Abstracts for ATCM 2013
Abstracts for Panel Discussion
"Technology
Integration in Math Curriculum"
Moderator:
WeiChi Yang (USA: wyang@radford.edu)
Members:
Douglas Butler (UK: debutler@argonet.co.uk),
Dinesh Kumar
(India: kvs.addlcacad@gmail.com),
Heechan Lew
(South Korea: hclew@knue.ac.kr),
Werner Olivier
(South Africa: waolivier@nmmu.ac.za)
Contribution from Douglas Butler
When technology first hit schools, it was
in the form of hand held calculators in the hands of the students. Then the
balance shift to the teachers when increasingly powerful computer software
solutions became available for the teachers to use dynamically and
interactively in front of the students. Now the pendulum is swinging back to
the students with tablets and smart phones offering a rapidly increasing menu
of mathematical apps. There is little doubt that students can learn mathematics
more securely if they do so by selfdiscovery. However, the need for routine
drill and practice never goes away, otherwise the learning can end up very
superficial.
The internet of course is the other major
factor, allowing peertopeer discussions, instant access to dynamic resources
and the flipped classroom concept. None of this has a place in the lives of
busy teachers without continual professional development (CPD), and in these
troubled economic times, training budgets are dangerously vulnerable to
pruning.
Contributed by Dinesh Kumar
Indian perspective: In the present era ICT
is considered to be an extremely powerful tool for teachers and students in the
area of school as well as higher education. It has tremendous potential not
only in providing access of education to a large number of deprived but also in
enhancing the understanding of learners. Mathematics education is no exception
to this. If we focus on understanding of concepts by learners then it is an
established and accepted fact that teachinglearning aids have always been in
use to enhance learning. ICT has provided tools for integrating all teaching
aids in highly effective way and also made easily accessible to teachers and
taught. It is also a fact that in the process of teaching and learning the
appropriate assessment of learning, diagnosis of difficulties in understanding
of concepts by taught and providing remediation for diagnosed difficulties are
of paramount important. ICT tools evolved to address these issues have proved
to be extremely useful nowadays. In addition, it has opened up the boundaries
of space and time for students as well as teachers and it has potentials for
anywhere and anytime learning. Even debates are there to switch to explore the
possibilities of exploiting potentialities of Mlearning by using mobile
phones.
But considering the diversities of access
as well as capabilities of teachers to use ICT tool, it is also equally
important to build their capacity in such a way that these tools are used in a
comfort zone by our teachers. In addition, uniqueness of ways of teaching by
teachers and varied pace of understanding of concepts by learners is also important.
This point is more important and relevant especially for teaching and learning
of Mathematics. From this perspective, available ready to use ICT resources
and tools may not prove to be all effective and panacea for all problems.
Therefore, the capacity building of both teachers and taught for these
technology enabled learning is of paramount importance so that all ICT
resources serve as building block in the process of conceptual understanding of
all subjects including Mathematics and ICT tools as a medium to achieve these
objectives.
Contributed by HeChan Lew
Korean Perspective: The current Korean
mathematics curriculum recommends technology in its “guideline for instruction”
that “computers and calculators should be actively utilized to improve
understanding of concepts and problem solving or thinking abilities in
classrooms.” According to this guideline, technology is being used even within
limited bound in most of all Korean textbooks. However, the problem comes from
the fact that the curriculum has been developed for teachers to be able to
teach without a computer. That is, its contents can be learned without the
computer, although teachers and students are permitted to use in their classes.
Another problem is teacher’s awareness toward technology. The use of computers
depends on the interests and abilities of individual teachers, but many
teachers are not rising to this challenge because they do not necessarily feel
the need to use the computer. Therefore, computer should be “substantialized”
in the mathematics curriculum, rather than just appeared on some pages of the
textbooks. To be so done, many mathematical contents to be learned far more
meaningfully than in a paper and pencil environment should be designed and
invited to the curriculum. Furthermore, various mathematical activities with
computers should be designed to be able to be used in the formal examination.
Contributed by Werner Olivier
South African perspective: In South Africa
a binary situation in schools exist with private and ex model C (mostly white)
schools (<10% in total) are vastly better resourced and infrastructure
compared to previously disadvantaged (black) schools. As a result, evolving
technologies are having some effect in the former category of schools with access
to internet, computer laboratories and teaching with laptops & data
projectors becoming part of the T&L pedagogical mix. A small percentage of
schools in this category are also beginning to experiment with Tablet
technology en elearning material to complement the predominantly textbook
support for pupils.
In contrast, the balance of schools in
South Africa (>90% of the total) are mostly without access to internet and
physical infrastructure to integrate similar elearning strategies. Additional
challenges in this regard are the acute shortage of available Math teachers as
well the lack of skills (content knowledge and ICT) amongst many practicing
teachers in this – category of schools.
Abstracts for Plenary Talks and Invited Papers

Exact Real Calculator for Everyone 
AUTHOR: Weng Kin Ho 
AFFILIATIONS: National Institute of
Education 
Despite its simplicity and versatility,
the wellknown Floating Point System (FPS) has a serious shortcoming: the
finite nature of a computer makes roundingoff inevitable. Because of this,
FPS can sometimes lead to serious computational errors, i.e., a small
roundoff 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 userfriendly scientific calculator ERCE using
Haskell, capable of ERA. With a functionalprogramming 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 userfriendly and seamless.
Our noncommercial software “VisuMatica” long ago supports well nonlinear
transformations of twodimensional 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, 3Dnonlinear 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), AutographMaths 
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 touchdriven environments, and a new wave of
writers has emerged who are serving up excitingly fresh ideas.
In this presentation Douglas will
cherrypick 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: Jenchung 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 thoughtprovoking 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: WeiChi 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/countryinformation/india/ 

Key factors for Successful Integration of Technology
into the Classroom: Textbooks and Teachers 
AUTHORS: Heechan Lew, SeoYoung 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 

A new tetrahedra origami model was
discussed in this paper. Sommerville in 1922 found four kinds of tetrahedron could
fill space. This model starts from a rectangle paper, whose shape ratio is 1:√2, to produce one Sommerville’s
main tetrahedron. It is proved that as long as the original paper is big
enough, one can produce by this origami method more and more so called
Sommervilletetrahedrons without cutting or pasting. Furthermore, these
tetrahedrons fill threedimension space in the same time. Just like Peano
curve fills twodimensional space, the original paper (two dimensional
manifold) used in producing tetrahedrons fills the threedimensional space.
This paper also introduces some interesting models in the lower number cases.

Case Studies in Experimental Mathematics 
AUTHOR: Shailesh Shirali 
AFFILIATIONS: Sahyadri School (KFI),
Krishnamurti Foundation India, Rishi Valley School (KFI) 
Experimental mathematics is now a
wellaccepted genre of study. It is a field in which computerassisted 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 integersided 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
paperpencil 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 RealWorld 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 RungeKutta method. We implement these using a MATLAB literate
programming approach and show how one can obtain best fit parameters for
given data from the realworld 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 realworld problems with big
data. The results obtained from both methods are comparable yielding similar
bestfit parameters for a given set of data and they suggest that the methods
proposed herein are reliable and robust for solving realworld applications. 
Abstracts for Full Papers

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 xy 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 threedimensional sphere and dynamic
construction of common perpendicular 
AUTHORS: yoichi maeda 
AFFILIATIONS: Tokai University 
In this paper, we introduce gKlein modelh of the threedimensional 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
threedimensional 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 threedimensional sphere has a relation with
Klein model of the threedimensional 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
countryIndia 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
problemsolving 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
eLearning 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 computeraided assessment system for
mathematics, and functions as a plugin 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 studentfs 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 STACKfs rich functionality, questions must be designed carefully.
