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Abstracts for Plenary Talks and Invited Papers
|
Students Will Excel If They Are Inspired |
Authors: Wei-Chi Yang |
Affiliations: Radford University |
It is well-known that the requirement of teachers’ content
knowledge in secondary schools (middle or high schools) varies greatly from
country to country (see [4] and [5]). It is also debated how much content
knowledge a future math teacher should possess before he or she starts
teaching. There are states in the U.S. that do not require future middle
school teachers to finish the calculus sequence in college; the rationale
simply being that middle school teachers do not need to teach calculus. On
the other hand, becoming a future math teacher at a secondary school in South Korea virtually requires finishing a B.S. degree in mathematics. In this paper,
instead of debating how much is enough, we introduce several examples to
demonstrate how technological tools can expand students knowledge of
mathematics if teachers can properly inspire them. In order to reach this
objective, teachers naturally need to have broader content knowledge. |
|
GEOMETRIC ORNAMENT IN ART AND ARCHITECTURE OF WESTERN
CULTURES |
Authors: Miroslaw Majewski |
Affiliations: New York Institute of Technology, Abu Dhabi Campus |
Keywords: geometry, Sketchpad, art |
For most of us the word art is a synonym of painting, sculpture
and sometimes calligraphy. We consider also music as a form of art. For an
average person art has nothing in common with mathematics or even geometry.
However, if we will look into the history then we will find that ancient
Greeks considered art and mathematics as tightly connected disciplines. There
were many artists who have been inspired by mathematics and studied
mathematics as a mean of complementing their works. The Greek sculptor
Polykleitos recommended a series of mathematical proportions for carving the
ideal male nude. Renaissance painters turned to mathematics and many of them
became accomplished mathematicians themselves. We can find mathematics in
creations of the middle century Islamic artists as well as Gothic masons.
In this lecture I will explore some examples of art from various regions and
cultures of the Western World. I will briefly examine the role of
mathematics, in particular geometry, in creation of these works of art. My
major objective will be to show how geometric constructions were used to
create these examples of art. I will start from ancient art and early
examples of geometric art, then I will examine some Cosmati designs, and
finally I will show the geometry behind the Gothic tracery. |
|
The Other Role of Technology: Communication Between
People |
Authors: Jonathan Lewin |
Affiliations: Kennesaw State University |
For the most part, the traditional role of technology in the
teaching of mathematics has been focussed on its ability to solve, to
evaluate, to produce images and even to guide students through stereotypical
working steps that are supposed to be employed in as one works through
exercises that appear in the textbooks. But technology has another role that
is sometimes neglected. It gives us new and efficient ways to talk with one
another. It gives us opportunities to convey mathematics in a much more
friendly form than we can find in any ordinary textbook. It allows instructor
and student to exchange mathematical ideas even when they are not standing
face to face in the same room. It can be a means of communication between
people.
In some of my earlier presentations at ATCM and elsewhere, I have emphasized
the value of screen capture videos in the creation of mathematical learning
materials and the role of video will again be featured this year. I shall
refer both to classroom video and to the video in products like my Virtual
Calculus Tutor. However, the production of video is not the whole story and I
shall not be confining my attention to this topic. My presentation will
demonstrate some of the unusual textbooks that I have designed for reading on
the computer screen and it will show how, in my two main video products,
Virtual Math Tutor and Virtual Calculus Tutor, a balance between video
material and document material can provide a very successful medium for
helping students to understand mathematics.
I shall show how an on-screen book can be just as easy to browse through as a
printed bound text and provide more help, more solutions to exercises, and
more development of the material. It can do so without becoming cluttered and
at a modest price. I should add that several of my works are provided for
free as public domain items. Some of my products involve coordinated use of
on-screen documents and video and I intend to demonstrate how these two media
can work with each other to help a student to understand mathematical ideas. |
|
Maximal Twistable Tetrahedral Torus |
Authors: Jen-chung Chuan |
Affiliations: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300 |
In the fascinating book "More Mathematical Activities"
Brian Bolt supplies a net for a rotating ring of six tetrahedrons. Based on
this net, the model forming a twistable tetrahedral torus can be constructed
with patience. In this talk we are to show how such a model can be built with
Cabri-3D. With the magic supplied by the dynamic geometry software we are to
show how ALL such models can be constructed. |
|
How Integration of DGS and CAS helps to solve
problems in geometry |
Authors: Pavel Pech |
Affiliations: University of South Bohemia |
The use of dynamic geometry (DGS) and computer algebra systems
(CAS) changed teaching geometry at all school levels considerably. To solve a
problem students first visualize it by DGS then by changing parameters the
problem is interactively modified and geometry properties like invariant
points, lines, circles etc. are
recognized. Using these knowledge a conjecture is stated and classically
proved or disproved.
But sometimes we do not have a key idea to find a proof (or a locus). Then
the use of CAS can help. By the theory of automated geometry theorem proving
we are able to prove many such theorems.
Thus the integration of DGS and CAS is useful and helps to solve problems.
This approach is demonstrated in many examples of elementary geometry in a
plane and space. |
|
INTERCONNECTIVITY of Mathematics & the
Educational Software INTERFACE |
Authors: Vladimir Nodelman |
Affiliations: Holon Institute of Technology |
The existing educational software rarely supports investigation
and visualization of different subjects and areas of mathematics, which, by
the very nature of the discipline, are intrinsically linked. This lack of
universal and simple to master virtual tools forces the educators to use
random pieces of available software in a nonstandard way to satisfy their
varied needs.
Visualization and dynamic modeling becomes one of the central requirements of
the mathematics educational software. They should provide an opportunity for
broad-range explorations and deeper understanding of mathematics by the
student. The positive role of user-friendly software interface, the second
after mathematics language the student has to master, cannot be
underestimated. As in any bilingual conversation, the richness of languages
helps to express the meaning. Unfortunately, except for some dynamic geometry
applications, the interface of available software remains cumbersome and
unfriendly.
Some professional CAS systems allow for a customized interface, but such
customization requires an advanced knowledge of the software and is not
suitable for mathematics teachers and students. We offer a different option:
a simple, natural and universal interface of educational software with
perhaps more limited abilities to handle advanced mathematics.
This paper demonstrates some ideas and possibilities of the second approach.
We present ''''VisuMatica''''— a tool developed by the author for teaching
mathematics in the manner that is integrated, visual and interactive. |
|
Integrating Certain Products without Using
Integration by Parts |
Authors: Tilak dealwis |
Affiliations: Southeastern Louisiana University |
In this paper, we will describe a novel method of integrating
certain products without using the integration by parts formula. In a
calculus class, the standard method of integrating products of functions such
as polynomials, exponential functions, logarithms, and trigonometric
functions is to use the integration by parts formula. Of course, every instructor
teaches that this formula is equivalent to the well-known product rule for
differentiation of functions. However, when a student uses integration by
parts, the idea behind the product rule usually gets lost during the
execution of the method. This probably happens because the student is trying
too hard to concentrate on the actual mechanics of the integration by parts
formula. In this paper, we will show how to use the product rule for
differentiation to integrate a variety of products. We will also use the
computer algebra system Mathematica to verify our results, and also to gain
some new insights. What we have used is Mathematica version 7.0 on a Windows
7 platform, but any other computer algebra system of reader’s choice can be
used for the purposes of the paper. |
|
Color Models as Tools in Teaching Mathematics |
Authors: Ma. Louise
Antonette De Las Penas |
Affiliations: Ateneo de Manila University |
In the mathematics classroom, a lecture or presentation can be
made more interesting and can captivate students’ attention with the use of
color models and patterns. More importantly, these models can be used as
tools in teaching and learning algebraic and geometric theories; and make
possible the visualization of abstract concepts and the development of
critical thinking.
In this talk we present situations where we use color models in teaching
students concepts in geometry and abstract algebra. We highlight the role of
technology in making these color models accessible in teaching middle school,
high school and undergraduate mathematics.
In the second part of the talk, we present how technology, through dynamic
geometry and computer algebra systems, facilitates the use of color models to
connect and apply mathematical concepts to other sciences. For instance, we
use colored patterns and tilings to establish the presence of geometric and
group theoretic concepts in the study of crystal structures and physics of
nanostructures. |
|
Mathematical Modelling as a Learning Experience in
the Classroom |
Authors: Keng Cheng Ang |
Affiliations: Nanyang Technological University, 1 Nanyang Walk,
Singapore 637616 |
Mathematical modelling has been gaining attention and becoming a
part of classroom practice in many countries. In Singapore, despite
recognizing its importance and relevance, curriculum planners and teachers
face various challenges in including and incorporating mathematical modelling
in their teaching curriculum. Nonetheless, the recommended practice is to
expose students to learning experiences in mathematical modelling whenever
and wherever possible. In this paper, a framework which serves a practical
guide for teachers in planning instruction in mathematical modelling will be
introduced. Examples illustrating the application of this framework by
teachers in crafting classroom learning experience in mathematical modelling
will be presented. In addition, a learning experience implemented for a group
of teachers in an in-service course will also be discussed. It is no
coincidence that technology had featured quite prominently in these examples
as mathematical modelling in practice would often involve the use of some
specific technological tools. |
|
Why should We Use Visualization within Math Science
and Math Education? |
Authors: Vladimir
Shelomovskii |
Affiliations: Murmansk State University, Deoma |
Visualization is powerful and effective tool for understanding
and in–depth study of mathematics. It helps students to better understand the
foundations of mathematics, engineers to calculate complicated geometric
constructions, and researchers to find new mathematical regularities. Modern
mathematical science presents such complicated events and phenomena, that
even the talented scientists often pass by hidden nuances, unobvious
mathematical rules, effects and properties in their math research. We show
some examples of scientific research of ATCM 2011 and ICGG–2012 authors,
based on math visualization provided by GInMA software. We also show the
examples of the calculations which have became possible largely due to the
fact that the authors were able to observe with GInMA the computational grid
behavior, and have compared the observed image and arising calculation
difficulties. Visualization is absolutely necessary in math education. Modern
students often memorize standard rule for solving a problem and do not
understand meaning of the statement standing behind the rule. We demonstrate
the examples of the solutions and their visualization using GInMA, which
helps to understand meaning of mathematical statements. With the use of GInMA
software we construct derived surfaces and curves, pedal curves, caustic
curves and surfaces, complicated intersecting solids, such as the solid
formed by intersection of an ellipsoid and a sphere, and many other
nonstandard objects, which represent the set of interrelated geometric
objects.
All the pictures in the electronic version of this paper are interactive.
Install GInMA software from the website
http://deoma–cmd.ru/en/Products/Geometry/GInMA.aspx
click on the Figures and investigate interactive solutions of the problems. |
|
A FORGOTTEN IMPORTANT TOOL IN THE NEW MATH
CURRICULUM: RECURSION |
Authors: Antonio R. Quesada |
Affiliations: The University of Akron, Depart. of Theoretical
& Applied Math., MAA, NCTM |
The capabilities of graphing calculators are changing the way we
teach as well as the content and scope of what is taught in basic
mathematics. In the United States, following recommendations of the NCTM
Standards, recursive procedures, traditionally excluded from pre-college
mathematics, began to appear at different levels from elementary to
introductory college courses. The ability to i) repeat an instruction or a
set of instructions with a single keystroke, ii) to make the output of a
calculation the input for the next, and iii) to be able to stop and analyze
or modify an iterative process provides a tool of great interest from both
the pedagogical and the practical point of view. At the elementary level
modern elementary calculators, allow to easily define constant operations
that can be used to discover patterns, to reinforce basic facts via the
"guess and check" approach, to investigate the relations between
basic operations or even their rate of growth, etc. It is however at the
secondary level where recursive procedures, accessible via graphing
calculators, have the potential for a major impact. In this presentation we
show examples from different mathematical areas to illustrate (i) some
recursive procedures, that can be easily implemented without programming,
(ii) associated powerful mathematical models traditionally taught in upper
levels to a selected group of students and now accessible at lower levels to
most students, and finally (iii) how recursion, in some cases, provides an
alternative problem solving approach less dependent on readymade formulas. |
|
The Elements: A Dynamic Perspective on Euclid’s
Geometry & Geometry’s Euclid: |
Authors: Nicholas Jackiw |
Affiliations: KCP Technologies, Inc., Simon Fraser University |
Modern tools—like The
Geometer’s Sketchpad—and modern applications—like fractals and computer
graphics—have energized the study of geometry both in school and in research.
Yet for millennia, geometry’s development has been dominated by “the most
famous textbook ever:” Euclid''s Elements.
In this talk, I’ll take a fresh look at the mathematical and cultural origins
and impact of the Elements, with a specific
emphasis on how essential dynamic technologies—both physical and
intellectual—have influenced 2,500 years of geometric development. |
|
Angles as turn: A dynamic geometry conceptualisation
for the primary grades |
Authors: Nathalie Sinclair |
Affiliations: Simon Fraser University |
The concept of angle is complex and has been shown to be very
challenging for learners. In this paper I show how the conceptualisation of
"angle-as-turn" can be developed effectively for young children
(starting at age 5) through the use of dynamic geometry software. I will
describe the design of the set of tasks based on "angle-as-turn."
It will also discuss the results of experimental work with kindergarten
children (aged 5) using Sketchpad to engage with these tasks. |
|
Perspective drawing... How can Cabri 3D help deeper
understanding of perspective? |
Authors: Jean-Marie Laborde |
Affiliations: Cabrilog, University of Grenoble and CNRS |
Perspective drawing has been a challenge for centuries if not
millenaries. Different cultures have been taking various approaches and came
to different solutions.
Nevertheless the so called central perspective (including its limiting case
parallel perspective) plays a dominant role and indeed rules the kind of
representation most of cameras tend to achieve.
Using ancient or more recent iconography I will use Cabri 3D for an overview
of these various issues.
From this "perspective" I will also look at the mathematically well
posed problem of perspective in other dimensions and not just at projecting
3D-objects on a canvas.
For a deep understanding of the concept of perspective we will explore how
things work when projecting a planar object on a line and, probably more
challenging, 4D-objects into our ordinary space. We will construct and then
contemplate the folding of their nets (actually 3D-bodies) back into their
original 4D-solids, all this projected in our space — and then onto a flat
screen. |
|
GRAPHING CALCULATOR USAGE IN MATHEMATICS ASSESSMENT
IN STPM AND MATRICULATION LEVEL IN MALAYSIA |
Authors: Noraini Idris |
Affiliations: Universiti Pendidikan Sultan Idris (UPSI) |
Proponents of graphing calculators generally contend that using
such hand-held technology in the classroom will save time on tedious
calculations and remaining time can be used for investigation of different
aspects of a given problem. It is also argued that the availability of such
hand-held technology enables students to access numerical, graphical and
symbolic representations of a given problem that will help the students find
connections among these representations to make sense of the problem.
