AFFILIATIONS: American University of Sharjah

In time series analysis, it is common to use the differencing filter to transfer a nonstationary time series into a stationary one, and normality is often assumed for such stationary time series if someone is interested in its distribution. The purpose of the present study is to look into the probability distribution of different time series, and find new simple models for different stocks using our newly developed methodology. In this study, we chose several major companies from the New York Stock Exchange and defined a percentage series using each of their daily closing prices. Some simple new models are proposed for these percentage series. Using some recent developments, these models are shown to have closed forms and so the potential for wide applicability.

Explore Runge-Kutta Method with Advanced Scientific Calculator

AUTHORS: Wei Ching Quek

AFFILIATIONS: Singapore Polytechnic

Students always find solving First Order ODE numerically by Runge-Kutta method tedious and prone to errors. We will use scientific calculator to assist the learning and implementation of Runge-Kutta method
This workshop is consists of two activities:
1. Getting Started
Begin with a quick introduction to Runge-Kutta method, followed by exploring essential features of the scientific calculator CASIO fx-991es plus that to implement the procedures.
2. Problems Solving/Discussion
Examine some applications of equations in engineering. Participants will explore the solution to gain further insights to the problem.

Learning functions and equations with an advanced scientific calculator

AUTHORS: Barry Kissane, Marian Kemp

AFFILIATIONS: Murdoch University

While scientific calculators have been available since the 1970s, advanced versions have been developed recently to suit the needs of mathematics education and extend the mathematical capabilities to equations, vectors, matrices, series, complex numbers, probability and statistics, as well as elementary calculus operations of integration and differentiation. So, these calculators provide powerful learning opportunities for many aspects of mathematics treated these days in senior secondary school and university curricula, as well as giving students access to efficient calculation. This workshop will use some of the activity materials for the CASIO fx-991ES-PLUS calculator that we have recently developed to consider some of the ways in which learning functions and equations can be enhanced. Previous experience with this calculator is not assumed.

Learning calculus and sequences with an advanced scientific calculator

AUTHORS: Marian Kemp, Barry Kissane

AFFILIATIONS: Murdoch University

While scientific calculators have been available since the 1970s, advanced versions have been developed recently to suit the needs of mathematics education and extend the mathematical capabilities to equations, vectors, matrices, series, complex numbers, probability and statistics, as well as elementary calculus operations of integration and differentiation. So, these calculators provide powerful learning opportunities for many aspects of mathematics treated these days in senior secondary school and university curricula, as well as giving students access to efficient calculation. This workshop will use some of the activity materials for the CASIO fx-991ES-PLUS calculator that we have recently developed to consider some of the ways in which learning calculus and sequences can be enhanced. Previous experience with this calculator is not assumed.

Learning with graphics calculators

AUTHORS: Marian Kemp, Barry Kissane

AFFILIATIONS: Murdoch University

Graphics calculators provide opportunities for both students and their teachers to engage with mathematics in new ways. This workshop is intended to offer an introduction, for those new to this technology, of some of the possibilities open to classrooms in which such technology is present. A key aspect is that graphics calculators can be used to support student learning of mathematics, even in situations for which external examination rules do not permit their use in formal assessment. We will illustrate the possibilities through drawing upon a range of mathematics areas, including the study of functions, equations, differential calculus and elementary statistics. The workshop will use some of the activity materials for these calculators that we have recently developed. The focus will be on teachers of senior secondary or early undergraduate mathematics. We will use both the CASIO fx-CG20 colour graphics calculator and the Casio fx-9860GII graphics calculator, but do not expect that participants will have prior experience with these calculators.

AUTOGRAPH – DYNAMIC SOFTWARE FOR 2D and 3D GRAPHING

AUTHORS: Douglas Butler

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

Why is Autograph different? Autograph is widely used by teachers and students in UK and many other countries of the world, and a version for IOS and Android tablets is well under way. Autograph can help to visualise key concepts through dynamic objects, and the user interface is straightforward and friendly. Autograph has been localised in 21 languages (including Arabic). There are a large number of resources online (videos, data, images, tutorials) and files can be saved straight to HTML for viewing on the web. This workshop will cover graphing topics in 2D (from coordinate geometry to differential equations) and 3D (from transformations of shapes to surfaces, lines and planes). The interface gives users time to explore and investigate using a controllable ‘slow plot’ feature, and animations are particularly effective because of the ability to control the step in real time.

Delegates attending this workshop may bring a laptop, and will be provided with a free installation of Autograph 3.3.
www.tsm-resources.com/autograph

Developing a Deeper Understanding of Mathematical Concepts Through Handheld Technology

AUTHORS: Wee Leng Ng

AFFILIATIONS: 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 several mathematical concepts through the TI-Nspire CX handheld.