Welldesigned questions can be valuable educational resources, especially in
an elearning environment. To promote the sharing of highquality questions
for use in online tests, we developed an Item Bank System for the mathematics
elearning 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 elearning 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 htoolh 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 theoryh. 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 ecommerce; electronic communications such as mobile
communications, sending private emails; business transactions; PayTV;
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 preservice
teachers. We show that such calculators, although very lowpowered compared
with standard computer based numerical systems, are quite capable of handling
textbook 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: JeanJacques 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 nonhomogeneous halfspace 
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 nonhomogeneous halfspace. 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 halfspace is homogeneous medium. The velocities of Love waves have
been calculated numerically as a function of wave number kh. The effect of
nonhomogeneity 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: CheeKeong Chong, Marzita Puteh,
SweeChoo 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. Pretest was carried out
to find out their performance. Later, they were exposed to spreadsheet
approach on the same topic. Then a posttest was administered to assess their
performance. Posttest 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. 

Intervalsymbol 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 intervalsymbol method with
correct zero rewriting or ISCZ method for short, which is an extension of the
socalled interval method, to obtain exact results while reducing exact
computations. Namely, this method uses not only a floatingpoint 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 floatingpoint
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 nonrational 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
problemsolving 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 Gtype seismic waves in
heterogeneous layer overlying a nonhomogeneous halfspace 
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 nonhomogeneous halfspace are varying with depth.
Dispersion equations have been obtained in closed form. As a special case
when the medium and halfspace 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. nonvisual communication analyze the potential of gaze
points to express subconscious intentions. 

Graphic Input System in Elementary Geometry for
Nonvisual 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 nonvisual 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 handwritten 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 BASICPASCAL 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. 
Abstracts for Papers with Abstract Only

A Comparison of Polytechnic Students’ Attitudes toward
Advanced Scientific Calculators 
AUTHORS: Wei Ching Quek, Chew Pheng
KokMak 
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 facultystudent research.
This presentation reports on one of several recent facultysponsored projects
that merge mathematics education research and technology. Groups of
prospective elementary school teachers received instruction in spatial
visualization using either concrete 3D 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, studentfaculty component of the project. Results showed (1)
significant gains only for the technology group; and (2) increasing
studentreported 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 eand 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 selfevaluation 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), AutographMaths 
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.tsmresources.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 
Keywordsintensity 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 + y1y2. 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, 2738). 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 technologyoriented 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
Beginnerlevel 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 highquality
graphics in LaTex documents which can be implemented in different Computer
Algebra Systems including R. R is a popular opensource 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_4a_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, SangJe Cho,
KwangSang 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 epsilondelta 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 upto 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 geometryrelated 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 oneclick 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 ubermodern technoblended
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 technoblended 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
culturalhistorical 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
gapfilling 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 multidimensions: 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, offsetting 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 technologyintegration, for
effective strategies to stimulate deep learning, for goaldirected assessments,
for addressing the needs of a wouldbe 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, McGrawHill have Connect and Alex and there are many
others. We would like to present our experience about McGrawHill 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
precalculus 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. 
Abstracts for Handson Workshops

Explore RungeKutta Method with Advanced Scientific
Calculator 
AUTHORS: Wei Ching Quek 
AFFILIATIONS: Singapore Polytechnic 
Students always find solving First Order
ODE numerically by RungeKutta method tedious and prone to errors. We will
use scientific calculator to assist the learning and implementation of
RungeKutta method
This workshop is consists of two activities:
1. Getting Started
Begin with a quick introduction to RungeKutta method, followed by exploring
essential features of the scientific calculator CASIO fx991es 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 fx991ESPLUS 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 fx991ESPLUS 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 fxCG20 colour graphics
calculator and the Casio fx9860GII 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), AutographMaths 
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.tsmresources.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 TINspire 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 computerlike 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 handson experience on the
calculator and activity worksheets with calculator enabled explorations will
be provided during the workshop. 

Relationship Among Familiar Polyhedrons 
AUTHORS: Jenchung 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 icosahedronrhombic triacontahedron pair;
4) same as 3) for the dodecahedronrhombic 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), AutographMaths 
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 onscreen 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.tsmresources.com/autograph 

Tricky constructions of folding nets of platonic solid
and experiments with their convex hulls with Cabri 3D 
AUTHORS: JeanJacques 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 longterm
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 â€œSequencerâ€ 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
gapfilling 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 multidimensions: 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, offsetting 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 technologyintegration, for
effective strategies to stimulate deep learning, for goaldirected
assessments, for addressing the needs of a wouldbe 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 codeveloped 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, problemsolving skills and creativity.
Some creative handson activities will also be demonstrated. 
Abstracts for Poster Sessions

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 oneclick 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. 


Abstracts for TIME 2013
Abstracts for TIME Invited Papers
Visualizing Mathematics with Mathematica
AUTHOR: Aravind Hanasoge,
girish@gteindia.com
AFFILIATIONS: Wolfram Research, Inc.,
Bangalore, India
In this talk we look at Mathematica and how
it can play a key role in teaching Mathematics and other related subjects such
as Image Processing, Control Systems, Wavelets, Signal Processing, Statistics
etc.
After briefly introducing Mathematica, the
talk quickly moves on to the key capabilities of Mathematica including Symbolic
& Numerical Processing, Dynamic Interactivity, Creating documents,
technical papers, presentations & automatic reports, before focusing on its
visualization
capabilities.
Visualization capabilities of Mathematica
include many routines for plotting both data and functions in 2 and 3
dimensions and also contour and density plots, parametric plots, vector &
stream plots etc. We look at how numerical solutions to differential equations
(ODE, PDE, DAE etc..) can be visualized and manipulated based on
initial/boundary conditions and parametric values using sliders and other
dynamic control objects. Several special plotting functions are available in
areas such as Control Systems (Bode Plot, Nyquist Plot, Root Locus Plot ...),
Statistics (2D & 3D Histograms, PDF/CDF, Charts...), Image Processing (Feature
Detection, Noise removal, Segmentation ...) and many more. These would be
looked at briefly.
Excerpts from a seminar given on
"Engineering Mathematics using Mathematica" based on Syllabus from
Pune University would be briefly looked at. We also look at how Mathematica can
be very useful in preparing quizzes, reports etc.
Finally, we look at how Mathematica
can be connected to other systems through links such as MathLink, JLink,
.NETLink, RLink, CUDALink etc..
ON THE SHOULDERS OF THE TECHNOLOGY GIANT
AUTHOR: Sneha Titus, sneha.titus@gmail.com
AFFILIATIONS: Azim Premji University,
Bangalore, India
Technology has become the persuasive
buzzword in hardselling educational institutions and educational packages. Yet
how much thought has gone into the creation of a ‘technoclassroom’? Are there
institutional practices and routines through which technology is incorporated
in pedagogical practice? When does technology enable the class? How do the
right questions in a tech enabled investigation push the student’s learning to
the next level? How do teachers ensure that real learning has occurred in the
techenabled classroom? This talk will focus on the last three questions.
A teacher who is a first time user of
technology in the classroom seeks to exploit the potential of the technology.
But there is a danger of shifting the focus to the technology rather than the
mathematics. It is time for teachers to let the mathematics speak through the
technology. Rather than seeing technology as an attention seeking device, I
propose that technology is the giant on whose shoulders students can see
further in mathematics. In this paper, I will define the concept of
‘functional fixedness’ and then move to the use of technology as a ‘path
smoother’. I will focus on the importance of Technology Pedagogy Content
Knowledge and illustrate with some examples the possibilities in the use of
technology in the mathematics classroom.