Graphing calculators should be used in ways which allow students to learn
mathematics in practical and meaningful context, using analytic methods
together with graphical and numerical techniques. When the use of graphing
calculator is allowed in the assessment, syllabus should be drafted in line
with the use of graphing calculator. This requires a clear knowledge on the
findings to be achieved. A good understanding of graphing calculator is also
important so that we can maximize the use of this technology in assessment.
Integration of graphing calculator in assessment requires more attention, not
just allow students to use in the assessment, even encouraging students to
explore the use of data in the real world. In this presentation, presenter
will share an overview of graphing calculator (GC) in Malaysia, benefit of GC
and finding of various studies. |
|
Can Mathematical Invention be Automated? |
Authors: Bruno Buchberger |
Affiliations: Johannes Kepler University |
The essence of both mathematical research and mathematical
education is explanation. Ex-planation means "making complicated things
plain or simple". In other words, in mathematics, we attempt at thinking
once deeply for understanding the simple principles behind a seemingly
complicated situation and, then, we enjoy potentially infinitely many times
that we do not any more have to think but can just apply the result of our
thinking for potentially infinitely many cases in a completely mechanical
way. In modern times, by the mathematical invention of the universal
(programmable) computer principle, this can also be described by saying that
the goal of mathematics is the invention and the proof of general knowledge
on the basis of which infinitely many instances of a problem can be solved by
one algorithm, i.e. a procedure that can be executed on a computer without
any insight-in a completely mechanical way.
Mathematical invention does not proceed in one layer, i.e. just by adding
more and more knowledge and more and more algorithms for solving more and
more problems on classes of mathematical objects like numbers, geometrical
figures, graphs etc. Rather, the mathematical formulae (definitions,
theorems, problem specifications, algorithms) themselves can be considered as
(linguistic) objects in a higher layer for which problems can be formulated
and, hopefully, solved by algorithms. Thus, the invention and proof of
theorems and algorithms itself can be considered as a mathematical problem -
on objects that are formulae - for which we may ask for an algorithmic
solution. This area of mathematics is called "automated reasoning"
with various variants (automated theorem proving, automated proof checking,
automated algorithm synthesis, etc.)
In this talk, we give an overview on the advances of automated reasoning in
the past decades. Notably, we report on recent research of the speaker in the
area of automated algorithm invention and the computer-support of
mathematical theory exploration. The approach developed in this research is
based on two natural and powerful concepts:
(a) Formulae schemata (that mimic basic ideas in the formulation of
mathematical knowledge and mathematical methods).
(b) Generation of conjectures from failing proofs (that mimic a fundamental
heuristic principle of human invention in mathematics).
In the talk we give some typical examples that demonstrate how much of
mathematical invention and verification can currently be automated. In fact,
it will be shown that what needed the ingenuity of a typical math PhD student
a couple of decades ago can now be generated automatically by systematic
meta-mathematical procedures. Also, in the talk, we will draw some
conclusions from these research results on the future of mathematical
education and, more generally, for the "mathematics of the 21st
century" in distinction to the mathematics of the 20th and the 19th
century. |
Abstracts for Full Papers
|
From Ancient ‘Moving Geometry’ to Dynamic Geometry
and Modern Technology |
Authors: Miroslaw Majewski,
Jen-Chung Chuan |
Affiliations: New York Institute of Technology, Abu Dhabi
Campus, NTHU, Taiwan |
Ancient Greek and later Medieval Muslim geometers highly valued
geometric constructions that can be created using a straightedge, i.e. a
ruler without marking, and a compass. However, solutions of a number of
problems in geometry of this period of time were not possible to obtain using
these traditional and noble, as it was considered, methods. Such problems
were, for example: trisection of an angle, construction of a regular nonagon
or heptagon, squaring the circle or doubling the cube. Because these problems
were fairly important at this time, slightly less noble, but reasonably
efficient methods to solve the mentioned problems were invented. One of them
is, so called verging constructions method or constructions with compass and
marked ruler. Ancient mathematicians used also a number of constructions
where by moving a segment, a line or even a larger group of objects, a
desired effect was achieved. For example the famous construction of heptagon
by Archimedes, commonly considered as the most unique and elegant
construction from ancient times, was created by using moving geometry.
Surprisingly verging and other constructions with moving elements resemble
activities that are the essence of the dynamic geometry software, e.g. create
a geometric construction with a free element (a point, a segment or a line)
and then move the free element to obtain a solution or to check if a
hypothesis is valid.
In this paper we analyze the origins of dynamic geometry and show how some of
the ancient Greek and medieval Islamic moving geometry constructions can be
created with Dynamic Geometry software – Cabri, Sketchpad or any other
program for geometry. We also show how the idea of moving geometry
contributed to the development of modern technology. |
|
Sequences of Integrals in Experimental Mathematics |
Authors: Hideshi Yamane |
Affiliations: Kwansei Gakuin University |
Some sequences of integrals have nice patterns as can be found
in CAS-assisted experiments. In the present paper, we present some
interesting examples
of this kind and explain useful tips about the use of Maple.
We also give a proof of a formula in Fourier analysis. It
is based on the study of a sequence of integrals and is well suited
for experimental mathematics. It can replace a conventional,
tricky proof based on a strange lemma. |
|
Monounary algebras and functional graphs in upper
secondary school mathematics. |
Authors: Helena Binterová,
Eduard Fuchs, Marek Šulista |
Affiliations: Pedagogical Faculty of the University of South
Bohemia in Èeské Budìjovice, Faculty of Science of Masaryk University in Brno
– associate professor of the Institute of Mathematics and Statistics, Faculty
of Economics and the Faculty of Economics of the University of South Bohemia
in Èeské Budìjovice – assistant at the Department of Applied Mathematics and
Informatics |
In the paper alternative descriptions of functions are
demonstrated with the use of a computer. If we understand them as mono-unary
algebraic functions or functional graphs, it is possible, even at the school
level, to suitably present many of their characteristics. First, we describe
cyclic graphs of constant and linear functions, which are a part of the
upper-secondary level educational curriculum. Students don''t expect to see
the surprising characteristics of such simple functions which can not be
revealed using traditional Cartesian graphing.
The next part of the paper deals with characteristics of functional graphs of
quadratic functions, which play an important role in school mathematics and
in applications, for instance in the description of non-linear processes. We
show that their description is much more complicated.
In contrast to the case with functional graphs of linear functions, it is
necessary to use computers. Students can find space for their own individual
exploration to reveal lines of interesting characteristics of quadratic
functions, which give students a new view on this part of school mathematics. |
|
Determination Stability Ray of a Decision Making Unit
in Definition of the Right and Left Returns to Scale |
Authors: REZA Shahverdi |
Affiliations: Department of mathematics , Qaemshahr Branch,
Islamic Azad University, Qaemshahr , Iran |
This paper calculates stability ray of a decision making unit ,
which the right and left its returns to scale , is given, such that its RTS
characteristic, in the RTS classification remains.
With regarding to definable hyperplanes of the right and left RTS and
classification of DMU, models for measuring stability ray, are proposed. |
|
Visualization of the Cross Ratio and its Geometric
Application |
Authors: Yoichi Maeda |
Affiliations: Tokai University |
Cross ratio is a special number associated with an ordered
quadruple of points. This number can be visualized in the three-dimensional
hyperbolic space as a configuration of two geodesics. Using this
visualization, we can show that the angle between two geodesics in the
hyperbolic space is a simple function of the cross ratio. Furthermore, we
will see that this angle has a relation with the triangle inequality in the
Euclidean geometry. |
|
The MCY-Activities:Constructing and Sharing Three
Types of Pattern |
Authors: Han Hyuk Cho, Ji Yoon Lee, Chul
Ho Kim, Dong Hun Lee |
Affiliations: Mathematics Education, Seoul National University,
Mathematics Education Seoul National University, Hana High School |
In recent years, an increasing number of viewpoints hold that
students should be engaged in a learning environment where understanding and
knowledge transfer take place. This study introduces Mathematics Created by
You (MCY)-mentoring program, which allows students to construct pattern
artefacts to explore and share. This program is Web 2.0 online-based and so
can be shared by several people and mathematics leaning takes place through
interactions within this carefully designed environment. In addition, this
studies the activities about three types of patterns and three types of
mathematical patterns (building block pattern, motion graph pattern and
recursive and probabilistic pattern) included in the activities, which are
currently taking place for a project that builds an amusement park called
¡®Mathland¡¯ as a part of MCY-mentoring program. It is observed that the
symbol expression and pattern that students designed to create their pattern
artefacts in the context of play were progressed from a personal expression
to a mathematical expression. |
|
Calculators and the mathematics curriculum |
Authors: Barry Kissane,
Marian Kemp |
Affiliations: Murdoch University |
Developers of mathematics curricula make choices regarding the
kinds of technology that are to be used by students, which in turn influences
the work of both students and teachers to learn and teach mathematics. This
paper analyses the potential relationships between calculators and the
mathematics curriculum, drawing implications for what can be learned through
student access to different levels of calculators. Three different levels of
calculators are considered in detail in the paper: scientific calculators,
advanced scientific calculators and graphics calculators. Significant
consequences of these choices are described and exemplified through a
consideration of a number of mathematical topics that are commonly taught in
many curricula in Asian countries. |
|
Applications of CAS to analyze the step response of a
system with parameters |
Authors: Takuya Kitamoto |
Affiliations: Yamaguchi University |
Recently, Computer Algebra
System (CAS) such as Maple and Mathematica increases its popularity in the community
of education, mathematics, sciences and
engineering, because they can treat symbols, which
conventional numerical software packages can not.
In this paper, we apply CAS to the control engineering where CAS are quite
useful, since symbols can represent unknown values such as unknown dynamics,
design parameters and modeling error in a natural way.
We focus on a system with linear differential equation x''(t) = A x(t) + B
u(t), y = C x(t)
where A, B and C are matrices whose entries are polynomials in
parameter k. We examine the behavior of the step response of the system,
which is expressed by y(t) = C ( e^{A t} - E ) A^{-1} B,
where e^{A t}, E and A^{-1} denote the matrix exponent of matrix
A t, the unit matrix and the inverse of matrix A, respectively.
To analyze the behavior of y(t), we approximate e^{A t} with matrix Pade
approximation, and compute a rational function approximation of y(t).
This enables us to examine various properties of y(t). For
example, we can compute approximations of the peaktime and the
peakvalue explicitly as a rational function of k, which makes clear
the relations between those values and parameter k. We
present some analysis and design examples of the system, utilizing
these computations. |
|
Exploring Pattern Generalization in the Logo-based
Microworld |
Authors: Han Hyuk Cho, Chul
Ho Kim, Dong Jo Shin, Ji Yoon Lee |
Affiliations: Seoul National University |
This paper aimed to design learning activities for pattern
generalization in the Logo-based JavaMAL microworld. We focused on figural
pattern activities using polycube pattern, included in the elementary school
mathematics textbooks in Korea. We designed web 2.0 based JavaMAL microworld
so that students can create and explore pattern objects interactively, and
provided students with virtual manipulative and expressive tools to support
their thought process for pattern generalization. We analyzed students¡¯
algebraic thinking based on their symbolic pattern expressions and responses
in the pre-test and post-test. The results suggested that students¡¯ pattern
reasoning became more structured and sophisticated, and the JavaMAL
microworld was very useful to support students¡¯ algebraic thinking for
pattern generalization in the context of pattern manipulation and
construction. |
|
Special Pythagorean Triangles and Pentagonal Numbers |
Authors: Mita Darbari |
Affiliations: St. Aloysius College, Jabalpur, India, Rani
Durgavati University, Jabalpur, India |
Keywords: Pythagorean Triangles, Pentagonal numbers, Mathematica
Abstract:The objective of this paper is to show that how research in
Mathematics can be facilitated by the use of softwares. In this paper,
Special Pythagorean Triangles, in terms of their perimeter to be Pentagonal
numbers, are obtained with the help of Mathematica. Cases, when one leg and a
hypotenuse are consecutive, are also discussed. A few interesting results are
observed. 3D graph of corresponding Pythagorean triplets is plotted using
software Mathematica. |
|
Effectiveness of the Smart Board Technology on Growth
of Mathematics Achievement and Critical Thinking Skills among Fifth Grade
Students |
Authors: Mamdouh Soliman |
Affiliations: Kuwait University |
The value and importance of critical thinking is clearly
established as an preliminary step to achieve the most important goal of the
teaching of mathematics; the challenge for instructors lies in successfully
promoting students'' critical thinking skills within the confines of a
traditional classroom experience. Since instructors are faced with a number
of students who are differ in their abilities in achievement and thinking ,
they have to change their policy to meet their instructional objectives and
facilitate learning, they are often forced to make instructional decisions
between content coverage, depth of understanding, and critical analysis of
course material. This study examined whether smart board technology increased
growth in mathematics performance and critical thinking of fifth grade
students. A descriptive–qusi survey approach was used in this study. The
sample consisted of 117 students randomly selected from four elementary
schools for girls. Two of the schools used smart board during mathematics
instruction, and two schools did not use smart board technology. All students
were taught the mathematics curriculum according to the Kuwait ministry of
education directions. Sample examined twice in mathematics achievement test
and filled also twice in a closed questions in critical thinking. Reliability
and validity of both instruments were determined by using Cronbach’s Alpha
and Kuder Richardson Formula 21 respectively (á=0.89 for achievement test
& 0.91 for the critical thinking scale). Descriptive and inferential
statistics were used to analyse the data using SPSS Win19. Results showed
that there was no significant difference among two groups of students
regarding the development of critical thinking, while there was a significant
statistical difference regarding mathematics achievement in favour of the
smart board technology group. The smart board significantly improved
students'' critical thinking skills, which could be solving many mathematical
teaching problems.
These findings suggest that using smart board technology could
not be an effective pedagogy to enhance students'' critical thinking skills,
while could be an effective to enhance students'' mathematics achievement.