EXPLORING CONCEPTS AND APPLICATIONS OF MATHEMATICS USING A GRAPHICS CALCULATOR

AUTHORS: Jonaki Ghosh

AFFILIATIONS: Lady Shri Ram College, Delhi University

Handheld technology in the form of graphics calculators has brought about a shift of paradigm in mathematics teaching and learning in many countries across the world. The last two decades has witnessed extensive research related to the pedagogical opportunities offered by these tools. Mathematics teachers and educators have been investigating various ways of integrating these devices with classroom teaching in order to enhance visualization, conceptualization and to make mathematics accessible to students of varying levels of ability. The computer-like features and easy portability of graphics calculators provide significant advantages over computer – aided software packages. These devices have proved to be extremely handy for performing mathematical modeling activities and exploring applications of mathematical concepts in the classroom.
This workshop session will illustrate the use of the CASIO fx 9860 GII graphics calculator in exploring mathematical applications from a wide range of areas which are relevant at the senior secondary school and undergraduate level. The explorations will be based on the topics of matrix theory, probability and statistics and will include
a) Application of matrices to weather forecasting, brand switching, ranking pages on the web
b) Cryptography
c) Statistical Inference
d) Simulating problems in probability, such as the Birthday Paradox and the Monty Hall Problem. Participants will be given a hands-on experience on the calculator and activity worksheets with calculator enabled explorations will be provided during the workshop.

Relationship Among Familiar Polyhedrons

AUTHORS: Jen-chung Chuan

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

With Cabri 3D as the tool, we are to guide the audience to construct
1) the largest cube included in a regular tetrahedron;
2) an animation displaying how a regular octahedron may be turned into a rhombic dodecahedron;
3) same as 2) for the icosahedron-rhombic triacontahedron pair;
4) same as 3) for the dodecahedron-rhombic triacontahedron pair;
5) "tight configuration" formed by a chain of five regular Platonic solids.

AUTOGRAPH – DYNAMIC SOFTWARE FOR PROBABILITY and STATISTICS

AUTHORS: Douglas Butler

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

This workshop will cover the use of Autograph in the teaching of probability and statistics topics from High School and 1st year College courses. Many teachers find this aspect of mathematics challenging, and Autograph can really help both teachers and students to understand the basic concepts through the use of dynamic objects and real data. The use of the on-screen scribble tool can be particularly effective in questioning their understanding before the computer undertakes a simulation.
The study of discrete and continuous probability distributions is particularly effective in Autograph, including a clear treatment of Type 1 and Type 2 errors.
Delegates attending this workshop may bring a laptop, and will be provided with a free installation of Autograph 3.3.
www.tsm-resources.com/autograph

Tricky constructions of folding nets of platonic solid and experiments with their convex hulls with Cabri 3D

AUTHORS: Jean-Jacques Dahan

AFFILIATIONS: IREM of Toulouse

With Cabri 3D, we will construct different nets of a given platonic solid using transformations : these nets will be foldable. These constructions are simple even if they are tricky. We will use some of these nets to construct their convex hull when not completely folded to evaluate experimentally their Net Factor (see the definition in my paper)

Interactive Learning and Teaching Mathematics with dynamic software MathDisk

AUTHORS: Ajit Kumar, Mohamed Jaffarali

AFFILIATIONS: Mathdisk Technologies, Department of Mathematics Institute of Chemical Technology Matunga, Mumbai 400 019

A growing number of researchers are uncovering evidence that show readers are better able to recall long-term what they have read in printed books as compared to similar materials read via an electronic screen. In the light of this evidence, the leading US textbook publisher Houghton Mifflin Harcourt conducted a study among California Students which concluded that when it comes to engaging students, format plays far more of an important role than the content. Equally well established, is how the interactive and exploratory nature of dynamic mathematical software improves the cognitive abilities of students. With an increasing number of teachers incorporating dynamic mathematical software in their teaching sessions, how can we retain the benefits of Textbooks without forgoing the interactivity offered by Dynamic Mathematical software? MathDisk (www.mathdisk.com), designed from the ground up, has striven to address this challenge by uniting the latest in educational research with advancements in technology. The features of MathDisk is specifically geared towards combining the format of the traditional book with multimedia capabilities available on Desktop apps and Tablets; so students never feel any disconnect, as they can instantly recognize and correlate the content. This workshop will demonstrate how using plain natural math notation enables users to create Mathematical models involving Vectors, Matrices and simple algebraic expressions to create an interactive MathDisk worksheet. The exercises will also demonstrate the overlapping capabilities of the equation editor, geometric transformations, graph sheets, and annotations with free form layout combining seamlessly to infuse dynamic interactivity with the look and feel of textbooks. The workshop will introduce the “Sequencer” module of MathDisk, a novel approach that allows users to deconstruct a given mathematical model by showing how individual steps are transformed and assembled to produce the final output. By the end of this session users will be familiar with the fundamental concepts of MathDisk and be able to create new 2D/3D Mathematical worksheets on their own.