NCF 2005 speaks of the importance of
inclusion. If teaching focuses more and more on the brilliance of technology to
deliver good teaching, then spaces for discrimination will naturally arise
along economic divides. If however, the focus is on the pedagogical brilliance
of the techenabled lesson, then even the simplest and most available technology
can align with the vision of NCF. In short, the clarities sought in teaching
with technology should be illuminating rather than blinding. Through this
paper, I show that it is time to enable the teacher rather than the technology.
Technology as motivation for learning
AUTHOR: Abhiram Ranade,
ranade@cse.iitb.ac.in
AFFILIATIONS: Department of Computer
Science & Engineering, I.I.T. Bombay, Mumbai 400076
Perhaps the most difficult problem in
education is motivation: how can we make the students want to learn? Extrinsic
motivation such as a prize or a promise of a job or just praise can be used,
but in the long run this is stressful for the teacher and the student.
Instead, if the learning produces some immediate excitement, and a feeling of
accomplishment, then students will learn happily.
Following in the footsteps of Papert and
others, we propose that elementary computer graphics can be a strong motivation
to study trigonometry at the high school level. We report some preliminary educational
experience in this area. Drawing and animating geometric objects in
interesting ways requires properly understanding geometry and trigonometry.
But once these subjects are mastered, fairly elegant and intriguing animations
can be produced. The resulting thrill is very different from the thrill of
winning a prize; it is much more direct and likely lasts longer. The thrill is
orders of magnitude stronger than the traditional motivation for trigonometry:
calculation of heights of buildings.
Most educational curricula do not empower
students to build things that they might want to. At best they are forced to
build what adults want and like. But computer graphics and programming can
open a world where the student is the master. But acquiring the mastery
requires learning good math and logic. Educationists must seize this opening.
Changing Dynamics of Mathematics Classroom
AUTHOR: Sangeeta Gulati,
sangeetagulati92@gmail.com
AFFILIATIONS: Sanskriti School, New Delhi,
India
Internet and faster broadband speeds have
changed the lives of today’s learner. Information is available to them at their
finger tips; teacher or the text books are not the only source of information
for them. Traditional teaching methods struggle to captivate students or
motivate them to learn. Changing the pedagogy in the classroom has been
identified as a solution to developing new learning environments. The change of
classroom dynamics seems to be directly related to the teaching strategies
incorporated in the classroom where students find that learning is fun. The
integration of technology in education is no longer a "new" idea;
this paper will illustrate how it is making a difference to the math classroom.
Use of YouTube videos which works as a
‘hook’ to grab attention of students or explain the concepts in an entertaining
and simple ways has found its place in Math classroom. Online tutorials allow
students to revisit concepts taught and assess themselves at their own pace.
Almost fifty percent of the syllabus (CBSE) in class XII is based on Calculus;
many of the students achieve high scores but have no understanding of the very
basic concept of Derivatives. Dynamic software like Geometer’s Sketchpad and
GeoGebra has given life to many of the dreaded concepts of Precalculus and
Calculus. Dynamic visualizations leading to explorations allow for meaningful
discussions and the ‘aha’ moments. In my presentation I will share these ‘aha’
moments and use of other resources which have made teaching and learning fun.
Math and City
AUTHOR: Ravi Shankar, ravi@brainstars.in
AFFILIATIONS: BrainSTARS, Bangalore, INDIA.
Can our children’s math educational
experience be located in the city they live in? In their daily urban lives our
children are exposed to and negotiate with patterns and happenings, shapes and
proportions, measurements and calculations  all conceptual maths areas. But
are we as educators able to capture their imaginations and reveal the maths in
all the things they see around and in the urban experiences that shape them?
Can an alternative Maths learning be fun, relevant, and full of surprises while
aligning with the school curriculum and what our children are learning in the
classroom?
The entrenched Maths phobia in many of us
makes us look for stopgap solutions. For example: we will enroll our children
for tuitions or short courses where they will be taught how to tackle Maths –
fast counting, quick problem solving, multiple tests etc. We have never allowed
ourselves to imagine that our children deserve to enjoy the beauty and ideas of
Maths by letting them discover that Maths animate the world around us in a
playful, stimulating way.
How does a fruit vendor arrange all his
fruits in different layers that never seem to fall off his cart? When we keep
telling our children to have a balanced diet, what learning in proportions and
percentage are we giving them? Do the traffic signals have something to do
with geometry? Can license plate numbers of buses, cars, motorbikes, autos tell
something about squares, cubes, or the wonderful irrational number pi? Are
festivals, when shops outdo each other with their discount sales, a time for
our children to learn something captivating about the infinite range of decimal
numbers?
It’s time to make maths learning a rich,
immersive experience for our children and connect it to our cultural and social
life.
To impart this unusual Maths learning, the
activities have to be handson where the children’s real life experiences play
a big role in learning the Maths concepts, where the manipulatives designed are
childfriendly, creative, and safe and allow them to explore Maths without any
fear, where the space in which they learn Maths embodies the city they live in
and triggers interesting ways of learning, where the children are encouraged to
share their works in groups and listen to each other for feedback and insights
on the mathematical concepts they are learning, where the teachers are enabled
to be highly imaginative with the activity space and initiate activities
(outside of the workbook) based on the child’s experiences and learning, where
the takehome activities reinforce their new learning and connect to the
child’s environment.
It is indeed an unprecedented practice in
Maths learning where we put the experiences of the child at the centre of the
practice. It is a practice where we enable the teachers to have the time,
empathy, creativity, imagination, skills and tools to engage with the child in
a unique exploration of Maths. It is a practice that enriches what a child is
learning in the classroom.
Smart Board & GDC into the Secondary School
Mathematics Class Room.
AUTHOR: Antony Dsouza,
director@apwschool.com
AFFILIATIONS: Asia Pacific World School, Bangalore,
India
Mathematics is conceived as a subject
meant only for few selected scholars who needs imaginative mind and strong
logic. Use of right kind of technology can simplify mathematics and appreciate
mathematics by all secondary students. Smart boards, GDC along with several
Software can help to appreciate mathematics by one and all. Smart boards can
both guide secondary school students to deeper understanding of mathematical
structure, and enable students to move away from the “tools and techniques”
view of mathematics and start developing mathematical thinking. Smart boards
could be an instrument whereby ideas can be explored and relationships
discovered. For such goals to be fully realized, the technology needs to be
successfully integrated into the mathematics classroom. A first step in
achieving this is for the teacher to be motivated to learn the various
manipulations available in the Smart board in planning and creating lesson
plans. Quality education is essential for workforce and society and ICT are
claimed to quality education. In particular GDC have gained widespread
acceptance in secondary school mathematics classrooms which has an influence
upon student learning. . However Use of Smart board and calculator in Indian
education with some traditional teachers would look at as: a demon; servant; an
idol; a partner or; as liberator. This presentation will examine the claim that
Smart boards and GDC act as a “pedagogical Trojan Horse” moving teachers
towards student centered learning in the secondary mathematics Classroom.
Reasoning in Mathematics
(How deductively inductive reasoning can
be improvised)
AUTHOR: P. K. Chaurasia,
praveenc1@gmail.com
AFFILIATIONS: RIE Ajmer, India
Mathematics is probably the only branch of
knowledge that has a formal proof for a number of propositions. The strength of
Mathematics is its ability to prove its propositions. Perception may change
with regard to certain ideas in Science but it is not so in Mathematics.