Due to this limitation, further research regarding the use of
creative technologies to stimulate and challenge the ordinary learners is
warranted. |
|
Bias of ML Estimator for Multivariate Regression
Model with Vector AR(1) Noise |
Authors: Wai Kwong Cheang |
Affiliations: National Institute of Education, Nanyang
Technological University |
This paper considers the use of technology to assess the
adequacy of a theoretical bias result in the maximum likelihood (ML)
estimation of multivariate regression model with vector autoregressive AR(1)
noise. We develop a relatively explicit and conveniently computable
approximation for the bias of the ML estimator of the AR parameters. This
bias estimate can be used to obtain a bias-corrected ML estimate. To assess
the adequacy of our bias approximation, R/S-PLUS programs are written to
calculate the theoretical biases and simulate the empirical biases for
polynomial regression. Simulation results suggest that the theoretical ML
bias approximations are in reasonable agreement with the empirical biases
when the mean is unknown. In the presence of a linear or quadratic trend, a
longer series length is needed for the bias approximations to be adequate. |
|
Teaching finite fields with open-source CAS |
Authors: Alasdair M |
Affiliations: Victoria University, Melbourne Australia |
Finite fields have long been studied for their intrinsic
interest, and more recently for their uses in the definition of some modern
cryptographic systems. The Advanced Encryption Standard is based on
the cryptosystem Rijndael~\cite{daem02}, which makes extensive use of finite
fields in its computation. We have taught a cryptography course to students
both locally, and interstate using the medium of the Access
Grid~\cite{acce12}. Many of these students have limited exposure to modern
abstract algebra, and the use of a Computer Algebra System has been vital to
aid their
understanding and assimilation of the material. Over the years we have used
Maple, Maxima, Axiom and Sage. This article concentrates on our use of the
last three, and shows that for abstract algebra, the open source systems are
far superior to the alternatives. |
|
Interactive Worksheets for Learning the Connection
Between Graphic and Symbolic Object Representations |
Authors: Hitoshi Nishizawa,
Takayoshi Yoshioka, Martti E. Pesonen, Antti Viholainen |
Affiliations: Toyota National College of Technology, University
of Eastern Finland |
Learning the close relation between graphic and symbolic object
representations is a key to conceptual understanding of mathematical
functions and vector equations. For learning such a relation, it is valuable
that students manipulate the graphs of functions, and transform the graphic
objects directly with observing the simultaneous change of related equations.
Here is the need for tailored worksheets, preferably embedded into a
www-based learning-support system.
Interactive worksheets concerning linear algebraic concepts like vector
operations, basis, linear functions and eigenspaces in the plane were tested
in university courses during the last decade. Such worksheets allow direct
interaction between the student and the dynamic figure containing geometric
objects. Each figure is accompanied by problems to be solved when exploring
relationships in the figure. The students’ and teachers’ positive feedback
encourages extending the idea to three-dimensional linear algebra.
Next implementation of the worksheets shows graphic objects as the targets
that students move and reshape their own objects to overlay. The simultaneous
change of graphic and symbolic objects provides the students with
opportunities to recognize their relations. This paper describes how the
worksheets are designed, implemented into www-systems, and what reflections
they received from students and teachers. |
|
Effects of Technological Gadgets Utilization in
Teaching College Algebra |
Authors: Thelma Abajar, Patrick Galleto, Craig Refugio |
Affiliations: Negros Oriental State University, Jose Rizal
Memorial State University |
This study investigated the effects of technological gadgets
utilization in teaching College Algebra at Jose Rizal Memorial State
University System, Philippines. Quasi – experimental design utilizing the
Pretest – Posttest Nonequivalent Group Design was used in the study.
Based on the findings, it is concluded that the knowledge students possessed
in both the control and the experimental groups on the topics included in the
experiment is equivalent or comparable before the intervention. The study
also discloses that the experimental group performs significantly better than
the control group after the intervention. It is deduced further that there is
a significant variation between the performance of the students who were
taught using the traditional method of teaching and those who were taught
using the technological gadgets in teaching and learning College Algebra. In
addition, the study concludes that both the interventions, traditional method
of teaching and technological gadgets in teaching and learning College
Algebra, made improvement in College Algebra performance of the students or
that students performed better during the posttest than during the pretest.
Moreover, the College Algebra performance of the students in the experimental
group is greatly influenced by the technological gadgets used by teachers and
students in College Algebra class which finally means that students in the
experimental group perform better than their counterpart. |
|
The Effects of a Portable Computer Algebra System
(CAS) on Pre-university Students’ Attitudes towards CAS |
Authors: Wee Leng Ng, Yee
Dat Sun |
Affiliations: National Institute of Education, Nanyang
Technological University, Anglo-Chinese Junior College |
The main objectives of this study were to investigate the
effects of a portable computer algebra system (CAS) on students’ attitudes
towards CAS and find innovative ways of teaching mathematics using the
portable CAS. An intact class of second year pre-university (Year 12)
students in Singapore participated in this study. The participating students
were each given access to a CAS calculator for approximately six months and
underwent a CAS Intervention Programme (CASIP). The CAS Attitude Scale
(CASAS) was administered on three separate occasions to the participating
class to measure students’ attitudes towards CAS. The CASAS comprises four
subscales of 10 items to measure students’ sense of Anxiety, Confidence,
Liking and Usefulness in regard to the CAS. Based on paired-sample t-tests,
even though the second and third surveys indicated improvement in all four
subscales and the overall scale, with the exception of the liking subscale in
the first comparison, the results were not statistically significant. |
|
STUDENTS’ SKILLS IN MATHEMATICAL COMPUTATION |
Authors: Patrick Galleto, Craig Refugio |
Affiliations: Negros Oriental State University, Jose Rizal
Memorial State University |
This study sought to find out the students’ skills in
mathematical computation using graphing calculator in teaching Mathematics
among freshmen College Algebra students of the College of Education of Jose
Rizal Memorial State University, Philippines. The skills that the students
possessed in both the control and the experimental groups on the topics
included in this experiment is equivalent or comparable before the
intervention. The study also concludes that the experimental group performs
significantly skillful than the control group after the intervention. It can
be deduced further that there is a significant variation in the students’
skills in mathematical computation between the control group with the
traditional method of teaching and the experimental group with the used of
graphing calculator in teaching and learning Mathematics. In addition, the
study concludes that both the interventions, traditional method of teaching
and using graphing calculator in teaching and learning Mathematics, make
improvement in the students’ skills in mathematical computation. This means
that students perform skillfully better during the posttest than during the
pretest. However, students’ skills in mathematical computation in the
experimental group are greatly influenced by the graphing calculator used by
teachers and students in College Algebra class. This concludes that students
in the experimental group perform skillfully better than their counterpart. |
|
Connecting Probability to Statistics Using Simulated
Phenomena |
Authors: Theodosia
Prodromou |
Affiliations: PME, MERGA, ICME, CERME |
This article addresses the use of probability to build models in
computer-based simulations, through which exploring data and modelling with
probability can be connected. The article investigates students’ emerging
reasoning about models, probability, and statistical concepts through an
observation of grade 9 students, who used TinkerPlots to model a sample
simulation based on probabilistic models of populations and tested models by
comparing their behaviour with the generated data. Results from this research
study suggest that students’ use of probability to build models in
computer-based simulations helps students to conceive of objects as
comprising a set of data and the data distribution as being a choice made by
the modeller to create approximations of real or imagined phenomena, where
approximations depend on signal and variation. |
|
Visualization of a Mathematical Model of Computation |
Authors: Pradip Dey,
Gordon Romney, Mohammad Amin, Alireza Farahani, Hassan Badkoobehi, Ronald
Gonzales |
Affiliations: National University, School of Engineering, Technology
and Media, National University, School of Engineering, Technology and Media |
Mathematical models of computation such as Turing Machines,
Pushdown Automata, and Finite Automata are useful in modeling real world
computational problems. This paper presents dynamic visualization of some
Turing Machines which clarify computational problem-solving aspects of these
models. The design and implementation of the dynamic visualization are
performed in an iterative process making improvements through successive
iterations. The dynamic visualization is available at the following website:
http://www.asethome.org/math/. An example of static visualization of one of
the models is presented for consideration of the relative advantages and
disadvantages of both visualization techniques. |
|
Cognizable, Learnable, Expressible, Accessible, and
Reasonable Model in Mathematical Thinking, Reasoning and Problem Solving |
Authors: Hsiu Ju Chang |
Affiliations: Department of Education, National Chengchi University,
Taipei County Shu-Lin High School |
By means of dynamic visualization, learners have multiple
cognitive channels to participate knowledge and information acquisition.
However, the acquisition and internalization processes may dependent on the
cognitive load of individual learners. The analogy algorithm of dynamic and
visual aid learning objects will lead individuals to make concept projections
and infer specific analogical and relational conceptions during mathematical
problem thinking, reasoning, and solving processes. The Cognizable,
Learnable, Expressible, Accessible, and Reasonable Model (CLEAR Model) is to
identify the core objectives of mathematic concepts and operations into
visible, comprehensible, and recognizable presentations. The transactional
analysis, inference, and analogy processes can express the essential
conceptions and eventual conceptualizations in thinking, reasoning, and
solving mathematical problems. In other words, the analogy algorithm of
dynamic and visual aid learning objects usually take ownership and share
leadership of instruction processes. In mathematical learning, the
expressions of conception may formulate by individual¡¦s psychological order
reasoning or generate by mathematical logic reasoning. In this paper, we show
the parallel learning objectives in 1) two sides of two angles are parallel
each other, 2) two sides of two angles are perpendicular each other, and 3)
two sides of two angles are one side parallel and another perpendicular each
other within using the CLEAR model to evaluate the analogy algorithm of
learning objects and try to build an adaptive and reasonable learning paths
for individuals to build their mental image. |
|
A Didactical Transposition of the Perspective Theorem
of Guidobaldo Del Monte with Cabri 3D |
Authors: Jean-Jacques Dahan |
Affiliations: IREM of Toulouse |
The parallel perspectives used to represent 3D figures in 2D
have the great advantage to respect the “parallelism” property, which is an
enormous help for those who use these figures in 3D geometry problem solving.
But these representations do not give a realistic impression. They do not
display what our eyes see. At the beginning of the 15th century Guidobaldo
(1545-1607) solved this problem mathematically in Perspectivae Libri Sex. He
was the first ([8]) to give the proof of the positions of the vanishing point
of a direction with respect to the position of the observer. Kirsti Andersen
considers him as the father of the mathematical theory of perspective ([1]),
We will see how Cabri 3D can help to understand what this theorem states. The
principal aim of this paper is to show how I rediscovered this theorem using
an experimental process ([11]), how I have discovered a more general form of
it, especially that which includes the angle between the plane of the
representation and the vertical plane parallel to the plane of the eyes (and
the chin) of the observer. Vanishing points arose to help us understand the
geometry of buildings, which we photograph with our cameras. This work
started with a special task I had to achieve: help middle school students to
understand the obtaining artistic results with their cameras before a
competition focused on “the mathematics in the city”. So, we can use the
stages of this discovery as the base of an approach of the teaching of the
conical representations. Back to the parallel perspective we will give some
results never published about the coefficient of such perspectives with
respect to the angles of their direction. |
|
Multiple Suggestions for Interactive SDE Estimation |
Authors: Ryoji Fukuda, Hiromi Yokoyama |
Affiliations: Faculty of Engineering Oita University |
We are developing educational software to estimate the
parameters of stochastic differential equations (SDE) using a single set of
time series data. Our target equation is a linear SDE with constant
coefficients, which is determined by four real parameters. In our previous
version, for a single set of data, we obtained a single set of estimated
parameters and suggestions to change them. In this study, we propose a method
to give several set of estimated parameters, assuming several situations for
the first estimation. Then, we will be able to find closer set of parameters,
and the interactive estimation will be improved. |
|
Improvements and Evaluations of Tactile Graphical
Viewer for the Visually Impaired |
Authors: Ryoji Fukuda,
Akihiro Miura |
Affiliations: Faculty of Engineering Oita University |
Our tactile graphical viewer recognizes the type of a
handwritten input curve and displays it on a tactile display. We propose new
recognition method and change function for input curves. With this
recognition method, we propose a procedure to add new curve types. Using the
change function, we are able to reduce the time taken to create the required
curves. This system has functions to provide some graphical information as a
tactile images. We present some evaluations for receiving the information and
understanding the underlying properties. |
|
Blending of Traditional Approach and Internet
Technology to Teach Engineering Mathematics |
Authors: Vipul Shah,
Rajesh Sanghvi |
Affiliations: G H Patel College of Engineering & Technology,
Vallabh Vidyanagar, Anand, Gujarat, India, G H Patel College of Engineering
& Technology, Anand, Gujarat Technological University, Gujarat |
Mathematics is an integral part of the study of engineering
regardless of which branch of engineering is chosen. In this article, we
suggest a blending of analytical approach and use of internet technology for
interactive teaching of computationally oriented undergraduate engineering
mathematics. In recent years, an increasing number of web sites have offered
significant material which is publically available. We believe that
integrating the traditional method, such as with chalks and black board, with
screen projections from the web pages for better visualization surely
increases depth of content knowledge and pedagogy through inquiry and
reflective practices.