Technology enhances classroom control and improves students’ performance

AUTHORS: Bikash Jain

AFFILIATIONS: Future Learning, Educomp Solutions Ltd

§ Education without proper assessment and gap-filling process is futile §
§ Sharing your knowledge without understanding your audience is not effective §
§ Concept sharing without dynamic, engaging and multiple representations is not modern §
Education today has changed its shape – it has oriented itself with multi facet aspect and technology. Explanation involves multi-dimensions: Text, pictures, video, animation, technology, and rehearsal. Pupils are from different culture/background; educators have to understand them and their understanding level before speaking the first bits of curriculum. Concept teaching and deliberation should have exploration suitable to everyone. And then there has to be a proper/quick assessment followed by remedial system in place. All this revolves around two critical persons: Educator and student. Both are under tremendous pressure to achieve excellence.
Use a UNIQUE bundle of technology, off-setting the pain area and supplementing education.
Won’t it be interesting to enquire which quadrilateral shape would cover the maximum area with constant perimeter, taking a check on prerequisite knowledge, dynamic exploration and then quick assessment, and to close it with remedial note, if any.
Analysis points:

1. What is the magnitude of the effects of technology on schooling outcomes concerning mathematics education?
My conclusions touch on the need for a proper technology-integration, for effective strategies to stimulate deep learning, for goal-directed assessments, for addressing the needs of a would-be mathematically literate. The evolution of students’ understanding after having gone through this kind of procedure is unmatchable.

Hands on workshop : TI Nspire CX Handheld

AUTHORS: PIYUSH MARU

AFFILIATIONS: IBO, CIE

This HoW (Hands on Workshop) addresses the application of the latest technologies (GDCs) in teaching and learning of Mathematics. The HoW discusses the International Standards in teaching and learning of Mathematics with respect to application of technology (GDCs).

The HoW will cover the major applications of the GDC in the international mathematics’ curriculum such as IBDP and IGCSE.

By the end of the HoW the learners will be better able to apply and understand the GDCs to the pedagogy of teaching and learning mathematics at par with the international standards.

Hands on workshop : TI 84 Plus C SE

AUTHORS: PIYUSH MARU

AFFILIATIONS: IBO, CIE

This HoW (Hands on Workshop) addresses the application of the latest technologies (GDCs) in teaching and learning of Mathematics. The HoW discusses the International Standards in teaching and learning of Mathematics with respect to application of technology (GDCs).

The HoW will cover the major applications of the GDC in the international mathematics’ curriculum such as IBDP and IGCSE.

By the end of the HoW the learners will be better able to apply and understand the GDCs to the pedagogy of teaching and learning mathematics at par with the international standards.

Dynamic Resources for International Baccalaureate Mathematics

AUTHORS: Kate Mackrell

AFFILIATIONS: University of London

A resource using dynamic geometry software is being co-developed by teachers in Ontario, Canada and Oxford, England for the new International Baccalaureate Mathematics at standard and advanced level. The aim is to promote student exploration of mathematics in dynamic and visual ways. This workshop will explore some of the resources for Geometer's Sketchpad, Cabri II Plus and Cabri 3D involving sequences and series, functions, vectors, and calculus.

Creativity Development in Mathematics and Technology Education

AUTHORS: Janchai YINGPRAYOON, Dr.rer.nat., Deputy Director,

AFFILIATIONS: International College, Suan Sunandha Rajabhat University, Bangkok, THAILAND, janchai.yi@ssru.ac.th

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 lecture 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. Some creative hands-on activities will also be demonstrated.

Consideration about the possibility of the technology in the department of elementary school arithmetic of Japan

AUTHOR: Tsutomu Ishii

AFFILIATIONS: Bunkyo Univ.

Although the skill of the lesson is excellent in the elementary school in Japan, it is cowardly to introduction of new technology at it.In order to overthrow it, it is necessary to clarify power of technology in an arithmetical lesson.This consideration examines a possibility of converting a lesson about a media board.Analysis of the protocol in a lesson attains the purpose of research.

GeoGebra for tablets and on other devices

AUTHORS: Zsolt Lavicza, Balazs Koren

AFFILIATIONS: University of Cambridge, Eotvos Lorand University, Budapest

The development of the GeoGebra software has been accelerated during the past years. GeoGebra 4.0 was released in September 2011 with many new functionalities, among others extended statistical features and one-click upload to GeoGebraTube. GeoGebra 4.2 has been available since September 2012, which includes the long awaited feature the Computer Algebra System (CAS) view. Meanwhile the GeoGebra Community has shared more than 40,000 examples on GeoGebraTube in less than two years.

In parallel with the improvement of the Java based GeoGebra software, the GeoGebra Team has started to develop an HTML5 version of the software to make it available on many different devices. The first step was to release GeoGebra in the Chrome WebStore and make it available running in any web browser. However, touch devices needed rethinking of the user interface as well as allowed introducing new functionalities. In September 2013, Tablet Apps for Windows 8, Android and iOS are to be released making GeoGebra available for even more students and teachers. In our talk, we will show functionalities of the new GeoGebra Tablet Apps, give an overview of software development on 3D, Statistics, STEM, GeoGebraTube and show some examples of GeoGebra use in different countries and learning environments.