VIRTUAL AND COLLABORATIVE ENVIRONMENT
FOR LEARNING MATHS
A. Queiruga Dios, A. Hernández Encinas, I. Visus Ruiz
Department of Applied Mathematics, E.T.S.I.I. de Béjar, University of Salamanca
C/ Fernando Ballesteros, 37700-Béjar, Salamanca, Spain
A. Martín del Rey
Department of Applied Mathematics, E.P.S. de Ávila, University of Salamanca
C/ Hornos Caleros 50, 05003-Ávila, Spain
Keywords: eLearning, Active Learning.
Abstract: This paper presents the experience of interaction between students and the new teaching-learning system,
using eLearning platforms to support and improve classroom teaching. The proposed system tries to achieve
a new common space between some European countries, that will allows the adaptation to a comparable and
compatible common system of higher education. This study has been developed specifically with students
from the first engineering courses and will show an online platform that helps them to interact with other
classmates and acquire knowledge using the computer.
1 INTRODUCTION
The origins of human-computer interaction (HCI)
could be found in the technological explosion that
occurred in the seventies, when it was necessary the
direct communication between humans and
computers (Hernández, 2008). Since then new and
several technologies have been used in educational
innovation.
Teachers are increasingly adopting computers as
a daily tool needed to carry out a more effective
teaching and greater quality levels. The Information
and Communication Technologies (ICT) are an
important element in the convergence of universities
to European Higher Education Area (EHEA)
(Queiruga, 2008), contributing to learning, and
culture changes associated with the common
European area. This common system of higher
education promotes the training of more responsible
and active citizens by making academic degree
standards and quality assurance standards more
comparable and compatible throughout Europe.
ICT has grown from being a simply object to be
viewed as an instrument to support innovation in
teaching, enabling the personalization of the learning
process and changes in strategies and methodologies
that enhance continuous learning to the students
(
García, 2006), (Kirschner, 2001).
The teaching of mathematics is not an exception
and is not liable for the use of these methods
(Queiruga, 2007). The subjects of mathematics
required for obtaining a degree in industrial
engineering include the linear algebra course which
will focus this studio. We are realizing the
integration of eLearning as a model of further
education by significantly increasing their use in
recent years (Mason, 1998).
The University of Salamanca has a virtual
environment called Studium (Hernández, 2006), and
also has licensing campus for various software
packages specifically suited for calculations in
general. Without going any further we might cite the
Mathematica (Wolfram, 1999) or Matlab (Moler,
2004) for solving equations, operate with matrices or
perform various simulations useful for practical
classes.
As we know, mathematics is very close,
generally, with computational sciences. The area of
mathematics is therefore, one of the most adapted
for the incorporation of the new technologies, since
it is not only one purely formative subject, but is a
86
Queiruga Dios A., Hernández Encinas A., Visus Ruiz I. and Martín del Rey A. (2010).
VIRTUAL AND COLLABORATIVE ENVIRONMENT FOR LEARNING MATHS.
In Proceedings of the 12th International Conference on Enterprise Information Systems - Human-Computer Interaction, pages 86-90
DOI: 10.5220/0002974800860090
Copyright
c
SciTePress
scientific tool for the students who must help them
to solve the problems that are generally throughout
their race and in its professional development.
This paper is organized as follows: In section 2
we show the work environment in which carried out
the experience detailled in this paper, the linear
algebra is detailled in Section 3, and in Section 4 the
conclusions of the study are presented.
2 WORKING ENVIRONMENT
The working environment in mathematics classes is
diverse and is now extended with the possibility of
using computers for classes. So far, traditional
classes consist of lectures in which most of our
students attend class as an auditor, without
participating and only to take notes.
In recent years, due to changes leading to the
common European space, we use computers to
complete the classes and provide students with
different activities and new tools.
2.1 Online Platform
Studium, the virtual campus of the University of
Salamanca, offers teachers and students at the
University a technological structure that channels
education through the Internet, and provides
different online tools that transport to the network
the student-teacher interaction processes. Studium is
based on the web platform Moodle (Modular Object
Oriented Distance Learning Environment), a virtual
teaching environment that allows placing contents
and tasks in the network and provides online
communication tools.
The Moodle environment is within the
construction learning mode, pedagogical approaches
in teaching, trying to establish consistent
relationship between what to learn (new knowledge)
and what already knows (prior knowledge), thus the
new information that get students is integrated into
the background and acquires a appropriate
significance with respect to what is already known
(Weiss, 2007). This platform is currently used by
many Spanish universities from that in 2004, the
University Jaume I of Castellon and University of
Las Palmas de Gran Canaria institutionally adopted
Moodle. On this platform the students construct their
learning through the use of different activities and
collaborative tools posed by teacher and
communication tools between participants (students
and teachers). This online platform is based on free
software and available, along with manuals and
installation software in http://www.moodle.org.