In this paper, we shall discuss how internet technology is useful for some of
the topics like differential equations, linear algebra, numerical methods, of
engineering mathematics while teaching in a class. There are numerous sites
explaining the concepts in depth as well as providing examples related to
field in different branches of mathematics. Students can learn the material
themselves also. Video lectures delivered by experts in the field to the
students of recognized institutes are also available on the internet. Many
e-books are also freely downloadable. |
|
Creative Learning of Analytic Geometry through NC
Programming with a Virtual Lab Application |
Authors: Pongrapee
Kaewsaiha |
Affiliations: International College, Suan Sunandha Rajabhat
University, Thailand |
This paper presents the use of NC programming as a part of
learning activities in analytic geometry class, with the use of a developed
virtual lab application. The aim of the designed learning activity is to
enhance the creativity of students in learning analytic geometry by
visualizing the relationship between course materials and a real application
in manufacturing industry. |
|
|
|
Expanding Plane Geometry Using The Geometer’s
Sketchpad |
Authors: Chaweewan Kaewsaiha |
Affiliations: International College, Suan Sunandha Rajabhat
University, Thailand |
This paper describes a very broad meaning of “expandable plane
geometry”. It includes any plane geometry that transforms by using the
tessellation transformation concept, a two-space expansion. The symbols used
to describe the tessellation forms (regular and semi-regular) use naming
conventions by choosing a vertex, then look at one of the polygons that touch
that vertex. How many sides does it have? The notation of a regular
tessellation of triangles has six polygons surrounding a vertex, and each of
them has three sides: the symbol used to describe is “3*3*3*3*3*3” or “36”
means there are six triangles at each vertex. A semi-regular tessellation is
a set of regular polygons of two or more kinds so arranged that every vertex
is congruent to every other vertex. |
|
Elementary proof of Sejfriedian properties |
Authors: Michael Sejfried,
Vladimir V. Shelomovskii |
Affiliations: METAL UNION, Czestochowa, Poland; Murmansk State
University, Russia |
In this paper we investigate a new type of symmetry for an
arbitrary triangle, so called Sejfriedian, and we show an elementary proof of
selected properties of Sejfriedian. This type of symmetry was obtained by
Michael Sejfried in 2008(?). Sejfriedian is a pair of triangles inscribed
into a circle, the circle and the set of lines coming out of all vertices of
the given triangle. It has many interesting properties. Sejfriedian gives
students an opportunity for in-depth study of the properties of stereographic
projection and spatial inversion and combining of mathematical expressions. |
|
e-Teaching and e-Assessment of Minimum - Maximum
Problems using Maple |
Authors: Bill Blyth |
Affiliations: School of Mathematical and Geospatial Sciences, RMIT
University, Australia |
Computer Algebra Systems, CAS, are now mature. For years, we’ve
used Maple, a leading CAS, in weekly computer laboratory sessions: a
component of an otherwise traditional first semester university calculus
course. The Maple topics come from the senior school curriculum, but with
innovative approaches to curriculum, pedagogy and assessment. A major
objective is that students have a positive attitude to using Maple.
First year calculus repeats some senior school calculus, for
example “Word problems” which students have always found difficult. This
presentation focuses on “Maximum” problems. Our Maple topics have no
lectures: students work collaboratively in small groups.
We demonstrate an explicit Polya approach to maximizing an area
problem, with an assignment on the Norman window problem that’s
individualized for each student group. We discuss a variety of assessment
methods: paper submission (marked by hand), Maple file submission (e-Marked
by annotating each Maple file with text or Digital Ink), Computer Aided
Assessment (CAA: automatic marking of the symbolic answer using Maple – which
MapleTA can also do). Alternatively, MapleTA can be used to mark student work
done by hand with just entering the result into MapleTA. Within Maple, we
have implemented a procedure to mark plots (which no other Computer Aided
Assessment can do). Surveys show students really like immediate automatic
marking. We demonstrate materials for a following session introducing
multiple representations and multiple solution methods: graphical (zoom-in),
animation, proof without calculus and with calculus; with an accompanying
parameterized assignment. Students are engaged, active and collaborative learners
with these Maplesessions. |
Abstracts for Papers with Abstract Only
|
UNION DISTINCT FAMILIES OF SETS, WITH AN APPLICATION
TO CRYPTOGRAPHY |
Authors: Mausumi Bose, Rahul Mukherjee |
Affiliations: Indian Institute of Management Calcutta, Indian
Statistical Institute |
A family of sets is called K-union distinct if all unions
involving K or fewer members thereof are distinct. If a family of sets is
K-cover-free then it is K-union distinct. In this paper, we recognize that
this is only a sufficient condition and, from this perspective, consider
partially cover-free families of sets with a view to constructing union
distinct families. The role of orthogonal arrays and related combinatorial
structures is explored in this context.
The results are applied to find efficient anti-collusion digital
fingerprinting codes which aim at deterring unauthorized utilization of
multimedia content by a coalition of users. These have been of considerable
recent interest. It is seen that our construction leads to an improvement
over the existing ones in the sense of accommodating more users for a given
resiliency. |
|
Impact of Using Scientific Calculator In Examination
Of Engineering Mathematics |
Authors: Wei Ching Quek, Chew
Peng Kok-Mak |
Affiliations: Singapore Polytechnic |
Advanced Scientific Calculators such as CASIO fx991-ES has been
available and approved for Singapore Polytechnic Examinations for many years.
However, many students are not aware of the capabilities of these calculators,
especially the first year engineering students who are still used to the
scientific calculators approved for O-level examinations. The author believe
that the “newly” available features in advanced scientific calculators can
help students to speed up tedious computations and improved accuracy during
examinations. The authors decided to explore methods of enhancing students’
understanding of such humble tool. In addition, it is hoped that through
these research, teaching staff will get to reflect on curriculum and
assessment. |
|
CLASSIFICATION OF WALLPAPER IN ISLAMIC ARTS FOUND IN
SINGAPORE AND MALAYSIA |
Authors: Wei Ching Quek,
Jiewen Kam |
Affiliations: Singapore Polytechnic, SIM University |
The presentation will introduce a wallpaper pattern
mathematically using the concept of wallpaper groups. The authors have
visited museums and mosques in Singapore and Malaysia and will share their
findings on classification of two-dimensional islamic arts based on wallpaper
groups. The author will also share some wallpaper designs activity worksheets
produced with Geometer’s Sketchpad® for upper primary students. |
|
Technological Tools and Chinese College Entrance Exam
Problems |
Authors: Qiuxia Li |
Affiliations: Xi'an Senior High School |
As stated in the Problem Corners at the eJMT
(https://php.radford.edu/~ejmt/ProblemCorner.php ): “Many mathematics
teachers present an answer to a problem too quickly before allowing students
to grasp the key concept behind the problem.” In this presentation, we will
describe some general obstacles students face when they solve a typical
college entrance problem, and we will show how technological tools can
enhance their understandings not only on solving one particular problem but
also on general related concepts too Since examinations play important roles
in Chinese education system, it is important to stress the knowledge
competency not only in math content and but also the use of technological
tools. Consequently, teachers’ training programs are essential. |
|
Using Spreadsheets to create different rug patterns |
Authors: Maryanne Bagore |
Affiliations: Divine Word University |
A spreadsheet is a powerful mathematical tool that is widely
used by math educators and learners to comprehend and solve many mathematical
problems. This paper will illustrate an innovative way on how Excel can used
to create different artistic rug designs or patterns using the concepts of
Geometry, Algebra and Calculus in a Spreadsheet Application. Mathematical
models are created to show how a particular rug patterns or designs can be
created in Excel. My examples of rug patterns or designs would be taken from
the traditional Papua New Guinean mats and/or rugs which are made mostly from
the pandanas and coconut trees. In addition to PNG mat/rug designs, other
examples will include rug patterns or designs from different countries and
cultures such as the ‘kilim’ from Turkey. Through my examples, the main point
is on how Excel can be seen as an application that can used to create
interesting, creative or odd things and not just for the fun of doing
mathematics. The concept of this paper can be used in both the classroom
teaching and teacher development. |
|
SPICE UP MATHEMATICS LESSONS WITH KODU |
Authors: ROHAIZA RAMLI |
Affiliations: JPNWP KUALA LUMPUR |
This presentation will discuss the role of kodu, in highlighting
the role of ICT as an evaluation steps in learning and teaching of
mathematics. Kodu is a powerful visual programming system invented at
Microsoft Research to allow creation of games and simulations in an intuitive
way within a richly detailed 3D world as to make learning more engaging and
it is the link to creativity and innovative ideas. This paper particularly
centers on lab activity that produced kodu games with simple programming
language to enhance effective learning of mathematics. The use of kodu could
be a catalyst variable to engage the students’ interest in studying
mathematics whereby rich graphic designed and 3D environment allow students
to become creative and innovative.
The discussions are based on the finding from a group of students at
secondary level in Malaysia. The objective of the study is to assess
students’ understanding after learning Coordinate Geometry using kodu as a
more mobile (stress-free) way of assessment approach. The findings indicated
that the exposure of kodu as a mean of evaluation is stimulating as the
students demonstrated a deep interest and total immersion as well as enjoyment
while carrying out the activity. Since kodu offers very simple, easy to
understand icon-based programming, some students took it to a higher level by
starting to create their own version of game activity. At this point, a
teacher may play a role to guide students to tailor-made their game to
reflect more on specific learning tasks that was intended. |
|
Teaching Graduate Statistics Through SPSS |
Authors: Craig Refugio, Ma.
Elsa Ilona Bulado, Evelyn Lazalita |
Affiliations: Negros Oriental State University |
This paper presents how a graduate statistics course is being
taught using SPSS in an ordinary state university classroom. A pretest was
given before the teaching-learning process was conducted. Data analysis and
interpretation were the main focus and the respondents were first taught
about appropriate research design and data collection as well as appropriate
selection of statistical tools.
Detailed,step-by-step hands on teaching was utilized on how to enter data and
obtain valid results. Interpretation of outputs and on how to present the
results in a research report were also emphasized.
Post-test showed that the respondents gained significant knowledge in
graduate statistics at 5% level of significance. |
|
GRAPHING INEQUALITIES AND SYSTEM OF INEQUALITIES
THROUGH TI 84 |
Authors: Craig Refugio, Ma
Elsa Ilona Bulado, Evelyn Lazalita |
Affiliations: Negros Oriental State University |
This study was conducted to the randomly selected freshman
college students of Negros Oriental State University, Main Campus 1,
Dumaguete City and sought to let students graph inequalities and system of
inequalities using the Texas Instrument (TI 84) after learning the paper and
pencil way of graphing those inequalities with an endview of letting students
understand the connections between technology and mathematical concepts.
Results showed that students understood that it is good, many times necessary
to graph inequalities/system of inequalities through TI 84 and that most of
the time TI 84 does not “find” answer” but merely helps to find appropriate
solutions to the problem. It is further showed by the students that if one
does not understand how to interpret the information that TI 84 provides,
then it is of no use at all. |
|
Teaching ANOVA Through MINITAB |
Authors: Craig Refugio, Ma
Elsa Ilona Bulado, Evelyn Lazalita |
Affiliations: Negros Oriental State University |
This paper presents the teaching of ANOVA using Minitab software
in an undergraduate Statistics class in Negros Oriental State University,
Dumaguete City, Philippines. The students were taught on how to enter data in
minitab and on how to run ANOVA. Interpretation of the output, post hoc
analysis and on how to present the results in a research report were
emphasized. Findings revealed that students found it easy and enjoyable in
analyzing data using ANOVA through minitab. With the many examples explored
by the students, they turned to be experts in analyzing data through ANOVA. |
|
Exploring Flipped Classroom Pedagogy in Teaching and
Learning of Sec 2 Mathematics in 1-to-1 Computing Environment |
Authors: Luis Tirtasanjaya
Lioe, Chik Leng Tan, Chin Wen Teo, Sharon Lee |
Affiliations: Nanyang Girls' High School |
In recent years, there is a pedagogical trend among educators
around the world to capitalise on video technologies and the Internet in
teaching and learning of various subjects across educational levels. An
increasingly-popular pedagogy is the flipped classroom model that includes
reversing activities in class and at home where lesson videos are used
outside of class time and more student-centred activities are conducted
during lesson time. In 2012, Nanyang Girls’ High School (NYGH) adopted a
1-to-1 computing programme across the whole Secondary 2 level (Grade 8),
where all students and teachers are equipped with an iPad for greater
engagement and collaboration in teaching and learning. Supported by this
school initiative, the team of six Sec 2 Mathematics teachers explored the use
of flipped classroom to teach 3 units of lessons to all Sec 2 NYGH students
(n = 406). The team adopted a semi lesson study model where all teachers came
together to plan, prepare, study, and evaluate their research lessons. Two
research cycles were carried out. The first cycle was completed in February
2012. All teachers in the team collaboratively created video lessons using
applications of their choice to go through concepts and examples on Solving
Simultaneous Equations involving Two Variables (2 weeks) for students to
watch outside lesson time. Students were taught two consecutive topics
Proportions & Variations (1 week) and Pythagoras’ Theorem (1 week) in the
second cycle held in May 2012. Based on the feedback and evaluation of the
first cycle, the instruction is refined in the second cycle to include videos
and lesson materials from Ace-Learning (http://ace-learning.com.sg). The
study adopts a mixed design approach where teachers’ qualitative surveys were
conducted three times (before 1st cycle, in-between the two cycles, and after
the 2nd cycle) and students’ mixed quantitative and qualitative perception
surveys were conducted after each cycle. The full paper will discuss the
emerging flipped classroom model of instruction from the two phases, challenges
that teachers experienced, and findings from teachers’ and students’ surveys. |
|
Fostering creativity in science amongst
kinaesthetically-inclined students through a simple mathematics-based toy in
Design & Technology (D&T) lessons |
Authors: Nazir Amir,
Subramaniam Ramanathan |
Affiliations: Ministry of Education, Singapore, National
Institute of Education, Singapore, National Institute of Education, Nanyang
Technological University |
This article describes an action research study conducted in a
secondary school in Singapore to show how a mathematical exhibit that is used
to demonstrate Pythagoras Theorem in the Singapore Science Centre has been
interpreted by a class of less-academically inclined students as they set out
to fabricate it in a creative manner during their Design & Technology
(D&T) lessons. By harnessing on the design and fabrication skills and
fundamental physics concepts that these students pick up in their D&T and
science lessons respectively, a platform is created for the hybridization of
mathematics to D&T and science through this toy.
Results from this study show that this simple mathematics toy can be a useful
D&T project as it offers an opportunity for the less-academically
inclined students to better understand the concept of Pythagoras Theorem and
at the same time offers opportunities for these students to make creative use
of physics principles to add value to the functionality of the toy. Students
in the study developed positive attitudes towards studying mathematics,
D&T and science after the project.
The study shows that it is possible to link mathematics to D&T and
science in a simple way that is within the school D&T curricula and one
that places focus on creativity in science as an outcome of curricula
interaction. |
|
Teaching Calculus with WebCT Vista and Maple Software |
Authors: Bakhodirzhon
Siddikov |
Affiliations: Professor of Mathematics, Department of
Mathematics, Ferris State University, Big Rapids, Michigan, USA |
For the last fifteen to twenty years there has been wide
exploration of innovative approaches to classroom instruction: the use of the
computer in teaching science courses. The results of those explorations have
proven that the use of the computer in teaching Calculus courses enhances the
students’ understanding. It is well known fact that students have difficulty
understanding Calculus, when it is taught in the traditional way: with chalk
and blackboard. The traditional method of instruction lacks the advantages of
the latest technology to demonstrate the applications of Calculus in the real
world.
In 2010, Ferris State University funded my sabbatical leave to develop
computerized Maple interactive teaching software for the Calculus 1 course.
