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

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

 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

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

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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