One advantage of the use of online learning
platforms is that are built based on social
constructivist pedagogy (
Brooks, 1999), which
favours a collaborationist model of learning, where
students share their experiences and work, and can
communicate among themselves or with the course
tutors at any time to answer questions or ask for
help, thus becoming a space for social interaction,
that connects individuals through a computer.
As is known, one of the main purposes of a
virtual campus is facilitate and enrich the interaction
between all members of the community.
This platform represents a graphical user
interface intuitive enough for students to use it
without prior knowledge of the environment.
Another important feature of this virtual campus is
that it allows the integration of interaction tools like
chats or foros, and activities designed specifically
for teaching, such as the Web-Quest
(http://webquest.org), which represent a new
methodology for teaching via the Internet, the Hot
Potatoes software (http://hotpot.uvic.ca), free
distribution, which allows developing exercises
interactively, especially useful and used to propose
questionnaires, games, online exercises for students,
or any other web activities, which makes the
Moodle platform considered a set of Web 2.0 tools
(Oberhelman, 2007).
2.2 The Internet and Classes
The Internet provides a comfortable and fast form to
access, to represent and to use the information (Díaz,
2009). Some of the advantages of its use that could
be mentioned are:
The ease and speed with which tasks and
problems are managed and resolved, allows
students to spend more time understanding and
analyzing the results to the mechanics and the
potential difficulty of its solution.
The students find the job in mathematics with the
more attractive possibilities that the computer
offers, since it eliminates the routine work and
power the creative part, which increases its
motivation.
It is able to quickly catch the attention of the
students.
The Internet use enables students to find information
quickly. The problem is that they often do not know
how to filter the information and data found, so it is
VIRTUAL AND COLLABORATIVE ENVIRONMENT FOR LEARNING MATHS
87
convenient and important the work of the tutor in
these cases.
Is of great importance that students learn to
discriminate the information obtained by browsing
the Internet and know that not all information is
equally valid or good. In addition, they must also
learn to develop the information obtained with their
own words, so they understand all the read and learn
how to summarize it.
2.3 Activities and Useful Tools
The ICT provide the students the possibility of
simulating experiences and of raising very different
situations, comparing them, something that manually
can be difficult or at least tedious in the majority of
the cases. It allows them, for example, to
include/understand the true reach of a problem or the
effectiveness of an algorithm analyzing the initial
results obtained when varying the hypotheses, initial
conditions, etc. Thus we can mention, in addition,
other possibilities that can be useful for math
subjects:
To graphically represent successive curves that
shows the different solutions from a problem.
To modify, to suggest to the student the data of
the proposed problem and to see the
repercussions of these modifications in the
solution.
The conviction power that gives the
accomplishment of the calculations with
computer in the presence of the students.
To represent graphically, in seconds, all the
solutions of different problems.
Thus, using computers in the classroom, it is
possible to offer to the school students’ more and
more complete and deep formation in mathematics,
that allow them to face their future professional
activity, adapting to the advances of science and
technology. From the appearance of computer
science, one of the main utilities of the computer in
relation to the mathematical work has been the case
of numerical calculation. Nevertheless, the
mathematical applications in engineering require not
only of numerical calculation, but rather an algebraic
mixture of numerical calculations and manipulations
on mathematical formulas. The symbolic calculation
is indeed the technology specialized in the automatic
manipulation of formulas, vectors, matrices, etc.,
with numerical and/or symbolic elements. It is in
this specialty where the use of specialized software
is especially useful, as can be the packages of
symbolic calculation Mathematica (Wolfram, 1999),
Maple (Bauldry, 1995), or Matlab (Moler, 2004).
These software packages have syntax easy to learn,
since the orders and commands remember the
mathematical operations that they execute and,
therefore, its learning is fast and intuitive. In
addition, the aid that offers these software packages
is very complete and is informed with numerous
examples. The University of Salamanca owns a
license “Campus” for some of the versions of this
mathematical software.
Mathematica package is a system of computer
algebra originally developed by Stephen Tungsten. It
is also a powerful programming language that
emulates manifolds paradigms using re-writing of
terms. It uses code blocks (bookstores), to extend the
capacities and to reorient the calculation. The
programming language of Mathematica supports the
use of functional programming and procedures
(although generally, the functional programming is
more efficient). It is implemented in a variant of the
Object Oriented Programming language C, but the
thickness of the extensive code of bookstores in fact
is written in the Mathematica language, that can be
used to extend the algebraic system.