The purpose of the project was to improve students’ understanding of the
course by using mathematical and scientific abilities of the latest
technology. I developed the web-enhanced Calculus 1 course, which is taught
entirely on-campus and uses WebCT Vista learning management system and Maple
software as a supplement. WebCT Vista software has been used to make the
instruction platform more accessible, and Maple software has been used to
make the teaching software more interactive and dynamic.
This talk is about the results of the development and implementation of the
computerized teaching platform for the Calculus 1 course. I will discuss
advantages of designing computerized tests, quizzes, lecture notes, and
homework problems. I will emphasize on the abilities of Maple software to
guide the students to solve complex calculus problems. I will share with the
audience my experience of overcoming difficulties of the development and
implementation of the computerized Maple interactive teaching software. |
|
Free vibration of symmetric angle-ply laminated
annular circular plate of variable thickness under shear deformation theory |
Authors: Viswanathan
Kodakkal Kannan, Saira Javed, Zainal Abdul Aziz |
Affiliations: Universiti Teknologi Malaysia |
In this paper, free vibration of symmetric angle-ply laminated
circular plates of variable thickness is studied. First order shear
deformation theory is included to derive the equilibrium equations of the
annular circular plate. Using the stress-strain and strain-displacement
relations, the equilibrium equations are simplified to obtain the coupled
differential equations in terms of displacement and rotational functions.
These functions are approximated using the Bickley splines and then applied
the collocation procedure to obtain the generalized eigenvalue problem. The
effect of transverse shear deformation and rotary inertia on the frequency
parameter with respect to the cone angle, thickness variation, radii ratio,
ply-angles and various types of material properties and boundary conditions
have been discussed. |
|
Contributing to mathematics education by enabling
community engagement with the GeoGebra software |
Authors: Zsolt Lavicza,
Balazs Koren, Markus Hohenwarter |
Affiliations: University of Cambridge, Eotvos Lorand University,
Budapest, Johannes Kepler University, Linz |
GeoGebra (http://geogebra.org), a free, open-source, dynamic
mathematics software, is rapidly gaining popularity in the teaching and
learning of mathematics around the world. Currently, GeoGebra is translated
to 62 languages, used in 190 countries, and downloaded by approximately
400,000 users in each month, and clearly making an impact on mathematics
education in most countries. This increased use compelled the establishment
of the International GeoGebra Institute (IGI) that serves as a virtual
organization to support local GeoGebra initiatives and institutes. There are
already 106 institutes in 75 countries, which pursue training and support of
teachers, develop teaching materials, and carry out research projects. In
this talk, we will outline the directions of GeoGebra software development of
versions 4.0, 4.2 and 5.0; its extension to STEM subjects; activities of its
community; and the work of GeoGebra Institutes. |
|
2015 Mathematics Curriculum reform with using
technology in Cambodia |
Authors: Chan Roath |
Affiliations: Department of Scientific Research, Ministry of
Education, Youth and Sport, Cambodian Mathematical Society |
The Education System in Cambodia has reformed in the last 20
years. According to the recommendation of Royal Government of Cambodia,
Ministry of Education, Youth and Sport plan to include the usage of
Scientific Calculator in the curriculum of mathematics in 2015. Since 2009,
Cambodian Mathematical Society has been do the pilot project on using
Scientific Calculator in Mathematics classroom in four Institutions with 200
students, the result almost students are satisfies. After that we start to
wrote the supplementary text book for students grade 11 and grade 12 included
the method using of scientific calculator for solving critical and difficult
exercises.
Key word: mathematics curriculum, supplementary text book, scientific
calculator, reform, critical and difficult exercises. |
|
Using Scientific Calculator in Supplementary text
book and in Mathematics Classroom Grade 11 in High School in Cambodia |
Authors: Ngeth Youdarith |
Affiliations: Khemarak University |
The Mathematics curriculum
varies from country to country. One fact, however, is that with the advent of
technology. Using Scientific Calculator in supplementary book and in
mathematics classroom for students in grade 11 have been used for solving
some exercises are difficult to calculation and for two years ago. In this
talk, I will presented the properties of using on buttons and their use in
the formulation of general computation, trigonometric function (identities
and exact value), Statistic in one variable ( mean and standard deviation ).
The aim of this note is to explore various properties of the mean and
standard deviation with the aid of a scientific calculator. Value table (
Value of the other functions ), to explore how to make use of scientific
calculator in finding the area by curve.
Key word: mathematics grade11, statistic , mathematics properties,
computation, classroom grade 11. |
|
Identification of Potential Instructional Hazards
& Design-based Countermeasures in Virtual Manipulatives |
Authors: William Speer |
Affiliations: Research Council on Mathematics Learning,
University of Nevada Las Vegas |
In the Principles and Standards for School Mathematics (NCTM,
2000), the National Council of Teachers of Mathematics states that electronic
technologies are "essential tools for teaching, learning, and doing
mathematics" (p. 24). More specifically, NCTM suggests that "work
with virtual manipulatives... can allow young children to extend physical
experience and develop an initial understanding of sophisticated ideas like
the use of algorithms" (p. 26-7). Virtual manipulatives are among
several web-based technologies being used by teachers of mathematics. The
development of virtual manipulatives is often an effort to enhance the
effectiveness of physical manipulatives and related tools by addressing or
overcoming limitations of access, cost, and adaptability. These materials are
of importance for the mathematical training of both in-service and
pre-service teachers.
Research on the assessment of virtual manipulatives in mathematics
instruction is limited. There is some suggestion that students who use
virtual manipulatives experience higher achievement or conceptual
understanding in mathematics than those using associated physical
manipulatives or no manipulatives (Kieran & Hillel, 1990; Schackow, 2007;
Smith, 1995; Thompson, 1992). Other studies suggest that students who use
both virtual and physical manipulatives show an increase in conceptual
understanding (Ball, 1988; Olson, 1988; Terry, 1996, Izydorczak, 2003). Still
other studies found no statistically significant differences in achievement
for students using physical manipulatives, virtual manipulatives, a
combination of both physical and virtual manipulatives, or no manipulatives
(Kim, 1993; Nute, 1997; Pleet, 1990, Drickey, 2001).
While research into the use of emerging technologies must continue, there are
numerous variables to consider when measuring the effects of virtual
manipulative use. For example, studies that show evidence of increased
achievement were administered when classroom teachers believed they fit in
with the natural flow of the curriculum. Studies with no noticeable increase
in student achievement were administered at times that interrupted the normal
curriculum. Research design, sampling characteristics, and the type of manipulative
used may influence achievement. Other variables include: previous experience
with computers, grade level, mathematical topic, treatment length, student
attitudes toward mathematics, and computer-to-student ratio. |
|
Some Thoughts on Mathematics Teaching, Learning and
Assessment by Using Information Technology |
Authors: Jiyan Wang |
Affiliations: East China Normal University |
With the rapid development of science and technology, it has
become a great concern of mathematicians, mathematics educators, mathematics
teachers and students in our country to make full use of information
technology and Internet technology in mathematics teaching, learning and
assessment in order to meet the demands of the times.
In fact, the integration of mathematics with information technology has been
considered as a basic concept in our country¡¯s mathematics curriculum
standards.
In more and more classrooms information technology, include scientific
calculator and graphing calculator, has become a powerful tool for teachers
and students in mathematics teaching, learning and assessment. For example,
the information technology can be used to:
1) Effectively simplify the mathematics operations on matrix and determinant,
solve the general triangles and so on;
2) Understand in death the mathematics concepts such as the existence of
irrational numbers, the behavior of the general functions;
3) Explore the existence of solutions of mathematics problems.
We surely believe that the integration of mathematics and the information
technology will improve the students'' ability to learn and students can be
better cultivated in the world of mathematics. |
|
Analysis of kinds and roles of technology presented
in Korean secondary mathematics textbooks |
Authors: Hee-Chan Lew, Min-Shik Cho, Young Ran Choi,
Seo-Young Jeong |
Affiliations: Korea National University of Education |
Most curricular documents throughout the world including Korea
now emphasize integrating technology with mathematics. Examples of various
use of technology have been presented across a broad range of mathematics
textbooks to reflect this curricular. In this paper, we categorized all kinds
of technology presented in Korean secondary school mathematics textbooks into
8 groups (GC-COM, GC-CAS, GC-GPS, CAS, SP, GPS, DGS, others) and analyzed the
role of them in mathematics teaching and learning according to our framework.
We examined the frequency and purpose of technology use in these textbooks.
Although technology can be used for exploration, conjecture, verification and
generalization purposes, most of the textbooks employ technology just for
exploration. We try to get pedagogical implications for using technology into
mathematics teaching and learning effectively through results of this study. |
|
Technology-based Instruction in Statistics for
Graduate Students |
Authors: Rebecca Tolentino,
Cayao Erlinda |
Affiliations: University of the City of Manila |
The National Council of Teachers of Mathematics contends that
technology is an essential tool in 21st century mathematics education and
that teachers should maximize its potential in increasing proficiency in
Mathematics. This study is an attempt to explore the application of
Technology-Based Instruction in Statistics for graduate students. Respondents
were students enrolled in the Master’s programs of a chartered university in
the Philippines. Two classes in Statistical Methods were used in the study.
The first class was taught to statistically analyze data with the use of a
Statistical software while the second class used calculators in data
processing. This study used mixed method research design. Quantitative data
were collected from the scores of the students in the examinations.
Qualitative data were gathered from the cases submitted by the students as
well as from informal interviews conducted from both groups. |
|
Interactive Learning and Teaching using MathDisk |
Authors: Ajit Kumar, Mohamed Jaffarali |
Affiliations: Mathdisk Technologies, ICT, Mumbai |
This presentation discusses new advances in technology for
teaching and learning through MathDisk (www.mathdisk.com) for the development
of e-learning for High school and College mathematics. MathDisk, which is
designed specifically for educational purposes, can help students to
experiment and explore mathematics, both in the classroom and at home using
web. What distinguishes MathDisk from the rest of the numerous other graphing
tools currently available is the approach and philosophy. In almost all the
Math tools, trying to do anything beyond graphing a simple 2D function would
require writing code using the tool''s own programming language. MathDisk on
the other hand allows the users to express equations as they see it in their
textbooks, be it is Vector, Matrix, algebraic expressions, differential
symbols etc. There is no artificial layer that stands between the user and
the native math expressions. Students never feel any disconnect, as they can
instantly recognize and correlate the content with their textbook material.
The equal emphasis to both the symbolic and visual representations of
Mathematics makes MathDisk an ideal tool to create online interactive
textbooks for teaching mathematics. MathDisk also uses Integrated Rigid body
dynamics which will help students understand the abstract nature of
mathematical structures using simulated physical objects. MathDisk also
allows teachers to build models and simulations to improve the cognitive
abilities of their pupils in Math and Physics. Users of MathDisk can also use
scripting based on the syntax of popular “processing” language to produce
amazing math and physics models enabling MathDisk to become truly open ended
and infinitely extensible. Unlike desktop based applications which dominate
the world of Mathematical software, MathDisk allows users to share their
individual resources and their entire working space over web, a key feature
in today’s interconnected world. |
|
DEVELOPING PRIMARY SCHOOL STUDENTS’ SPATIAL ABILITIES
THROUGH TRANSFORMATIONAL GEOMETRY: A COMPARISON OF THE EFFECTS OF TWO
INTERACTIVE DYNAMIC SOFTWARE |
Authors: Xenia Xistouri,
Demetra Pitta-Pantazi |
Affiliations: Department of Education, University of Cyprus |
For a number of years, a critical issue in the field of
mathematics education has been the role of spatial abilities (SA) in
geometrical understanding, and the importance of finding effective ways for
their development. Due to the obvious connection between SA and
transformational geometry, a number of researchers have claimed that work
with the latter can have a positive impact to the former (Clements &
Battista, 1992). Although there have been many research attempts to provide
evidence for this position, the relationship is still unclear. One possible
reason for this may be that most of these studies consider SA as a unitary
construct. This study draws on a theoretical framework from the field of
psychology which discriminates three SA sub-components: Spatial Orientation,
Spatial Visualization and Spatial Relations (Lohman, 1988). Moreover, since
the evolution of multimedia technologies, a number of studies concentrated on
the prospective of dynamic geometry software (DGS) training SA. However,
there have been some considerations regarding the potential of some DGS in
the development of student’s spatial and cognitive abilities. Hence, the aim
of this paper is to compare the potential of two similar transformational
geometry instructions, one with the use of a discrete dynamic DGS and one
with a continuous DGS (Moreno-Armella, Hegedus, & Kaput, 2008), to
develop primary school students’ SA. Two groups of approximately 40
sixth-grade students (total of 79) received a twelve-session instructional
program on transformational geometry concepts, with the same activities, but
each with a different type of software – a discrete motion software or a
continuous motion software. Students’ SA were measured before and after the
instructional program. The results suggest that the group which used the
discrete dynamic software program had a significant increase in the Spatial
Visualization factor, whereas the continuous dynamic instruction group had a
significant increase in the Spatial Visualization and Spatial Relations
factors, as well as in their overall Spatial Abilities. Comparisons between
the two groups’ post-test means suggest that the continuous dynamic
instruction group significantly outperformed the discrete dynamic instruction
group in their mean performance in Spatial Relations and overall Spatial
Abilities. This suggests that instruction of transformational geometry
concepts with a continuous DGS may have more potential for developing primary
school students SA.
ACKNOWLEDGMENTS
This work falls under the Cyprus Research Promotion Foundation’s Framework
Programme for Research, Technological Development and Innovation 2009 -2010
(DESMI 2009-2010), co-funded by the Republic of Cyprus and the European
Regional Development Fund (Grant:PENEK/0609/57). |
|
Globally Asymptotic Stability of Impulsive Neutral
Type Neural Networks with Delay |
Authors: Haydar Akca |
Affiliations: Abu Dhabi University, College of Arts and Science,
Department of Applied Science and Mathematics, Abu Dhabi POB 59911, UAE |
Neutral-type neural networks model is generalized with presence
of
impulsive afect. Existence and uniqueness of the equilibrium as well
as globally asymptotic and exponential stability neutral type neural
networks with impulses are derived. |
|
Visualization of linear transformation with animation |
Authors: Shigeki Ogose |
Affiliations: Kawaijuku |
Visualization works well for teaching geography, and it works as
well for lineartransformation-especially when it is combined with animation.