Scientific observation depends upon the condition under which the observations
were recorded. Over the last few decades, perceptions of a number of ideas in
Science have changed. Mathematics does not depend on observation alone. Once
proved mathematically, a proposition holds good for all times to come.
There are five basic characteristics of
mathematics and also known as the inviolable scientific principles in
mathematics as defined below:
• Precision: Mathematical
statements are clear and unambiguous. At any moment, it is clear what is known
and what is not known.
• Definitions: Bedrock of the
mathematical structure
• Reasoning: Lifeblood of
mathematics
• Coherence: Every concept
and skill builds on previous knowledge and is part of an unfolding story.
• Purposefulness: Mathematics
is goaloriented. It solves specific problems.
In this article author is focusing
particularly on reasoning characteristic of Mathematics along with how
technology can support us to get maximum of it during teaching learning
practices.
There are two kinds of reasoning that
feature prominently in doing mathematics Deductive and Inductive reasoning.
Inductive reasoning is the kind of thinking
involved in recognizing patterns, similarities and equivalences, and using
these to predict further results and to formulate generalizations.
Deductive reasoning is the formulation of a
valid, logical argument to explain, demonstrate or convince others that a
solution to a problem must be correct, or that a mathematical theorem is proved
beyond doubt, or that a particular conjecture is true or false.
It is well experienced that at initial
stages in learning mathematics inductive reasoning is more significant than
deductive reasoning for children in that age range. For example, children in
beginning will learn to ‘describe patterns and relationships with numbers and
shapes, make predictions and test these with examples’. In the continuation
children will ‘propose a general statement involving numbers or shapes and
identify examples for which the statement is true or false’.
Deductive reasoning in its most powerful
form is used when we provide a proof of a mathematical result or theorem.
Formal mathematical proof is certainly beyond most children at upper primary
stage, but this does not mean that there is no place for deductive reasoning.
In this article author is giving few
examples to demonstrate how deductive flavour can be provided with in inductive
reasoning even at upper primary stage. In fact, this approach has been
discussed with several teachers during teachers training programme and their
feedback has also been observed while interaction with them for a period of
time. The approach of mixing deductive flavour while inductive reasoning has
given more enthusiasm among the learners and an increase level of children’s involvement
and engagement within the concepts has also been realized. Author also
emphasis how a technology based environment can be utilized to achieve the
approach comfortably by a common teacher in a common classroom.
Thinking with Pictures
AUTHOR: Ujjwal Rane,
Ujjwal.Rane@bentley.com
AFFILIATIONS: Bentley Systems Pvt. Ltd.,
Mumbai, India
In this paper we will revisit the graphical
or geometric approach for teaching mathematics. Its historic triumphs and its
current state of disuse are reviewed revealing the prevailing analytical bias.
Its applicability and benefits are highlighted with some examples from school
level topics. Common objections to conventional graphical techniques are
reviewed in light of the technological advances of today, offering Computer
Aided Drafting (CAD) as a tool to overcome these shortcomings. The power of CAD
and its unique advantages in modeling, analyzing and solving problems and
presenting the solutions to reveal patterns/ trends is demonstrated via two case
studies. These are taken from recreational mathematics and industrial
application to cover a wide range over which the graphical approach with CAD as
a tool can be effectively employed.
Teaching Mathematics Effectively using TINspire
AUTHOR: Thomas Yeo, thomas.yeo@ti.com
AFFILIATIONS: Education Technology
Consultant, Texas Instruments Singapore
As Mathematics educators, teaching
Mathematics effectively to our classes of students involves hard work and long
hours of preparation. We want our students to understand our lessons and be
able to apply the concepts, but our lesson plans do not always work out well,
given that we have a multitude of different types of learners in our classes.
Lesson design is an important part of any mathematics teacher’s work: To
prepare and deliver an effective lesson for optimal learning.
How can mathematics teachers design a
lesson well? In the modern world where our students are born digitalnatives,
lesson packages need to be engaging and fun for the students to participate
actively and be engaged in learning. Using the TINspire as a teaching and
learning tool, we are able to create interesting yet brainstimulating
activities to achieve that goal. Concepts can be taught through activities and
exploration of concepts. It can even be selfdirected, at the student’s own
pace. This handson approach encourages student participation in class and
promotes critical thinking. The multirepresentation and crossapps
capabilities of the TINspire also facilitates students to make the connections
between different concepts they have learned.
One other question mathematics teachers
always get is “Why are we learning this?”. Through mathematical modeling via
the TINspire, mathematics educators can bring the world closer to the
students, and show how the physical world can be modeled mathematically using
real world data. This realworld approach encourages interest in mathematics in
students, as mathematics will no longer be just numbers and formulae.
With these approaches, mathematics
educators can move a step closer to our common goals: Higher engagement of
students in lessons, deeper understanding of Math concepts and ultimately
contribute to the students’ success.
Abstracts for TIME Regular Papers
Teaching Fraction Using Constructivist Approach: An
Experimental Study
AUTHOR: Ashwini Karwande and Indu Garg
Emails: ashkrwande@gmail.com and
indu55garg@gmail.com
AFFILIATIONS: Department of Education,
University of Mumbai
The concept of fraction is one of the most
important concepts in primary mathematics as it offers a solid foundation for
learning other concepts. School students however find fractions a difficult
topic. Various meanings of fraction which are relevant to students are
partwhole relationship, partitioning and dividing, ratio meaning i.e.
equivalent, proper, improper, mixed fractions and the measure meaning. The
experimental research was carried out to develop achievement in Mathematics for
the students of secondary school using constructivist approach. The achievement
was measured using Mathematics Achievement Test based on topic of fraction and
its components. The test was designed on the basis of revised Bloom’s taxonomy
of educational objectives. From the study it was found that there was a
significant difference in their achievement in Mathematics. A significant
difference was found in the post test scores of Mathematics achievement test
among the students in the experimental group for the components of fractions
the partwhole relationship and part of a group or set meaning and partitioning
and dividing. But no significant difference was found in the post test scores
of group for the other components of fractions like ordering, comparing,
equivalence and improper fraction, mixed numbers, number line. The magnitude of
the effect of treatment on variable achievement in Mathematics was 0.63. Hence
as per Wolf’s criterion, the treatment was found to be effective at a moderate
to high extent in enhancing achievement of the students in Mathematics.
Innovative practices in teaching Mathematics
AUTHOR: Ashish Kumar Mittal,
ashish.s.mittal@gmail.com
AFFILIATIONS: Head, Department of
Mathematics, Indirapuram Public School, Indirapuram, Ghaziabad, Uttar Pradesh,
India (201012)
Mathematics is one of the most important
subjects and it occupys a central position in the education of a child, yet it
is the most feared subject. So while teaching mathematics one should use the
teaching methods, strategies and pedagogic resources that are much more
fruitful in gaining adequate responses from the students. Considering the aims
of teaching mathematics, it can be seen that more focus is laid to the higher
level of objectives underlying the mathematics subject, like critical thinking,
analytical thinking, logical reasoning, decisionmaking, problemsolving. Such
objectives are difficult to be achieved only through verbal and mechanical
methods that are usually used in the traditional mathematics classroom. The
verbal methods of instruction give all importance to speech and texts, to the
book and to the teacher. From an historical point of view this method was
majorly used until the end of the nineteenth century. In one of these verbal
methods teachers are simply satisfied with giving the mathematical rules to
pupils and having them memorize it. Their task is to transmit to their pupils
the knowledge which has accumulated over the centuries, to stuff their memory
while asking them to work exercises. Commenting on the prevailing situation in
schools, it is observed that in the average school today instruction still
confirms to a mechanical routine, continues to be dominated by the old
besetting evil of verbalism and therefore remains dull and uninspiring.
