New Challenges in e-Learning of Mathematics via EVLM and IDeLC - PDF document

5th WSEAS / IASME International Conference on ENGINEERING EDUCATION (EE'08), Heraklion, Greece, July 22-24, 2008 New Challenges in e-Learning of Mathematics via EVLM and IDeLC projects SNEZHANA GOCHEVA-ILIEVA, ASSEN RAHNEV Faculty of Mathematics and Informatics University of Plovdiv ‘Paisii Hilendarski’ 24 Tzar Assen St, 4000 Plovdiv BULGARIA Abstract: - We present the key problems, ideas, aims and results in introducing and developing new ICT for the education of mathematics in Plovdiv University (Bulgaria) within the frames of the Leonardo da Vinci pilot project EVLM (European Virtual Laboratory of Mathematics) and university scientific project IDeLC (Interfaculty Distributed e-Learning Center). Key-Words: - E-learning, M-learning, Virtual Laboratory, Computer Algebra Systems (CAS), MathML, Xml, Jsp, Distributed E-learning Center, J2ee-based Environment. In this paper we present the key ideas, aims and 1 Introduction results of introducing and developing new ICT The total popularity of computers and ICT, combined technologies in the education of mathematics within the with the power of mathematical software has provoked frames of two projects: EVLM and IDeLC. The EVLM radical changes in methods of teaching and learning project afforded our faculty the opportunity to contribute mathematics. This is pursued of some negative trends in to the development, storage and dissemination of large higher education not only in Europe but all over the databases of e-learning materials by using the newest e- world. A declining level of mathematical knowledge content technologies as MathML, xml, computer algebra among secondary school graduates and first years systems, etc. On the other hand, the university funded university students, more and more unattractive outdated research project IDeLC, is devoted to build new ICT traditional ways of teaching mathematics without ICT, a tools for teaching and learning a specific type of misusage of some new technologies by part of the knowledge (including mathematics) and also develop the university teachers, and others are all examples of this. tools provided easy and effective access to available These and other problems were first found in the materials for big groups of users. In this way the IDeLC education of mathematics in engineering [1], but they are project will enlarge the impact of the EVLM resources in also present in higher education of natural sciences and favor of the content and methodology review that continue to be a spreading phenomenon. However, European society requires. Bulgarian education of mathematics is not an exception to these trends. The European mathematical community has to 2 The EVLM project redouble its efforts to meet the general needs in the field in order to keep abreast with the advance of science, The European Virtual Laboratory of Mathematics which is in direct conformity with the directives of the (EVLM) is a European pilot project in the Leonardo da Lisbon (2000) and Barcelona (2002) meetings and the Vinci program of the European Commission scheme for eLearning Action Plan 1, approved by the European Education and Science, for the period 2006-2008 [3]. Commission [2]. The general needs that can be found Nine institutions, predominantly in the engineering include: upgrading the overall level of mathematical education, were involved in the project: Technical knowledge; promoting innovative methods in teaching university in Bratislava, Slovak Republic (promoter), mathematics, as e-learning, m-learning, online tests, University of Plovdiv, Faculty of Mathematics and usage of interactive computer algebra systems, online Informatics, Bulgaria, University of West Bohemia, Faculty of Applied Sciences, Plze ň , Czech Republic, consultancy and other blended solutions; improving the quality of teaching and training e-content of mathematics Miskolc University in Hungary, University of Limerick, materials by applying the newest ICT. Ireland, University of Salamanca, Spain, Faculty of Informatics and Computing, Coventry University, ISBN: 978-960-6766-86-2 437 ISSN: 1790-2769

5th WSEAS / IASME International Conference on ENGINEERING EDUCATION (EE'08), Heraklion, Greece, July 22-24, 2008 United Kingdom, Tullossilta, Finland and Slovak and the use of innovative ICT, applicable in Society for Geometry and Graphics, Slovak Republic. mathematical educational process. The main objectives of the project are the big mount of electronic materials in different mathematical subjects Fig. 1. EVLM project: Central portal. 2.1 Aims of the project mathematical resources and e-learning materials available from the partner institutions. EVLM and each The aim of EVLM is to promote better understanding National Portal are freely accessible on the internet. In and utilization of mathematical knowledge, to promote addition, the National Centers offer consultancy services e-learning in all aspects of mathematics, to provide to those wishing to learn about the latest results in solutions for different target groups and help teachers mathematics and mathematics teaching. Communication and trainers enhance their skill in using the most between the project team ensure that any request for advanced educational tools and environments. EVLM assistance and consultancy will be dealt with by the aims to provide a range of online resources to support partner with the most relevant expertise. Feedback is and enhance the teaching of mathematics in secondary enabled and welcomed from all users of ELVM to assist schools and higher education and to help the research in the quality control process. needs of individuals in a number of areas including mathematics, statistics and mathematics education [3]. 2.3 Main results of the EVLM project The mathematical e-content of the EVLM database was 2.2 Project outline developed on the basis of the innovative ICT. It was The EVLM is comprised of a network of National built on the principle of diversity, in response to the Centers of Mathematics located at eight partner countries partners with a higher competence in a given throughout Europe. Figures 1 and 2 show the homepages mathematical subject. of the Central Portal, hosted by the Technical University The EVLM Central Database provides free access to in Bratislava, Slovak Republic (promoter) and Bulgarian different e-learning educational material in mathematics Portal in Plovdiv University, respectively. covering the following subject areas: Fundamental Each National Center hosts a portal in the respective Mathematics, Algebra, Calculus, Geometry, national language providing a virtual database of ISBN: 978-960-6766-86-2 438 ISSN: 1790-2769

5th WSEAS / IASME International Conference on ENGINEERING EDUCATION (EE'08), Heraklion, Greece, July 22-24, 2008 Optimization, Numerical Analysis, Difference and problems and modules are provided to facilitate easier Differential Equations, Multivariable Calculus, navigation within the database. In addition, two didactic Probability and Statistics, History of Mathematics, guides for teachers and students of mathematics are Mathematical Games. Within each mathematical subject provided to act as standalone resources to aid in either area a selection of frequently asked consultation topics the teaching or studying of mathematics. (FACTs), reusable learning objects (RLOs), related Fig. 2. EVLM project: Bulgarian national portal. The EVLM database provides e-content coded in introductory didactic chapters for engineering XML, MathML, pdf, jsp, nb, html and other file formats. mathematics, examples and problems. The Extensible Markup Language (XML) is a text-based The following CAS are included: Mathematica, general-purpose specification designed to transport and Maple, Matlab, SPSS, Derive, etc. The EVLM database store structured data. It is used both to encode provides also simple guides and examples to software documents and to serialize data, and allows custom tools for development of e-learning materials with online defined tags. MathML is an XML application especially calculations and interactive demonstrations, created by aimed to encoding mathematics and its meaning. It the powerful environments as webMathematica and enables mathematics to be served, received, and GeoGebra. processed on the World Wide Web, just as HTML has Figure 3 represents an illustration of an online enabled this functionality for text. Authors may use consultation topic about surface patch modeling, coded equation editors, conversion programs, and other as webMathematica applet – jsp file, enabling online specialized software tools to generate MathML, XML or calculations and manipulations. Users can type their own other descriptive languages. Such editors, presented in input data that will be inserted interactively, while all EVLM are SciWriter, Publicon and others. necessary calculations will be done, and the new graph Special attention is given to the use of computer will be plotted. Perspective view of the created surface algebra systems (CAS) in mathematics education, not patch is provided, which can be interactively rotated in only in view of materials, but also by providing the space by simple mouse movements. ISBN: 978-960-6766-86-2 439 ISSN: 1790-2769