Here I''d like to show how animation help students to understand the idea of
linearity, rotation, expansion and jordan forms of linear transformation on a
plane. |
|
PERFORMANCE PATTERNS IN CALCULUS BASED ON THE
INTERACTIVE FACTORS OF LEARNING FOR CURRICULAR FRAMEWORK DEVELOPMENT |
Authors: Maria Isabel Lucas |
Affiliations: Pamantasan ng Lungsod ng Maynila |
This study sought to analyze the relationship of the interactive factors of
learning—curriculum, instruction and performance. The researcher considered
the interactive process of these elements of learning based on the framework
developed by Howell, Fox and Morehead (2003).
The focus of this paper is on the performance patterns of selected students
in Calculus under the integrated and subject-centered curricular approaches.
It also aimed to look into the performance of students in the two curricular
approaches and looked into how teachers assess their present curricula and
teaching instructions.
Four (4) universities in Manila that offered Calculus were selected in the
study. The population consisted of students who had already taken three
Calculus subjects and faculty who have taught these subjects. The researcher
used both purposive sampling and cluster sampling.
The study employed descriptive method of research. It also used the
correlation method. Two types of instrument utilized in this study were: the
instrument for curriculum assessment was a researcher-made patterned with
Characteristics of Effective Curricula by Kentucky Academic Performance Standards
(Missouri MSIP Performance Standards); and the researcher-made instrument
following the instructional model identified by Robert Marzano (2000).
|
|
Teachers'' Conjecturing and Proving with Sketchpad |
Authors: Zhonghong Jiang |
Affiliations: Texas State Univesrity, NCTM, SSMA |
This presentation will
discuss how high school mathematics teachers develop their own conjecturing
and proving abilities and their mathematics knowledge for teaching through
participating professional development workshops offered by a research
project. Interviews with three teachers provided evidence that teachers in
the dynamic geometry group were very competent in using the software to
conduct geometric explorations, and then make and test conjectures. However,
as to proving their conjectures, teachers varied considerably. From the
proving activities, we learned the following ideas related to professional
development: (1) It is by no means easy to really increase teachers’
mathematics content knowledge. To develop effective strategies to achieve
this goal is a long-term task. (2) To take full advantage of the dynamic
features of Sketchpad to verify whether a conception is true before using it
in the reasoning process is an important learning habit, which many teachers
didn’t have. We should spend enough time and energy to help teachers develop
this habit. |
|
Improving Performance of Intrusion Detection Systems
using Artificial Neural Network |
Authors: Jamal Hussain |
Affiliations: Mizoram University, Aizawl, India |
The dependence of computer systems in today’s world on networks
and internet has made security of these systems crucially important. In order
to increase the accuracy of intrusion detection systems, false alarms need to
be highly reduced. This paper presents an approach to minimize false alarm in
intrusion detection based on artificial neural network. Different neural
network structures are studied to find the most suitable neural network. An
early stopping validation method is applied in the training phase to
eventually minimize false alarms and also increasing the generalization
capability of the neural network.
Keywords: Network security, Intrusion Detection, Artificial Neural Networks,
Optimization, Training Strategies, False Alarm |
|
Seeing the beautiful mathematics with technology |
Authors: Shin Watanabe |
Affiliations: The Mathematics Certification Institute of Japan |
Many mathematicians think that it is most beautiful formura
exp(ipai)=-1. In this formula has basic numbers, pai and e. These number are
infinte pai=3.14 and e=2.71. We want to see these numbers are beautiful. Why
numbers are beautiful? We use the grahpic calculator and see them.
We have two units on angle, degree and radian. First time we use the unit
degree and next changing the unit radian. Why its change is important? The
number pai is good on differential. And other number is same.
We show the expansion of numbers, we see 0,1 and i. The operations, adding
and multiplication are defined by operations. So we can see the beautiful
number i. |
|
To Fulfil Track Simulation With HP39GS |
Authors: Liu Chengyang |
Affiliations: Quanzhou No.7 Middle School Fujian, China |
In this presentation, we investigate the program inside APLET of
HP39GS; we break the limit of static function of HP39GS; fulfil dynamic
stimulation of conic curve (part of track). We consider actual education
situation in China and design more applicable APLET for students to explore.
As teachers, before a class, we can send students the APLET
stimulator which was edited earlier, and create a case to guide students
personally to observe and test the running of stimulator. This is to ensure
students understanding "Track Concept" more vividly and factually.
In addition, this is to inspire students’ desire of doing research, and
explore mathematics questions actively and forwardly. The stimulator which is
mainly described in this paper, i.e. track issue of conic curve, intend to
let students find and reveal internal relation of conic curve by themselves
with HP39GS, and have a more essential understanding on "Track
Issue". |
|
Some Analogous Forms For Locus - convenient way for
students to deepen their understandings on locus |
Authors: Liu Chengyang,Yang Jianyi |
Affiliations: Quanzhou No.7 Middle School, China |
We investigate HP39GS program APLET, break the limit of static
function of HP39GS, fulfil dynamic stimulation of conic curve (Part of
locus), and finally design more applicable APLET in line with the actual
education situation.
Teachers can send students the APLET stimulator before a class,
which was edited earlier, and create a scenario to lead students to observe
and test the program of stimulator, so as to ensure students understand
"the concept of locus" completely, and inspire the desire of
research and explore mathematics questions (see [1]) actively. We notice
students prefer this way of teaching style and allowing students to explore
mathematics with HP39GS makes a positive impact on teaching. In this paper,
we describe three ways of exploring locus: Program, Sequence APLET, and
Statistics APLET. The objective is to encourage students learn independently
find and yet to stimulate a more natural understanding on locus. |
|
Discuss the Eccentricity of the Conic Section With
HP39GS |
Authors: Rao Zhenping |
Affiliations: Quanzhou No.7 Middle School Fujian, China |
One of the conic section is an important content of high school
mathematics, as well as a mathematical difficulty of college entrance
examination. Eccentricity of the conic section reflects the essential
characteristics of conic sections, revealing the geometric nature of the
condition. Also the study of conic sections regarding the nature of the
geometry theories.is an important characterizations conic section shape
parameter, we can generally determine opening size of the flat level of the
ellipse and Hyperbola.
In this article we use HP39gs graphic calculator features and
graphics capabilities to show unity equations of conic sections, and to show
readers the relationship between eccentricity and an ellipse, a hyperbola and
a parabola. Graphic calculator is a wonderful tool to clearly reveal the
connections among the three kinds of cone curves.
We hope readers appreciate graphing calculator as a wonderful
learning tool to better consolidate and enrich the mathematical knowledge,
understanding the inherent laws of mathematics, mathematical knowledge the
intrinsic link between the points, and thus can be creative learning and
development, better adapted to the changing world, and innovation to
transformation of the world. |
|
Make Analogical Inference From A New Angle |
Authors: Wu Min |
Affiliations: Jiyan Junior High School Fujian, China |
Abstract: Among research methods in junior mathematical
problems, there is a method which specializes in “from reasonable inference
to deductive inference”. Meanwhile, the ability to think from individually to
commonly, inference ability and how to develop the students’ ability of
analogical inference and deduction are specifically demanded in the Seven
Methods of Mathematical Thoughts. In this article, author will introduce a
new method, with which the students can find, compare and solve the problems
by using HP39GS under the guidance of the teacher. This new method will offer
the average students and those who are weak in mathematics a more proper tool
to think and research the problems from a new angle. The teacher will give
respective examples of sequence, orbit and triangle, etc. in this article. |
|
Help students learn new plausible reasoning methods-A
new attempt Under the MCL environment |
Authors: Wu Min, Yang Jianyi |
Affiliations: Fujian Quanzhou Jinjiang Jiyan Middle
School; Quanzhou No.7 Middle School |
In the junior middle school education in mainland China, a very
important task is to enable students to acquire the "plausible reasoning”.
And there is a section devoted to "from plausible reasoning to deductive
reasoning"; ‘’the math exam outline’’ for high school and ‘’examination
notes in Fujian province’’ had also clearly proposed 7 general methods
"from the special ones to the ordinary ones", and the capacity of
"reasoned argument", and develop students ' analogical reasoning
and deductive ability. This article describes a new approach, under the
guidance of teachers, and in the MCL environment, students use the graphing
calculator, with the aid of HP39GS, to make an independent discovery, analogy
and solution of problems. Allowing students to study from new angles and make
a research on the issues, may provide a more appropriate tool in favor of the
students at medium or less advanced level. This article will give the
examples from tree aspects including arithmetic progression, trajectory, and
Delta, one by one |
|
HP39gs graphing calculator in mathematics teaching
effect |
Authors: Li Jianhua |
Affiliations: Beijing city in the first secondary school in the
one nine, China |
With the new curriculum standards and the aid of the graphing
calculator, it examines students' mathematics learning style change; as a
teacher in teaching methods, and to inspire. Along with our country basic
education reform, mathematics education is committed to " take the
student as the main body ", " to foster the spirit of innovation
and practical ability as the core ", " information technology and
curriculum integration for the bridge" the new education concept change.
The subjects of physics, chemistry, biology and other disciplines are
classified as experimental classes, that may be one reason why majority of
the students like to learn these courses, and mathematics has always been
considered a "dry ", and an "abstract " subject, which
may be one reason many students stopped pursuing. Today with the graphic
calculator, one can make mathematics teaching a positive impact on students’
learning and understandings. |
|
Graphing calculator expand the students' learning
space About "SSA" further exploration |
Authors: Li Haiying |
Affiliations: Beijing Tuan Jiehu No. 3 Middle School |
This paper introduces “”SSA" further exploration that is
based on the Hp39gs graphic calculator in the junior middle school geometry
congruent triangles. We propose some ideas to improve Hp39gs graphing
calculator "Triangle Solver" Aplet through this exploration. With
the implementation of the new course standard, student's beginning ability,
inquiry ability, innovation ability concerned, in order to further enhance
the junior middle school students experience, explore mathematics study level
of knowledge, the development of mathematics cognitive domain, deepen
"hand technology and the new curriculum standards of junior high school
mathematics teaching integration" topic research, especially with plane
geometry knowledge integration, our school positive response HP calculator
facing the whole country carried out based on the Hp39 series of geometry
application design competition, this paper explores some of the research
achievements and ideas in this activity of my class teachers and students. |
|
Explore graphing calculator and discover mathematics |
Authors: Li Yu |
Affiliations: NO.12 Middle School of Taiyuan City, Shanxi
Province, P.R.C |
Abstract: This paper uses "HP 39gII graphing calculator to
explore natural logarithmic with base number of e" and "students'
autonomous exploration graphing calculator built-in functions". Through
the description and analysis of these two cases, we can explore how to guide
students to use GC exploration and discovery mathematics and how to explore
development graphing calculator built-in function. Our goal is to let students
understand how to master a technological tool to discover more mathematics. |
|
The HP graph calculator brought us exploration and
innovation opportunities |
Authors: Liu Ping, Wang Bin |
Affiliations: Beijing No.94 Airport Branch Middle School |
Abstract: In this paper, I will show some ways which direct us
to make use of HP39gs.When we first encountered the graphing calculator,
students and teachers all felt very strange, we didn’t know where to start.
Furthermore, we didn’t have any confidence at first. But students and
teachers kept trying our best to study the capability of graphing calculator.
Later we discovered many interesting ways of using it and understanding a
complex mathematical concept.This is our first work, we’ll continue to
research using HP graphics calculators in our classrooms. |
|
My Perspective On The Effect Of The Graphic
Calculator In Training Junior High School Students' Autonomous Learning
Ability |
Authors: Guo Shuangshuang |
Affiliations: Beijing’s 80th Middle School, China |
Graphic calculator is an advanced tool for education which makes
students much more active and initiative in the procedure of practice. From
passive study to positive study, the autonomous learning ability of students
can be well developed and their comprehension about the value of mathematics
can be much enhanced. |
|
PROMOTING THE USE OF INFORMATION AND COMMUNICATION
TECHNOLOGY (ICT) IN THE TEACHING AND LEARNING OF MATHEMATICS: SEAMEO QITEP IN
MATHEMATICS’ EXPERIENCES |
Authors: Wahyudi, Pujiati |
Affiliations: SEAMEO QITEP in Mathematics, Yogyakarta, Indonesia |
This paper describes SEAMEO QITEP in Mathematics’ experiences in
promoting the use of ICT in Mathematics classroom in Southeast Asian region.
SEAMEO QITEP in Mathematics is one of Centers under SEAMEO which was launched
on July 13, 2009. The Center concerns to improve mathematics education in
Southeast Asia. One of its core business is to conduct training courses for
mathematics teachers and educational personnel, namely (1) Course on
Utilization and Development IT-based Mathematics Learning. The other courses
are: (2) Teacher-made Teaching Aids; (3) Joyful Mathematics Learning; (4)
Differentiated Instructions; (3) Clinical Supervision; (5) Lesson Study in
Mathematics Education; and (6) Southeast Asia Mathematics Realistic Education
(SEA RME). In line with UNESCO (2007) concern, SEAMEO QITEP in Mathematics
also stresses the importance of the use of ICT in mathematics education by
putting it in its core business. The 1st Course on ‘Utilization and
Development of IT-Based Mathematics Learning’ was conducted from 20 September
to 15 October 2010 in Yogyakarta. Through the course the participants were
guided to explore and use the power of ICT in teaching and learning
mathematics. The core activities ranges from the simplest use of ICT such as
slide presentation to more complex use of ICT for example utilising Learning
Management Systems and developing e-Textbook from Student’s textbook. Participants’
journey during the implementation of ICT use in mathematics classroom is
presented. The factors that support and hinder the participants in employing
the ICT are discussed. |
Abstracts for Hands-on Workshops
|
A Hands-On Experience with Virtual Calculus Tutor |
Authors: Jonathan Lewin |
Affiliations: Kennesaw State University |
Virtual Calculus Tutor is the combination of a complete 4
semester calculus textbook in a friendly on-screen form and 101 hours of
sound video that the reader can use at any time to enter a virtual classroom
where the exact material he/she is reading on the screen is provided as a
classroom lecture.
Students appreciate contact with a teacher when they need more help and
guidance than any book can provide. Instructors may appreciate the option of
being able to direct a student to the Virtual Calculus Tutor virtual
classroom instead of having to sit with the student for long periods of time
during office hours.
Participants will also be given the opportunity to install Virtual Calculus
Tutor on their own computers. The auithor will also be available at ATCM to
help those who may interested in creating their own on-screen content and
videos.