Innovations in teaching of mathematics can be diversified in terms of Methods,
Pedagogic Resources and Mastery Learning Strategy used in teachinglearning
process. This paper discusses the new understanding about the innovations in
teaching Mathematics among Mathematicians.
Technology enhances classroom control and improves
students’ performance
AUTHOR: Bikash Jain,
Bikash.trainer@gmail.com
AFFILIATIONS: Future Learning, New Delhi
Education today has changed its shape – it
has oriented itself with multi facet aspect and technology. Explanation
involves multidimensions: Text, pictures, video, field, animation, technology,
and repetition. Pupils are from different culture & background and
educators have to understand them and their understanding level before speaking
on the first few bits of curriculum. Concept teaching and deliberation should
have exploration suitable to everyone. And then there has to be a proper a
quick assessment followed by remedial system in place. All this revolves around
two critical people: Educator and student. Both are under tremendous pressure
to achieve excellence.
Use a UNIQUE bundle of technology
offsetting the pain area and supplementing education.
Won’t it be interesting to enquire which
quadrilateral shape would cover the maximum area when perimeter is constant,
taking a check on prerequisite knowledge, dynamic exploration and then quick
assessment one by one, and to close it with remedial note, if any. Wouldn’t it
be nice to correlate a*sin(b*x+c) graph with sound wave and differentiate
frequency/magnitude (prerequisite knowledge!) and many more. We may start off
with a quick quiz (using technology) to understand prerequisite knowledge on
quadrilateral and perimeter and then dynamic representation to explore/research
and to conclude with the result. Then a quick re check on students be done
using technology to understand the comprehension and quick fix, if required an
where.
With the use of technology, let us analyze
the following:
1. What is the magnitude of the effects of
technology on schooling outcomes concerning mathematics education?
2. How does the magnitude of the effects of
technology fluctuate in response to various study features (e.g., gender,
age,race) and design features (e.g., randomization, sample size, instruments)?
My conclusions touch on the need for a well
integration on technology, for effective strategies to stimulate deep learning,
for goaldirected assessments, for addressing the needs of a wouldbe
mathematically literate The evolution of students’ understanding after having
gone through this kind of procedure is unmatchable.
Mathematics Anxiety in Isolated Students
AUTHOR 1: Christopher Jefferson Y.,
christo_jefferson@yahoo.com
AFFILIATIONS: Department of Mathematics,
Spicer Memorial College, Pune, Maharashtra
AUTHOR 2: Chandramouleeswaran M.
moulee59@gmail.com
AFFILIATIONS: Department of Mathematics,
S.B.K. College, Aruppukottai, Tamilnadu
An annual national survey in 2012 called
the “Annual Status of Education Report” revealed that the students from
Maharashtra are the weakest in Mathematics in the country. It was found that
77.4% of fifth standard students couldn’t do simple problems taught in third
standard. Hence this study was conducted in Maharashtra to analyze the causes
of poor performance in Mathematics. Functioning under severe economic and
personal constraints, educational equity within a nation is improbable. In
schools there are students found to be isolated with very less interaction with
peers, their parents and teachers. They appear to be unhappy, tense, nervous,
frustrated, operate independently, quiet, sober, easily discouraged, abandon
tasks if it is difficult, do not initiate or volunteer and are mostly employed
in day dreaming. Some of them are disobedient, indiscipline, poor in studies
and with more anxiety towards Mathematics. Mathematics education plays a vital
role in a student’s performance in his/her studies. The purpose of this study
was to examine the correlation between math anxiety and math scores of isolated
students. Two schools each from rural, urban and metro areas of Maharashtra
were selected randomly. 910 students of eight standard participated in the
survey and by sociometric method 223 were found to be socially isolated
students. The isolated students were selected for this study along with their
parents and Mathematics teachers. It was found that home isolation and home
rejection are the major causes for mathematical anxiety. Parents need to take a
proactive role in the education of their children. Mathematics teachers need
to give students psychological assistance along with Mathematics learning.
Computer Assisted Instruction can be a supplement to these students. With the
parents’ involvement a mathematics teacher can change the behavior of isolated
students and can bring them to the main stream of society.
Teaching Mathematical Modeling in School and Students
Response
AUTHORS: Jamal Hussain and L. P. Lalduhawma
Email: jamal.mzu@gmail.com,
lpduhawmaa@yahoo.com
AFFILIATIONS: Department of Mathematics and
Computer Science, Mizoram University, India
In this paper, we studied the effect of
teaching and learning Mathematics in School through Mathematical Modeling. A
short term training course was organized for students in Higher Secondary
Schools. The course was intended to reveal the relevance of Mathematics in
reallife and understanding the concepts that students learned in their
Mathematics curriculum. 36 students of Dawrpui School of Science and
Technology, Aizawl, Mizoram were selected for the course. It consisted of 12
contact periods (one hour each) and was held in November/December, 2012.
Mathematical Modeling was introduced to the students for the first time. Some
of the models from Population dynamics were discussed with the aim of better
understanding of Mathematical concepts and its real life applications. The
experimental design was based on prequestionnaire and postquestionnaire in
order to find out whether and in what ways a Mathematical modeling experience
could influence student’s beliefs and attitudes towards Mathematics. It was
found that the course was successful in generating more interest and motivating
students for learning Mathematics.
Use of innovative teaching aids
AUTHOR: Kalpana Gairola,
gairolamaths@yahoo.com
AFFILIATIONS: TGT MATHS, DPS Sushant Lok
Gurgaon
To Thales the primary question was not what
do we know, but how do we know it. Aristotle
Mathematics is a very important subject and
occupies a central position in school curriculum. Except our mother tongue,
there is no subject other than Mathematics which is more closely related to
our daily life. Yet it is the subject which is most feared by students and
their parents alike. Because its concepts are hierarchical and interconnected
and unless lowerlevel concepts are mastered, higherlevel concepts cannot be
understood. Moreover, Mathematics is highly abstract. Therefore, teaching and
learning math is often found challenging. To face the challenge as a teacher we
need to use a variety of teaching strategies in the classroom. One of the
effective strategies is using teaching aids innovatively, effectively and
enthusiastically. Teaching aids ensure that your point is understood. They
engage students’ other senses in their learning process. It works as the
support to both teacher and taught in the pursuit of knowledge and curriculum
transaction. Any method that serves the purpose of teaching and learning math
without destroying the objective, could be considered as innovative aids of
teaching. Teaching aids can be anything that create a positive environment and
enhance the fun element from manipulative to computers and mind maps etc. They
could be ready made or prepared by teachers as well as by students. They need
not to be costly. Teachers should look at new ways to incorporate technology
and other available materials, as teaching aids, methods and strategies into
teaching .Therefore, we need to find ways that can help us make better
educators, and make our students better learners.
A module explaining definition of limits and continuity of
real valued function using Geogebra
AUTHOR: Mandar N. Khasnis,
mandar.khasnis@gmail.com
AFFILIATIONS: Department of Mathematics,
Smt. C H M College, Ulhasnagar
Certain fundamental topics like Limits,
continuity, differentiability of a function, are taught to students at the
higher secondary school level. It is essential to bring out the rigour in the
fundamental concepts from Calculus in order to give better insight to students.
It is observed that students are not comfortable with definitions of these
concepts. Thus leads to difficulties in further learning and also results in a
dislike for the subject.
This paper describes a Geogebra driven
module which can be one of the tools for the teachers to build a strong base of
very fundamental concepts from Calculus. In fact, many definitions can be
illustrated using various examples, which is time consuming if only blackboard
and chalk is used. This will also help students to build modules using this
software, since it is an open source software. A study was conducted where this
module was implemented among students and its effectiveness visàvis was
traditional chalkblackboard method was tested.