Unlike other languages, like Maple or Matlab,
Mathematica tries to use the transformation rules
that know as much in every moment as it is possible,
trying to reach a stable point. In a basic level,
Mathematica can be used to realise numerical and
symbolic calculations, as well as to realise graphical
representations of functions. But in more advanced
levels, it can also be used like programming
language of great versatility to own built-in
functions and instructions that in the traditional
languages would require additional routines.
At the School of Industrial Engineering in Béjar,
we use both Mathematica and Matlab. The first one
has a great advantage that could be use together with
the network through the WebMathematica
environment. We do not know that possibility for the
case of Matlab. On the other hand, Matlab with
Simulink is the math software preferred by engineers
for its versatility and utility in simulation process
and toolbox availability.
3 LINEAR ALGEBRA SUBJECT
An important task for engineers is to learn how it is
possible to model daily events and objects with
mathematical tools. It is considered that problem
solving is an important part of their education; by
interpreting such problems as a context within which
they can apply Mathematics in general and Linear
ICEIS 2010 - 12th International Conference on Enterprise Information Systems
88
Algebra in particular, to aspects of the “real world”.
Thus, students can learn how to make practical use
of their mathematical skills (Lantz-Andersson,
2008).
Industrial engineering studies are based on a
solid initial technical knowledge, complemented
with enhancements that, depending on the choice of
the student, go deeper into the study of specific
technical problems and problems in industrial
organization. However, in the training of industrial
engineers, emphasis tends to be placed on the
generalist, polyvalent and integrative nature of the
teaching, and on the development of skills to learn
and solve the technical, organisational, and
management problems that are inherent to any
industrial or services company. Owing to their
multidisciplinary education, industrial engineers are
able to develop a career in any technical industrial
activity.
Within this type of training for engineers, of
special interest is to solve different activities
proposed in classes and in the virtual campus. We
propose the students to solve some questionnaires,
one for each module of the course. Besides the
questionnaires, students must work in an application
of linear algebra to daily life. To carry out this work
students use the internet as the best resource.
Our teaching programs allow us not only to
clarify -for our students- the processes they should
follow to be able to understand the mathematical
concepts they are in taught and to consult and take
maximum advantage of the literature, but they also
enable us to instil a solid formation in how to work
with Mathematics. This, we hope, allows students to
address new problems and research and hence to
appreciate that both intuition and the real world can
become bottomless sources of new studies and
results in the field of mathematics. Additionally, the
students must attempt to solve as many problems as
possible, understanding by problems not only those
that require an approach in which a rule or an
algorithm is implemented for their immediate
resolution, but also those in which the students must
gauge the appropriateness of different strategies in
order to tackle the problem in hand and must choose
a method to solve it.
Engineers working in industry must acquire and
develop basic knowledge and skills, in which the
ability to work in interdisciplinary teams, an
ongoing interest in new knowledge through the
students’ own work, the ability to address the
different problems of the company for which they
work, and criteria to use the mathematics necessary
to solve specific problems must all be combined.
One way to tackle the problems that arise for
engineers in their job is to learn how to find
solutions on the internet or with colleagues, so the
activity that we propose, the realization of a work in
groups, involves both learning algebra development
and other skills such as teamwork, information
search, and the use of tools like Mathematica or
other open source language that can be found on the
Internet.
As well as having knowledge of applied
mathematics, engineers must be able to apply maths
from the perspective of a true engineering
professional. Knowledge of mathematics helps
engineers to systematise logical and analytical
thinking, with the help of other disciplines that will
in turn help them to structure their synthetic thinking
and awaken their creativity.
4 CONCLUSIONS
After using the eLearning platform and the activities
mentioned in this study, which complement
traditional teaching, at the end of the course we
made a survey to students and we found the
following aspects of online teaching and learning
system (
Kearsley, 1998): the student and teacher can
access the application at any time, both to aid and to
all information and documentation of the course,
students have available and affordable all resources,
like questionnaires, problems, practices, and the
means for optimum use of the subject. The
flexibility of platform involves a cooperative, rather
than independently environment (
Aliev, 2001),
allowing students to interact and organize the course
as needed. The online platform allows continuous
contact with the students' work. These may solve
questionnaires, exercises and the application
proposed work, using forum or chats to be in contact
with teachers and other students.
ACKNOWLEDGEMENTS
This work has been supported by the Project FS/5-
2009 from “Fundación Memoria D. Samuel
Solórzano Barruso” (University of Salamanca).
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