For more information, please click on the Virtual Calculus Tutor link in the
ATCM website. |
|
RESISTED MOTION: A CRTICAL ANALYSIS USING CLASSPAD
MANAGER |
Authors: Wei Ching Quek |
Affiliations: Singapore Polytechnic |
In engineering mathematics,
resisted motion is usually introduced as an application of ordinary
differential equation to make mathematics relevant to students’ discipline of
studies. The ClassPad Manager is a popular learning tool. We will explore how
the tool will assist the learning of resisted motions. This workshop will
present some common strategies to critically analyse the resisted motion with
ClassPad’s symbolic, graphic and numerical capabilities..
This workshop is consists of three activities:
1. Getting Started
ClassPad Manager is a popular handheld CAS calculator. The workshop intends
to share with participants essential features of the ClassPad Manager and
explore the potentials to solve differential equations. No previous
experience with the ClassPad Manager is assumed.
2. Problems Solving
Examine some interesting resisted motion models. Participants will explore
the problem from different perspectives, numerically, graphically
symbolically and provide further insights to the problem.
3. Lesson Plan
Approaches and views from mathematics and physics will be discussed. |
|
Using Grapher to Help Students Visualize Concepts |
Authors: Drew Ishii |
Affiliations: Sage Hill School, California Mathematics Council |
Grapher is a powerful program found on all Mac computers and
laptops that can help students with 2D and 3D visualization of concepts
ranging from basic functions in Algebra through multivariable Calculus.
Students should not be stifled in their learning of mathematical topics
especially advanced topics because of their lack of visualization skills or
lack of programming knowledge. In this session, we will work with many
different concepts including three-dimensional coordinate systems, quadratic
surfaces, vector functions, and the TNB frame. Participants will see how
intuitively students can investigate various mathematical topics by
experimenting with the program. |
|
TI 84 Plus Workshop |
Authors: Craig Refugio,
Patrick Galleto |
Affiliations: Negros Oriental State University, Jose Rizal
Memorial State University |
This workshop intends to present the capability of the TI 84
plus in: solving equations in one variable; solving quadratic equations;
drawing families of graphs; finding maxima, minima and zeros of functions;
verifying trigonometric identity; solving exponential and logarithmic equations;
and finding determinants and inverses as well performing operations on
matrices.
Thirty (30) sets of TI 84 plus will be brought to this workshop so as to have
30 participants. |
|
Learning 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. In this workshop examples will be used to consider some of the
ways in which sophisticated mathematical and statistical concepts can be
developed. |
|
Learning with a graphics calculator |
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, elementary statistics, probability,
trigonometry and differential calculus. The focus will be on teachers of
senior secondary or early undergraduate mathematics. We will use the Casio
fx-9860GII calculator, but do not expect that participants will have prior
experience with this calculator. |
|
Using a scientific calculator for learning
mathematics |
Authors: Marian Kemp,
Barry Kissane |
Affiliations: Murdoch University |
Scientific calculators have been used by both students and
teachers for almost forty years, mostly for simple and more complex
arithmetic calculations and for tasks involving logarithmic, exponential and
trigonometric functions. More recently, modern scientific calculators have
been developed to become more user-friendly and to extend their mathematical
capabilities to suit modern curricula. While calculators are sometimes
regarded as merely devices to produce numerical answers, in this workshop we
will also consider instead some ways in which the development of mathematical
ideas in the secondary school can be supported with such a calculator. We
will use the Casio fx-82 ES PLUS calculators, but do not expect that
participants will have prior experience with this calculator. |
|
Problem Solving with the TI-84 Plus Graphing
Calculator |
Authors: Wee Leng Ng |
Affiliations: National Institute of Education, Nanyang
Technological University |
Equipping students with a set of concepts and skills that enable
them to solve a wide variety of mathematical problems is one of the primary
aims of mathematics education. To facilitate students’ acquisition of problem
solving skills, many educators have advocated the use of handheld technology
to empower students to learn across different visual representations of a
mathematical problem.
The TI-84 Plus Graphing Calculator is a useful tool for students in
developing a deeper understanding of mathematics through exploring,
investigating, conjecturing and discovering. In this workshop, participants will
explore the usefulness of the TI-84 at different stages of mathematical
problem solving. |
|
Developing Deeper Understanding of Mathematical
Concepts Through TI-Nspire Learning Handheld |
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 teaching and learning of
mathematics by empowering students to learn across different visual
representations of a mathematical problem. With the aid of such technology,
teachers have the means to help students develop a deeper understanding of
mathematical concepts and broaden their critical thinking skills.
In this workshop, participants will explore several mathematical concepts
through the TI-Nspire Technology. |
|
New features of GeoGebra for teaching mathematics
(3D, HTML5 version, tablet optimized version, etc.) |
Authors: Balazs Koren,
Zsolt Lavicza, Markus Hohenwarter |
Affiliations: Eotvos Lorand University Budapest, University of
Cambridge, Johannes Kepler University Linz |
GeoGebra 4.2 (currently in Beta version,
but expected to be released in autumn 2012) includes a full Computer Algebra System (CAS) window by which symbolic
calculations can be fully integrated into teaching mathematics. When the development of GeoGebra started it was Java based.
Java has the advantage to run on every desktop platform. With the
introduction of tablet computers and smartphones, the development of GeoGebra
changed. In the beginning of summer 2012 we introduces the html5 based
version of the software. The next
release of GeoGebra is version 5.0 with real 3D. The proposed workshop will consist of two 60-minute sessions
introducing different features of the software: Session 1: CAS and the use of
dynamic symbolic calculators Participants will be introduced to the CAS
window of GeoGebra 4.2 and can discover how
dynamic symbolic operations can be integrated into lessons of different levels. Demonstration of version 5.0 with real 3D. Session 2: GeoGebra in the browser, the html5 version, GeoGebra
for tablet devices. Showcase and demonstration of the new versions of
GeoGebra. During both sessions, participants will learn how to use GeoGebra
as a visualization tool for teaching and to create student-engaging
interactive online materials. Free software and ready-to-use materials will
be provided. No special computer experience is required. |
|
Technology, mathematics and hands on experiments |
Authors: Christopher
Longhurst |
Affiliations: Hewlett Packard |
Have often have our students complained about why are we doing
this? Or math is irrelevant to life!
Putting together real life experiments can make mathematics come to life.
How is this done when time and syllabus constraints don’t allow it? This
workshop will focus on three experiments that can be set up simply and make
math more relevant. I will demonstrate the set up procedure and develop the
hands on activity for the teacher and student, followed by a worksheet.
Materials: emulator, MCL, probes and calculators. |
|
Teaching calculus using a visual and discovery
approach. |
Authors: Christopher
Longhurst |
Affiliations: Hewlett Packard |
In this workshop I will provide an overview of how I teach
calculus with a visual approach. Firstly, I will summarise my program and
take parts of it and demonstrate how investigation, discovery and
visualisation can be used to make calculus more interesting and
understandable for the students.
This will be a hands on workshop using graphing calculators and emulators |
|
Using Scientific Calculator in Mathematics Classroom
and Supplementary text Book grade 12 |
Authors: Koy keolong |
Affiliations: Using Scientific Calculator |
- The Education System in Cambodia has changed in the last 20
years
- According to the recommendation of royale government , they plan to include
the usage of Scientific Calculator in the curriculum of hight schools of
Ministry of Education, Youth and Sport in 2015 .
- In 2009 ,we tried the Project included Scientific Calculator of Mathematics
learning and teaching at 4 places :
PreahSisovath High school.
National Institute of Education
Royal University of Phnom Penh
Khemarak University
Then we also wrote the textbook for grade 12 sdtudents included the use of
caculater for solving difficult Exercises . |
|
Colourful Activities using TI-Nspire CAS |
Authors: Raymond Rozen |
Affiliations: RMIT University, Jacaranda-Wiley, MAV, Accredited
T3 Trainer |
In this hands-on session participants will have the opportunity
to engage with a number of mathematical activities which use the TI-Nspire
CAS calculator with Operating System v3.2. Investigations include some of the
new features of Version 3.2, including creating a locus of points for
parabolas, graphing parametric equations and visualizing the solution to
simultaneous equations using three dimensional graphing. These activities are
suitable for the TI-Nspire CAS ClickPad and TouchPad and Teacher Software.
Previous experience with using the TI-Nspire is desirable but not essential. |
|
The Application of Graphing Calculator in High School Function Teaching |
Authors: Jie Shen |
Affiliations: Tianjin Teaching and Research Institute, Tianjin, China |
As the basic knowledge in high school mathematics, function takes the cultivation of students¡¯ thought of number-shape combination, rational thinking, applying awareness and innovation awareness as efficient carriers throughout high school mathematics. The biggest characteristic of function learning is the combination of ¡°formula¡± and ¡°Shape¡±. Graphing calculator is of various functions, such as calculation, construction and statistics. At the same time, with its portability, appropriability, interactivity and networking, it provides a studying environment of audio-visual, automatic and polybasic for mathematics learning, contributing to the demonstration of knowledge forming, breakthrough of mathematics difficulties, permeation of thinking method and promotion of rational thinking. Several specific cases are illustrated to explain the application of CASIO graphing calculator in function teaching and problems needing attention. |
|
Visualization with GInMA in algebra teaching |
Authors: Vladimir
Shelomovskii, Svetlana Nosulya |
Affiliations: Murmansk State University, Deoma |
This Workshop is focused on the aspect of visualization during
teaching of algebra. We consider visualization with GInMA software, its
features and benefits. We show the samples of visualization of such topics
as: the function and the parameter, addition of fractions, rounding,
multiplication of polynomials, the scale, the numerical ray, the number line,
the coordinate plane. We show how visualization in algebra allows us to
perform necessary intermediate transformations. Prior experience with GInMA
is not necessary. The knowledge on how to use GInMA and its tools will be
introduced. At the end of the Workshop you will create your own interactive
picture. |
|
Visualization with GInMA in geometry teaching |
Authors: Vladimir
Shelomovskii, Svetlana Nosulya |
Affiliations: Murmansk State University, Deoma |
This Workshop is focused on the aspect of visualization during
teaching of geometry. We consider visualization with GInMA software, its features
and benefits. We use visualization as a basic tool in the study of all major
geometric topics. We start with interactive pictures that allow younger
students to understand the basics of geometry, that is, the concepts of the
area and the volume, the similarity of the shapes, the symmetry about the
point, a line and a plane, the concepts of parallelism and perpendicularity.
We show how the concept of distance between two points is transformed into
the concept of distance between shapes and solids, then into the concept of
the shortest path inside the shape or the solid, as well as on its surface,
that is, we tell about optimization and bifurcation. We show how to construct
the cross-section of a pyramid, and the cross-section of a parallelepiped in
a convenient way. Prior experience with GInMA is not necessary. The knowledge
on how to use GInMA and its tools will be introduced. At the end of the
Workshop you will create your own interactive geometric draft. |
|
Guidobaldo’s theorem: central perspective understood
with Cabri 3D |
Authors: Jean-Jacques Dahan,
Jean-Marie Laborde |
Affiliations: IREM of Toulouse, Cabrilog |
We will use Cabri 3D to rediscover where are the vanishing
points of the direction of parallel lines in the pictures we take with our
cameras. These points will appear in pictures of buildings pasted in Cabri 2
plus files. Their position with respect to the eye of the observer and the
head angle of the camera will help us to rediscover Guidobaldo del Monte’s
theorem. This workshop is an illustration of Jean-Jacques Dahan’s
presentation about this theorem. |
|
Construction of Maximal Twistable Tetrahedral Torus |
Authors: Jen-chung Chuan |
Affiliations: National Tsing Hua University |
In the fascinating book "More Mathematical Activities"
Brian Bolt supplies a net for a rotating ring of six tetrahedrons. Based on
this net, the model forming a twistable tetrahedral torus can be constructed
with patience. In this talk we are to show how such a model can be built with
Cabriâ€3D. With the magic supplied by the dynamic geometry software we
are to show how ALL such models can be constructed. |
|
Drawing Conchoid of de Sluze with the Peaucellier
Cell, a workshop with Cabri II Plus |
Authors: Jen-chung Chuan |
Affiliations: National Tsing Hua University |
The Peaucellier Cell was the first (1864) planar linkage capable
of
transforming the rotary motion into a perfect straight line motion.
Interchanging the role of the rotor and the fixed rod, the output is observed
to trace out an interesting curve satisfying the equation
r = cos(t) + a sec(t)
the equation of the conchoid of de Sluze.
In this workshop we are to explore the dual role of the Peaucellier Cell
offering a novel perspective to study the duality between the circle-conchoid
pair in the same way as the telescope-microscope pair. |
|
Turning between Rhombic Triacontahedron and
Dodecahedron Back and Forth, a workshop with Cabri 3D |
Authors: Jen-chung Chuan |
Affiliations: National Tsing Hua University |
In this workshop, we are to guide the participants to construct
an animation showing how a 30-faced regular rhombic polyhedron can be
decomposed into several pieces and then reassembled to form a dodecahedron.
The two do NOT enclose the same volume! |
|
Workshop for Introducing MathDisk |
Authors: Ajit Kumar, Mohamed Jaffarali |
Affiliations: Mathdisk Technologies, ICT, Mumbai |
The workshop aims to help users understand the basic techniques
involved in creating worksheets using MathDisk (www.mathdisk.com).
• Introduce the Equation Editor, Geometric Computations, Auto Variables, 2D
and 3D Function Graphing, and Animation
• Provide specific examples to highlight different tips and tricks involved
in creating simple to complex mathematical expressions using MathDisk''s
equation editor.
• How to seamlessly interconnect expressions and models drawn using direct
user interface.
• Providing specific of natural math notation in vector and geometric operations.
• A step by step tutorial of building a worksheet will be discussed which
will help users understand the various menu options involved and how to
effectively combine them.
• Users will also learn function graphing both in 2D and 3D which will be
followed by using animation, image manipulation and annotation to enhance
their worksheet''s visual appeal.
• Users will also be briefed about tips and tricks of using multiple
expression groups and graph sheets using an applied example.