Explaining Mathematical Concepts with Innovation and
Personification
AUTHOR: Manisha Malhotra,
mani2307@gmail.com
AFFILIATIONS: Faculty, Department of
Mathematics, D.P.S. Sushant Lok, Gurgaon
Mathematics learning in a class room
requires concentration and a lot of patience on part of a student as they tend
to get distracted very easily. So, if initial few minutes of the class are made
a little different from the usual sums and solutions, then the classroom
learning can be a lot of fun and much easier. A catchy introduction to the
topic with fun filled activities combined with innovative teaching strategies
and ‘Personification of the mathematical concepts’ simplifies the understanding
and leaves a long lasting impact on the students.
In this paper, I would present some
interesting teaching strategies including the method of ‘personification of the
concept’ to explain mathematical concepts to the middle school students.
Introduction of a mathematical concept can
be done by involving each student through puzzles, games, handson activities
etc. so that they are excited to know further about the topic . For example,
asking the students to find out the names of the polygons with sides equal to
their roll numbers, made them discover about the large polygons and also
generate enthusiasm and readiness to learn more about the topic.
Also, the method of ‘personification of
concepts’ as mention above, helps the students to grasp the concepts easily by
making a picture of the concept in their minds. For instance, I explained the
distributive property a(b+c)= ab+ac by personifying ‘a’ as a person who wants
to go to the home of ‘b’ and ‘c’ and would obviously say hello to both.
This paper thus covers teaching strategies
to suffice the understanding of the mathematical concepts and clip the
attention of the students.
Changing Dimensions of Mathematics Education in 21st
Century
AUTHOR: Neenu Gupta, neenugupta01@gmail.com
AFFILIATIONS: PGT (Mathematics), Department
of Mathematics, Ahlcon International School, Delhi, India
Technology has become a helping hand for
teachers for accomplishing the goals of teachinglearning of 21st century.
Since Mathematics at senior secondary level becomes more abstract so Online
Tools like Prezi, screenr, toondoo, pizap. popplet etc. can also be used to
make Mathematics teachinglearning interesting. Only three of the above
mentioned tools are being discussed hereunder.
TOONDOO is an online tool for creating
cartoon strips. This tool can be used to introduce any topic in Mathematics in
an interesting way, especially in junior classes, but can also be used for
teaching Mathematics at senior secondary level. For example, it is used to
teach Permutations & Combinations (Class XI) to introduce the topic, to
differentiate between Permutations & Combinations & to solve problems
given in the textbook. SCREENR is used to make videos which can be used as
virtual classes and act as a good tool for revision of topics and also to teach
underperformer students during remedial classes. It is used to teach abstract
topics such as Limits, Continuity and Differentiation (Classes XIXII). POPPLET
is an online tool used for mindmapping or concept mapping. It is an effective
brainstorming tool for presentation as entire topic can be planned sequentially
and PPTs and videos can also be included in concept map. For example, it was
used to teach Vectors (Class XII) and it was welcomed by students as science
students do it in class XI and commerce students don’t take much interest in
this topic.
All these online tools are free of cost. It
is need of teachers to use technology for Mathematics teachinglearning to
egeneration.
Easy learning of basic mathematics at school level
AUTHOR: Sandeep Kumar Bhakat,
skbhakat77@yahoo.co.in
AFFILIATIONS: SikshaSatra, VisvaBharati
(University), P.OSriniketan731236; DistBirbhum, WB
In order to create good interest in any
subject, particularly in mathematics, there should be a very logical and
scientific base in the curriculum at the early stage of learning. The method of
teaching basic mathematics should be done in such a manner so that an interest
for mathematics is created in young learners, particularly at the primary
level. With this objective, two basic concepts in mathematics have been
considered. The study of natural numbers and their properties can be easily
introduced in the early stage of learning mathematics. In this paper a sample
of a curriculum is introduced with new approach of learning. In this approach,
it is suggested that simple properties of numbers be introduced so that
students can find their interest in mathematics. The paper suggests some
interesting explorations with natural numbers other than those done in the
conventional study of natural numbers for arithmetical operations. The paper
also deals with the study of “Triangles and Angles” in an experimental manner
through a project in geometry with a completely new look. Both the approaches
discussed in this paper are very attractive, new and very easy to perform.
These approaches have proved to be effective in the schools in remote areas and
also in the open school systems.
Use of Geogebra Software by prospective Teachers' in
Developing Lessons for teaching of mathematics
AUTHOR: Shanti Amol Pise,
shantipise@ymail.com
AFFILIATIONS: Swami Vivekanand College of
Education, Affiliated to University of Pune.
Mathematics is the gate and the key of all
the sciences. Though the subject is very important it is always considered to
be the most difficult and fearful. The dryness of the subject can be
contributed to the teaching of the subject. In the pedagogical study of
mathematics we mainly concern ourselves with two things; the manner in which
the subject matter is arranged or the method the way in which it is presented
to the pupils or the mode of presentation. "Technology is essential in
teaching and learning mathematics; it influences the mathematics that is taught
and enhances students' learning" (NCTM 2000) implies the importance of
technology in mathematics education. Observing this principle the main aim of
this study was to examine the effect of use of Geogebra software for teaching
mathematics by prospective teachers'. Technology enables users to explore
topics in more depth (e.g., interconnect mathematics topics, write programs,
devise multiple proofs and solutions) and in more interactive ways (e.g.,
simulations, data collection with probes). There is widespread agreement that
mathematics teachers, not technological tools, are the key change agents to
bringing about reform in mathematics teaching with technology. Geogebra
software provides new opportunities for using technology effectively in the
field of education. In this study, usage of Geogebra software by prospective
mathematics teachers for teaching and learning mathematics concepts was
investigated. It was for the development of prospective secondary mathematics
teachers' Technological Pedagogical Content Knowledge as they worked
individually and in small groups to develop and present lessons with Geogebra
software. Qualitative research methodologies were used in this study.
Participants first learned basic commands about GeoGebra. During lessons
prospective teachers of mathematics used dynamic worksheets. Data were
collected by participants' works and opinions on Geogebra software. Our results
suggest that the prospective teachers' perspectives on teaching and learning
mathematics with technology were enriched and according to responses of
participants, prospective teachers' want to use Geogebra software for teaching
mathematical concepts. Prospective teachers need to develop technology skills,
enhance and extend their knowledge of mathematics with technological tools, and
become critical developers and users of technologyenabled pedagogy.
A Unit of Measurement and Learning
AUTHOR: Tanya Saxena
AFFILIATIONS: municipal primary school of
Ahmedabad
Six weeks of intervention in a municipal
primary school of Ahmedabad was enough to challenge my stereotype regarding
children’s attitude towards mathematics. The stereotype ripened after learning
that dropoutrates due to mathematics and was more about fear and anxiety
pertaining to the subject. A content based intervention was planned with an objective
to develop mathematical competencies of 30 students of grade 5 and to refine my
own understanding about the process of learning mathematics. The topic of
“Units and measurement” was taken as a tool for the process, which came from
the observation and experiences that “children often forget to write units
along with the measurements”. I started with a condition of uncertainty along
with an urge to get a sense of clarity and a way out to make this concept and
process meaningful for every stakeholder. Base line assessment of required
basic competencies was done, plotted and mapped over the chart; on the basis of
which mixed groups were formed to encourage team work. Each session was
followed by presentations by students with some process oriented questions
which worked as a catalyst to generate need of the topic. And we worked further
for a month keeping some nuances of kinesthetic learning in the process. Right
from beginning to the end, the study unfolded the hidden potential of children
and made them acquainted with the process of reasoning.