• The workshop will end by introducing the users to rigid body dynamics and
scripting. |
|
The Geometer''s Sketchpad Introductory Workshop: Tessellations and Tilings |
Authors: Nicholas Jackiw |
Affiliations: KCP Technologies, Inc., Simon Fraser University |
Participants will meet and learn the basic operations of The
Geometer’s Sketchpad, the most widely-used school mathematics software,
in the context of exploring regular tessellations of the plane via regular
polygons. This hands-on workshop is for mathematics teachers at all grade
levels, and is recommended for users new—or relatively new—to Dynamic
Geometry technology. Bring your laptop! |
|
The Geometer's Sketchpad: Beyond
Geometry |
Authors: Nicholas Jackiw |
Affiliations: KCP Technologies, Inc., Simon Fraser University |
This hands-on technology workshop will focus on applications of Sketchpad outside
the typical geometry curriculum---especially to algebra, trigonometry, and
calculus. While representative topics and activities will be visited, our
attention will be split between topics and the tool itself---particularly
those aspects of the technology appropriate to mathematical modeling
involving equations and their graphs. Some prior Sketchpad experience
useful but not essential. Bring your laptops! |
|
ATCM 2012 Pre-Conference Workshop: Introduction to
e-Teaching and e-Assessment of
Secondary School / Undergraduate Mathematics using
Maple |
Authors: Bill Blyth, Asim Ghous |
Affiliations: Australian Scientific & Engineering Solutions
(ASES); School of Mathematical and Geospatial Sciences, RMIT University,
Australia |
Maple is a leading Computer Algebra System, CAS, used and
developed continually for 25 years. At RMIT University, Maple has supported
student learning for 20 years. This hands-on workshop offers different
activities according to each participant’s Maple expertise. Participants are
invited to bring their own laptop: a 30- day free evaluation copy of Maple
will be provided. Participants will be encouraged to work collaboratively (in
small groups) on activities without lectures (but with tutor help), just as
the students do.
Beginners will be invited to work through
B1. (some of) an Introduction to Maple file (first year students
complete in two hours, higher years students take one hour),
B2. a basic “Polya: How to Solve It” file on maximizing the area
of a fenced region,
B2 a basic assignment, the Norman window problem, with
parameterization and simple automatic marking of the answer.
B3 Time permitting, look at
(a) the advanced Norman window problem introducing multiple
representations and solutions using graphical methods (zooming-in),
animations and proof without calculus, or
(b) a simple trapezoidal rule (for data) application, the Fish
Pond problem, with immediate automatic marking (of several steps) within the
Maple file. (Students like immediate marking!)
Experienced users will be invited to
E1. OPTIONAL: bring their own work to seek advice.
E2. Work through B2 and B3 (see above), or
E3. Spot the Curve: identify the randomly generated translation
of a curve, with immediate automatic marking. Great fun: understanding of
animation is required, so an Introduction to Animation file will be provided.. |
|
ATCM 2012 Conference Workshop: Introduction to
e-Teaching and e-Assessment of Secondary School / Undergraduate Mathematics
using Maple |
Authors: Bill Blyth, Asim Ghous |
Affiliations: Australian Scientific & Engineering Solutions
(ASES); School of Mathematical and Geospatial Sciences, RMIT University,
Australia |
Maple is a leading Computer Algebra System, CAS, used and
developed continually for 25 years. At RMIT University, Maple has supported
student learning for 20 years. This hands-on workshop offers different activities
according to each participant’s Maple expertise. Participants are invited to
bring their own laptop: a 30-day free evaluation copy of Maple (and several
Maple files) will be provided. Participants will be encouraged to work
collaboratively (in small groups) on the activities without lectures (but
with tutor help), just as the students do. This workshop will be either:
I. a shortened version of the Pre-Conference workshop for those
who did not attend the Pre-Conference workshop. See the abstract for the
topics for beginners or for experienced users of Maple.
II. a continuation for those who attended the Pre-Conference
workshop. According to interest, another topic could be chosen: such as the
Animation Assignment (with a choice of a secondary school level animation
project – this is an extended project that is designed to be interesting) or
a more advanced topic such as Taylor Series (designed to support standard
lectures and could be completed in the workshop time available).. |
|
ATCM 2012 Conference Workshop: Introduction to
Computer Aided Assessment of Secondary School / Undergraduate Mathematics
using MapleTA |
Authors: Bill Blyth, Asim Ghous |
Affiliations: Australian Scientific & Engineering Solutions
(ASES); School of Mathematical and Geospatial Sciences, RMIT University,
Australia |
MapleTA is the major Computer Aided Assessment, CAA, system for
courses using mathematics. It is now in version 8 and very many features, see
http://www.maplesoft.com for a detailed summary, including a recorded webinar
“Introduction to MapleTA”. MapleTA has much mathematical appeal because it
uses Maple as its Computer Algebra System, CAS: the full power of Maple is
available, but invisible to the student who does not need to know anything
about Maple. MapleTA keeps full records of student results and can
communicate directly with most Learning Management Systems, LMS, such as
Black Board and Moodle.
This workshop offers different activities according to each
participant’s Maple expertise. Participants are invited to bring their own
laptop: connection with the internet will allow participants to direct trial
some MapleTA materials. Participants will be encouraged to work
collaboratively (in small groups) on the activities.
In this workshop participants will:
1. (internet connection permitting) use a guest login as a
student to complete a couple of standard questions on first year calculus.
MapleTA has a large data bank of questions, so assignments could be
constructed from just choosing questions that are already provided.
2. Work through the design of a MapleTA question for the Norman
Window problem (see the Pre-Conference or Conference workshop on Maple). The
question formulation is simple, but does use a parameter (to individualize
the question) and we also include a diagram (generated by Maple, within
MapleTA). To mark the answer, we only need a simple match of the symbolic
answer (and Maple is used invisibly by MapleTA to accept any mathematically
equivalent answer).
3. Work through the design of a MapleTA question for Chris
Sangwin’s problem: “Give an example of an even function”. We’d like to ask
this the type of question. However, in this case, we cannot specify all
possible correct answers. Since the full power of Maple is available, we can
test whether the student’s response satisfies the properties that are
required.
4. Work through the design of a multistep MapleTA question, if
time permits. Universities in many countries have decreasing staff/student
ratios. First year courses, in particular, have large enrolments so MapleTA
(the only commercially available CAS-enabled CAA) has much to offer staff in
managing their marking load. |
|
TI-Nspire CX: a new experience in teaching and
learning of Mathematics |
Authors: Ms Kwee Tiow Choo |
Affiliations: Senior Consultant of Hwa Chong Institution
(College) in Singapore |
The launch of the new calculator TI-Nspire in 2007 was an
exciting development in GC Technology. Multiple representations and dynamic
links enable multiple approaches to solving problems. Working documents can
also be saved, recalled, edited and transferred between handheld and
computer. This is an optimal tool for concept and skill development in the
classroom. It offers a new experience in teaching and learning of
Mathematics, it has the potential to provide the opportunities for learning
through mathematical investigations. We will demonstrate and share how the
TI-Nspire can be used to enhance the teaching and learning of Mathematics.
Participants will experience how it can be used to engage students and
promote understanding in a Mathematics classroom. Topics shared will include
graphing, calculus and statistics. |
|
How to develop mathematical thinking in the classroom with DbookPro in Thai |
Authors: Masami Isoda, Maitree Inprasitha |
Affiliations: University of Tsukuba, Japan, Khon Kaen University, Thailand |
In this workshop, participants learn how to use simple mathematics for Earth science in relation to Earthquake and Tsunami and how to use interactive board in the classroom with dbookPro. International Edition of the DbookPro for editing and using tool of e-textbook is developed by Dr. Masami Isoda and Dr Devadason Robert Peter. On this workshop, participates use the e-textbook (Isoda, 2012) which developed by dbookPro. The e-textbook is produced by the grant from ATCM 2011: Masami Isoda sincerely acknowledges for the support from the ATCM, special thanks to Dr. Wei-Chi Yang for his whole-hearted supports toward the Tsunami disaster in March, 2011. Reference: Isoda, M. (2012). The Tsunami in March 11th, 2011 : what can we learn from the disaster beyond the expectation in the case of Japan? Tsukuba: CRICED, University of Tsukuba. |
|
Mathematical Modeling for High School Mathematics on Earthquake and Tsunami with the freeware 'dbookPro' |
Authors: Masami Isoda |
Affiliations:University of Tsukuba, Japan |
In this workshop, participants will learn how to use simple mathematics for Earth science in relation to Earthquake and Tsunami and how to use interactive board in the classroom with dbookPro. International Edition of the DbookPro for editing and using tool of e-textbook is developed by Dr. Masami Isoda and Dr Devadason Robert Peter. In this workshop, participates shall use the e-textbook (Isoda, 2012) which developed by dbookPro. The e-textbook is produced by the grant from ATCM 2011: Masami Isoda sincerely acknowledges for the support from the ATCM, special thanks to Dr. Wei-Chi Yang for his whole-hearted supports toward the Tsunami disaster in March, 2011. Reference: Isoda, M. (2012). The Tsunami in March 11th, 2011 : what can we learn from the disaster beyond the expectation in the case of Japan? Tsukuba: CRICED, University of Tsukuba |
Abstracts for Poster Sessions
|
Virtual Game in Classroom for Introducing 3D Vector
Operations |
Authors: Hitoshi Nishizawa,
Kohtaro Shimada, Takayoshi Yoshioka |
Affiliations: Toyota National College of Technology |
The virtual game presented in this poster is designed to
motivate students to learn 3D linear algebra in pre-college mathematics.
Students are expected to be familiar to graphical image of 3D vector
operations though this game and feel the reality in them because the rules of
the game and how the winner are decided are shown graphically using 3D vector
operations. The game is a good introduction to the lessons of 3D vectors and
their operations.
The game is a tournament, where an avatar of a student or a team of avatars
compete each other in various kind of battles at every stage of the
tournament. Every student owns an avatar for the game, and the avatar has a
characteristic vector of three elements: physical strength, thinking ability,
and musical skills. And the battlefields also have 3D characteristic vectors,
and the winner of a battle is decided by vector operations. For example, a
dot product calculates the effective strength of each player in a battle,
with its performance in the battlefield. The operations are first shown
graphically in the game, and later explained using their symbolic operations
in the rulebook, which becomes the introduction to formal lessons of vector
operations.
The game is conducted by a client/server system, which consists of a terminal
computer for each team and the host computer connected to a data projector,
which display the game to the spectators. Each computer has a terminal
program coded with MATHEMATICA using its graphical interface and built-in
functions, and connected to the database management program running on the
server.
The authors demonstrate how the game-system actually works using a set of
notebook computers. |
|
Exponential stability of switched linear systems with
interval time-varying delays |
Authors: Grienggrai
Rajchakit |
Affiliations: Major of Mathematics, Maejo University, Chiangmai
50290, Thailand |
This paper is concerned with exponential stability of switched
linear systems with interval time-varying delays. The time delay is any
continuous function belonging to a given interval. By constructing a suitable
augmented
Lyapunov-Krasovskii functional combined with Leibniz-Newton''s formula, a
switching rule for the exponential stability of switched linear systems with
interval time-varying delays and new delay-dependent sufficient conditions
for the exponential stability of the systems are first established in terms
of LMIs. Numerical example is included to illustrate the effectiveness of the
results. |
|
Exponential mean square stability of stochastic
systems with interval time-varying delays |
Authors: Manlika Rajchakit |
Affiliations: Major of Statistics, Maejo University, Chiangmai
50290, Thailand |
This paper is concerned with mean square exponential stability
of stochastic systems with interval time-varying delays. The time delay is
any continuous function belonging to a given interval. By constructing a
suitable augmented
Lyapunov-Krasovskii functional combined with Leibniz-Newton''s formula, new
delay-dependent sufficient conditions for the mean square exponential
stability of the stochastic systems are first established in terms of LMIs.
Numerical example is given to show the effectiveness of the obtained results. |
|
Ten years of GeoGebra |
Authors: Balazs Koren,
Markus Hohenwarter, Zsolt Lavicza |
Affiliations: Eotvos Lorand University Budapest, Johannes Keppler
University Linz, University of Cambridge |
GeoGebra is free and multi-platform dynamic mathematics software
for all levels of education that joins geometry, algebra, tables, graphing,
statistics and calculus in one easy-to-use package. It has received several
educational software awards in Europe and the USA.
The poster is going to show the development of GeoGebra. How it started,
developers joined the OpenSource project. New versions of the software, new
features included. The current state of development and the future of the
software, including beta state development and plans.
Beside the development of the software, the poster shows the development of
the community. The community of users, developers, translators from all
around the world. |
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A classification and extension of the linkage -from
the view to constitute- |
Authors: Chieko Fukuda,
Kyoko Kakihana |
Affiliations: Teikyo University, JAPAN, Tsukuba Gakuin
University |
A planar linkage is a collection of fixed-length, one-dimensional
segments lying in a plane, joined at their endpoints to form a connected
graph. Linkages have been applied with various machines or tools in our lives
for a long time. Then some classification of the linkage is considered by the
aspect of a practical function. For example, there are linkages to pull a
straight line (i.e. Peaucellier''s exact straight-line linkage) or to stretch
or shrink figures (i.e. a pantograph). Here, I emphasize geometrical elements
of linkages, and classify them from a constitutive viewpoint which is
different from a functional aspect. The constitutive viewpoints refer to
changing the position of the pinned point or bar, increasing the numbers of
the bar or rearranging some linkages in the three dimensions from the two dimensions.
I try to look for a new function of linkages by this way of expansion. |
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Learning to Solve Least Squares Curve/Line Method by
Using Spreadsheets |
Authors: Sammy Khayat, Craig Refugio |
Affiliations: Negros Oriental State University |
Least Squares Curve/Line is a mathematical procedure for finding
the best fitting curve to a given set of points by minimizing the sum of the
squares of the offsets or "the residuals") of the points from the
curve/line. The sum of the squares of the offsets is used instead of the
offset absolute values because this allows the residuals to be treated as a
continuous differentiable quantity. . However, because squares of the offsets
are used, outlying points can have a disproportionate effect on the fit, a
property that may or may not be desirable depending on the problem at hand.
In this paper, all of the aforementioned terms are calculated using
spreadsheets and the procedures are emphasized on a step by step manner. |
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Matrix Operations Through Spreadsheets |
Authors: Craig Refugio, Sami
Khayat |
Affiliations: Negros Oriental State University |
Matrix operation is tedious if it is done through manual
computations. This paper presents how spreadsheet can do matrix operations
such as addition, subtraction, multiplication, determinants, inverse, adjoint
and transpose. Applications are also emphasized in this paper like solving
systems of equations as well as areas of triangles drawn in a rectangular
coordinate plane through spreadsheet.
A group of 19 Bachelor of Secondary Education major in Mathematics students
were pre-tested and post-tested about the aforementioned matrix operations
through spreadsheet. Results showed that students gained significant skills
in performing matrix operations. |
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