Misconceptions in mathematical concepts leading to fear
among students: Possible solutions
AUTHOR 1: Manjusha P. Gandhi,
manjusha_g2@rediffmail.com;
AFFILIATIONS: Department of Applied Mathematics,
Yeshwantrao Chavan College of Engineering, Nagpur, India;
AUTHOR 2: Prashant R. Gandhi,
gandhi_24prashant@rediffmail.com
AFFILIATIONS: Department of Physics,
Ramdeobaba College of Engineering and Management, Nagpur, India
The Mathematics is used as a tool to solve
various problems in engineering, science and other streams of education field.
The effective utilization of these tools becomes easy due to development of
computer software. The computer software will be used effectively if one understands
it and knows the fundamental of mathematics utilized in it. Also mathematics
develops logical thinking, critical thinking, analytical thinking, reasoning
power and power of decision making. Therefore learning mathematics is
essential.
Now a days understanding mathematics is a
major burden for the students, as there is misconception among them that it is
difficult. Therefore the role of the teacher is to develop the interest in
mathematics and remove the fear of the subject among the engineering students.
The real job of the teacher is to identify the weakness and try to rectify it.
The weakness has been observed among the students who have scored very less
marks in mathematics, this is due to lack of knowledge of basic formulas and
rules they have learned during schooling. It has become implicit now that
instead focusing on the good students, one can target weak students in the
class, which are in mass.
In the present paper weaknesses of the
students are outline and possible methods like:
Activity Technique: The common problems
related to arithmetic are resolved by assigning the tasks in groups and making
them realize about the reality and its significance.
Deductive Technique: This technique
inculcates the proper method of solving problem and it also develops the skill
like when to move from known to unknown or visaversa.
Memory Training Technique: This method will
help the students to memories the formulas, theorems and properties by
understanding the concept and logic behind it.
Heuristic Technique: This technique deals
with two methods where one can explain to solve problem by using generalization
method or adopting inductive approach.
The techniques mentioned here are turn up
in such a way that it gives proper understanding of basic concepts of
mathematics and eradicate the mistakes done by the weak students.
Appropriate examples are given to validate
the above methods.
The real crux of the paper is to implement
these techniques and motivate students to adopt it.
BRTS – (Bus Rapid Transit System)
SOLUTION TO A PROBLEM OR A PROBLEM ITSELFI
AUTHORS: Ana Amir, Chhaya Joshi, Radhika
Khandelwal, Saurabh Jain; info@shishukunj.in
AFFILIATIONS: The Shishukunj International
School, Indore(M.P.), India
The persistent problem of traffic jams,
increasing accidents and heavy load on roads led to the establishment of the
BRTS project. But, ever since the corridor has been constructed, it is being
criticized by the masses for allegedly taking up too much road space. “BRTS
poses to be the solution to the above mentioned problem.”Using the data
obtained from the AiCTSL (Atal Indore City Transport Services ltd.) office, we
established a strong correlation between the number of days of operation and
the ridership. The coefficient of correlation according to Karl Pearson’s
method came out to be 0.87. Further using the Scatter Diagram, we derived the
equation of the best fit line and used it to estimate the ridership towards the
end of the first year of the BRTS project being launched. In sync with the
actual progress of the project, our result of more than 80,000 riders in less
than one year clearly indicates that AiCTSL will be able to attain its
Breakeven Point (BEP) in less than the expected 3 years period. We also formed
various graphs to compare the time taken by each mode of transport, its
capacity to carry passengers and fuel consumption to show how ibus is a better
means of transport. We have also made a model that shows the continuous
transition of the A.B. Road from narrow twolane road to broad fourlane road
with a separate corridor for ibus. We have also come up with our
recommendations for making this BRTS project more effective and efficient.
BRTS : A SOLUTION TO A PROBLEM OR A PROBLEM IN ITSELFII
AUTHORS: Anubha Barve, Praveen Jangid,
Rohan Shrimal, Rohit Jangid
Email: prestigepublicschool@ymail.com
AFFILIATIONS: Prestige Public School,
Indore (M.P.), India
Entering the 21st century, the Indian
transportation system has been rapidly expanding; still it has not been able to
keep pace with the congestion in our cities which continues to grow at an
alarming rate. This increased congestion is adversely impacting our quality of
life and increasing the potential for accidents and long delays. To fight and
mitigate congestion, transportation professionals in India are working towards
increasing the productivity of existing transportation systems through the use
of advanced technologies. Intelligent transportation systems (ITS) encompass a
broad range of wireless and wire line communicationsbased information and
electronics technologies. When integrated into the transportation system's
infrastructure, and in vehicles themselves, these technologies relieve
congestion, improve safety and enhance productivity. All this led to need of
the better public transport system for balanced and proper development which
should not only include all the above mentioned parameters, but should also be
cost effective and time saving. Bus Rapid Transit System (BRTS) provides a very
good solution for public transport.
A BRTS essentially gives priority to buses
through dedicated bus lanes, and provides dedicated lanes for pedestrians and
nonmotorized vehicles like cycles and rickshaws. BRTS is sometimes called a
High Capacity Bus System (HCBS), as in Delhi.
The capacity of the system is increased
because buses have unimpeded rightofway, which reduces the turnaround time
and because more buses can operate in the dedicated bus lanes. Simplistically
put, a BRTS is like a metro with the flexibility of a bus system.
Bus Rapid Transit is highquality, customer
orientated transit that delivers fast, comfortable and lowcost urban mobility.
BRTS systems have some or all of the following elements; many of these can also
make a valuable contribution to improving regular bus services.
Keeping the above ideas in mind, BRTS was
launched in Indore, but after a period of time, Hon’ble High Court, Madhya
Pradesh, Indore Bench gave a decision to open BRTS lanes for four vehicles as
well.
The paper deals with the mathematical study
of elements of BRTS in Indore like cost comparison, waiting time and average
time calculation, total journey time comparison of BRTS and other vehicles,
modal shift – which shows the willingness of passengers to shift to BRTS and
also the effects of the High Court Decision on BRTS. The study can be used to
analyze the BRTS systems of various cities and its scope in that particular
region.
Facilitating Student to learn Geometry Practically
AUTHOR: M. S. Solanki, ms.solanki@gmail.com
AFFILIATIONS: Maharishi Vidya Mandir
Schools Group, Bhopal,India
This article discusses use of a device
known as “Solanki’s Multipurpose Model” to verify the validity of many theorems
and Axioms of geometry taught in classes VI to VIII. The effects on different
types of students' interactions while learning geometry in a particular
cooperative smallgroup setting. Data were collected through classroom
observations, students' written selfreports, and an attitude questionnaire. A
group of three/four students from one of the classes was allowed to work
together under the guidance of the teacher.
Analysis of classroom observations and
students' selfreports focused on students' activeness, interactions, and
attitudes toward the experimental method. Findings for the cooperative
smallgroup setting indicated
(a) an increase in students' activeness,
(b) a shift toward students' ontask verbal
interactions,
(c) various opportunities for students to
explore and learn the concept and
(d) positive attitudes toward the
cooperative experimental method.
Abstracts for TIME Workshops
LaTeX Workshop
AUTHOR 1: Amitava Saraswati,
amitava.saraswati@gmail.com
AFFILIATIONS: St. Pauls School, Indore,
India
AUTHOR 2: Girish Belkar,
girishbelkar@gmail.com,
AFFILIATIONS: Indus School, Indore, India
The LaTeX is a mathematical typesetting
tool. The workshop will include typesetting mathematical ideas, coding to write
a bibliography for a thesis or a dissertation and also teach the art of
presenting an article in LaTeX using LaTeX Beamer.
Teaching PreCalculus and Calculus with GeoGebra
AUTHOR: Sangeeta Gulati,
sangeetagulati92@gmail.com
AFFILIATIONS: Sanskriti School, New Delhi,
India
Participants: Maximum 30 teachers teaching
classes 11 &12 with some basic familiarity of GeoGebra.
Duration:2 hours
Requirements: Computer lab with 30
computers, GeoGebra software, LCD projector
Aim of the workshop:
In this two hour workshop teachers will create
GeoGebra worksheets which can be used for teaching of PreCalculus and calculus
topics in Senior Secondary school. The workshop will use basic and some
advanced features of GeoGebra. The aim of the workshop is to create dynamic
visualizations of certain important concepts of Pre –Calculus and Calculus,
which can be used as a demonstration and exploration tool in teaching and
learning of these abstract concepts.
The Mental Maths Workshop
AUTHOR: Gaurav Tekriwal, gtekriwal@gmail.com
AFFILIATIONS: The Vedic Maths Forum India.
Consider this:
• It is estimated that in the
UK, 17 million adults have the mathematics capabilities of an 11 year old or
younger. Source: The Telegraph, UK.
• 910 year olds and 1314
year olds in the United States continue to lag behind several East Asian and
European nations in Maths. Source: The New York Times
• In India in 2012, 46.5% of
children in Class V could not solve a twodigit subtraction problem without
seeking help. Source: The Pratham Report.
• South Africa ranks second
last in the world for education in Mathematics. Source: World Economic Forum
Currently we are witnessing a global maths
crisis where we are experiencing low numeracy levels across countries. Students
and teachers are looking for alternative solutions in Mathematics.
In such a grim scenario, Mental Maths
Skills can be useful to students as there is more than one way to reach a
correct answer in mathematics. This workshop on Mental Mathematics will show
some simple methods and proofs of mental mathematics in use globally like
Chisanbop (Finger Calculation Method from Korea), The Trachtenberg method and
the Indian Mental Maths Methods.
Exploring senior secondary level calculus with a Graphic
Display Calculator
AUTHOR: Jitendra Pathak,
jitendrap@casioindiacompany.com
AFFILIATIONS: Casio India Pvt. Ltd., Delhi,
India
This workshop intends to make mathematics
educators aware about the power of graphic display calculator and utility of
the same while teaching and learning calculus of senior secondary school level.
We can very efficiently introduce the
concept of limit, continuity and discontinuity by using graphic section of the
Casio graphics model fx9860 G II. Apart from that we can also explore local
linearity, visualize the derivative, derivative using first principle and
relative maxima and minima.
Visualizing and exploring Linear equations, Quadratic and
Linear inequalities using Casio Graphic calculator.
AUTHOR: Jitendra Pathak, jitendrap@casioindiacompany.com
AFFILIATIONS: Casio India Pvt. Ltd., Delhi,
India
In this workshop mathematics educators and
learners will learn to plot linear equations using Casio graphic display
calculator fx9860 G II/ fxCG 20, finding the solution of a pair of linear
equations graphically and fitting straight lines to data. This workshop also
intends to give an insight of the nature of quadratic functions and the
significance of the coefficients of a quadratic function.
Exploring concepts and applications of mathematics using
Casio Graphic Display Calculator
AUTHOR: Jitendra Pathak,
jitendrap@casioindiacompany.com
AFFILIATIONS: Casio India Pvt. Ltd., Delhi,
India
This workshop session will highlight the
basic features of the Casio fx9860 GII/ fxCG 20 graphic calculator. This
device as a teaching tool as well as a tool for performing investigation will
be demonstrated and participants will be given a hands on experience. The
problems will be from the topics of function, calculus, matrices, simulation
and probability.
Visualizing and Exploring mathematics using Casio Teaching
tools A Hands on Session on fx9860 GII /fx CG20
AUTHOR: Jitendra Pathak,
jitendrap@casioindiacompany.com
AFFILIATIONS: Casio India Pvt. Ltd., Delhi,
India
This workshop session will highlight the
basic features of the Casio graphic calculator fx9860 G II/ fxCG 20. The use
of this device as a teaching tool in the classroom will be highlighted through a
calculus lesson. Further the use of the calculator for performing
investigations will be demonstrated through some math lab activities based on
the topics of matrices and probability.
The participants will be given a handson
experience on the calculator and emulator software of the tools would be used
as whole class teaching tool.
Learning to do math with TINspire CX handheld
AUTHOR: Thomas Yeo, thomas.yeo@ti.com
AFFILIATIONS: Education Technology
Consultant, Texas Instruments Singapore
The workshop, will have three components:
Part 1: Perform the basic keystrokes on the
TINspire CX handheld (15 min)
This section covers the layout of the
TINspire handheld. Participants will learn how basic keystrokes are performed
on the handhelds to perform calculations. Participants will learn how to create
new documents and save them on the handheld for future use. An introduction to
some shortcut keys will be covered as well.
Part 2: Graphing on the TINspire CX (25
min)
This section covers the graphing capability
of the handhelds. Participants will learn how to draw graphs using equations
and plot graphs using a table of values, and edit the various attributes of the
graph. Various graphing techniques will be discussed here, including
intersection points, graphing inequalities, graphs of absolute functions and
graph transformations.
Part 3: Mathematical modeling on the
TINspire CX (15 min)
Participants will try out a Mathematical
modeling activity created by the speaker. This activity allows participants to
model a real life scenario using scatter plots and regression functions. This
activity shows how the TINspire CX capability to have crossapp collaborations
help in better understanding and engagement of students.
GeoGebra & LaTeX
Authors: Amitava Saraswati,
amitava.saraswati@gmail.com; Girish Belkar, girishbelkar@gmail.com
Necessity is indeed the mother of
invention. The genesis of all mathematical development stems from practical
needs. But soon it transcends the confines of its immediate utility.
Mathematics has always played and will always keep playing an important role in
our day – to – day life.
Gone are the days when students remained
passive listeners and the teacher ruled the roost in the class. Today, the
students , being more tech savvy, are far more enlightened and often a step
ahead of their teachers. To keep pace with the changing scenario , teachers
need to upgrade themselves , and what better way than to attend a conference
like TIME. This would help them to motivate themselves, share ideas, discuss
new problems , broaden their horizon and ignite the spark within .
Contrary to popular belief that mathematics
is nothing but a mind game , a lot of mathematical conjectures and results were
a consequence of serious mathematical doodling. Today we have enough tools to
experiment with mathematical concepts.
One such popular tool is GeoGebra. Being
the founding fathers of The GeoGebra Institute of India based at NCERT New
Delhi , we would like to take up the cause of promoting GeoGebra, for school
and college teachers for effective teaching ,by conducting workshops or
seminars at
TIME ’13 on GeoGebra.
Another mathematical tool for
the researchers and for those who indulge in writing
mathematical articles or books, is LaTeX.
We would be happy to take up parallel sessions in GeoGebra and Latex for the
uninitiated during TIME’13 , much like the way it was done in TIME’11 at
Indore.
This time around , we would like to conduct
GeoGebra tutorials for Secondary and Senior Secondary teachers. The content
would include Geometry , Calculus and optimization using Linear Programming.
The LaTeX content would include type
setting mathematical ideas , coding to write a bibliography for a thesis or a
dissertation and also teach the art of presenting an article in LaTeX using
LaTeX Beamer. 