Slobodan S Marolov
email: smarolov@med.auth.gr

Stathis Th Konstantinidis

Panagiotis D Bamidis
email: bamidis@med.auth.gr

Maria M Nikolaidou

Costas Pappas
email: cpappas@med.auth.gr

Cross-border collaboration between greece and bulgaria: the use of ict in improving social medicine education arrangements

Keywords: Social Medicine Education, Geographic Information System, learning management environment, South East European collaboration, e-learning standards, public health

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INTRODUCTION

Some European countries are facing similar social and financial challenges today and will probably seek for the same kind of achievements in the future as well. Cross-border collaboration between countries exists in various fields, but very limited collaboration has been reported regarding medical issues across the borders.

Newborn European countries and more specifically South-East European countries experience a lack of knowledge, especially in topics of social medicine. The actual knowledge improvement and knowledge sharing has been so far focused on non-IT based solutions, mainly through seminars, conferences etc. There exist numerous software tools that allow collaboration and education, independent statistical tools that could be used to support decision making, as well as, other student-teacher or doctor-patient collaboration environments, online courses and exams that have been exploited to support the educational process.

The question that arises is whether the collaboration across countries can cultivate the appropriate conditions for enhancing knowledge sharing and whether Information Technology can effectively contribute towards this aim.

The aim of this paper is to show how Information Technology and its different tools can contribute to the improvement of education and how it can be used to improve social medicine education and (ultimately) practice across borders. The solution proposed consists of an integration of software tools that accept inputs from different sources, and produce outputs that may be utilized in different ways. The system was developed in the framework of an INTERREG IIIA Greece-Bulgaria cross-border collaboration project, named "CrossBorderHealth".

The rest of this paper is structured as follows: Section 2 contains background information, presenting the usefulness of web collaboration and its effects on knowledge sharing and education. The following section illustrates the educational needs for such an endeavour. In Section 4 the detailed technical aims and objectives are presented, while in Section 5 the proposed solution and its architecture is described, followed by some (technical) development aspects in Section 6, and a discussion on the advantages of the proposed idea/system and some suggestions for future work.

BACKGROUND

Knowledge sharing is the behaviour of disseminating one's acquired knowledge with that of other members within one's organization. The focus of knowledge management is on how to share knowledge in order to create value-added benefits to the organization [START_REF] Liebowitz | Knowledge management and its link to artificial intelligence[END_REF]. Physicians are forming the most knowledge-intensive and principal professional group in hospitals. Their theoretical and practical knowledge is vital for the care of patients, and the quality of their clinical practices is a major determinant for patients' use of medical services. Knowledge sharing in this sense becomes even more important for physicians in tertiary hospitals, because they are required to be research-oriented, evidence based, creative in medical care, and ready to receive new medical knowledge opportunities that can be acquired through various organizational learning mechanisms [START_REF] Lipshitz | Organizational learning in a hospital[END_REF].

However, knowledge is created out of information extracted from processed data and fused with experience, so as to add value to a specific activity. In this context, ICT systems extracting knowledge may facilitate different human activities. For example, Geographic Information Systems (GIS) have the ability to gather general and specific information about the real world and deliver useful solutions on social issues (Ian P, 2006). GIS handles a wide range of information and knowledge based on scientific rules, sophisticated materials and specific values of land information, to present the appropriate solutions with respect to the defined objectives.

The combination of GIS technology with other information systems and the merging of data that could be represented in the same manner can be very effective. England's Strategic Health Authorities have created a map to represent the region's health units by using Google Maps API, Google Earth KML, and MSN Virtual Earth Map Control (England SHA Locator, 2005).

What is more, collaboration that is supported by proper collaborative tools and work environments may increase knowledge sharing among working teams and may assist them in accomplishing mutual goals; much of this may currently occur over the web. Web collaboration environments are applied in medicine as well. A lot of web medical systems have been introduced and created through web collaboration tools, offering doctors and medical stuff collaborative environments for improving knowledge and skills.

Contemporary web collaboration may be accomplished via the Internet in real time. It consists of a package of mostly Web-based tools within Web sites. Collaborative tools are software applications that enable working teams to collectively author and archive their work, to be notified for events on a group calendar, and to collaborate with vendors and partners on a secure web server. These collaborative tools can be hosted or non-hosted, and may take the form of synchronous (real-time, conferencing and instant messaging) or asynchronous modes (calendars, schedules, and discussion forums).

Finally, a growing interest has been noticed for the last generation of Web-based collaboration ware (also known as Web 2.0 tools), namely wikis, blogs and podcasts; these are highly adopted for health-related professional and educational services online [START_REF] Boulos | Wikis, blogs and podcasts: a new generation of Web-based tools for virtual collaborative clinical practice and education[END_REF].

RATIONAL AND REQUIREMENTS

In our new era of rapid changes due to the expansion of technologies and the globalization, countries and societies are forced to develop alternative forms of education. Since the beginning of human societies education has always been a priority, and the emphasis now is put on the way technology, which is involved in e-learning, in knowledge sharing, in collaboration between distant locations, can improve medical education. Many methods exist for teaching and learning social medicine. Nevertheless, there exists a debate about the effectiveness of various social medicine teaching and learning activities, resulting in a lack of consensus, what methods constitute the best educational practice.

There is a need for a clear hierarchy of educational activities that can effectively lead to the acquirement of competence in social medicine skills [START_REF] Khan | A hierarchy of effective teaching and learning to acquire competence in evidenced-based medicine[END_REF]. All health care professionals need to understand and implement the principles of social medicine to achieve improved health care of their patients. Interactive and clinically integrated teaching and learning activities provide the basis for the best educational practice in this field. Web-based learning, online learning, distributed learning, computer-assisted instruction, or Internet-based learning are very important in improving social medicine education because today's medical educators are facing different challenges from their predecessors. The integration of ICT into existing medical curricula should be the result of a well-devised plan that begins with a needs assessment and concludes with the decision to use ICT. In undergraduate medical education, ICT offers material to the learners for self-instruction and collaborative learning. In graduate medical education, the Accreditation Council for Graduate Medical Education has established six core competencies towards which ICT can be applied [START_REF] Ruiz | The Impact of E-Learning in Medical Education[END_REF]. The use of such technologies to encourage learners' deeper engagement with learning materials, and the maintenance of shared working spaces to improve collaboration between learners, are desirable outcomes.

It is acknowledged by many educators that students of all ages learn best when immersed within a culturally and socially rich environment in which scaffolding of learning can be achieved [START_REF] Boulos | Wikis, blogs and podcasts: a new generation of Web-based tools for virtual collaborative clinical practice and education[END_REF]). In the case of social medicine, such an environment should entail enough public health information. For instance, information on population/inhabitants and their needs, their health problems, and other appropriate statistics regarding the health care services as such. Furthermore, there is a clear demand for a dynamic provision of such information, as any variations and changes done in the society must be appropriately reflected and specified by updating and modifying those statistics and databases. If ICT can provide the means to merge e-learning environments with suitable controlling and fusing such information, then an obvious improvement of social medicine education may be envisaged.

AIMS AND TECHNICAL OBJECTIVES

As mentioned already, the aim of the work described in this paper is the development of a concept that would integrate different solutions for improving social medicine education. Technically speaking, the paper's objectives are as follows.

The first objective is the demonstration of geographically localized information (GLI) comprising medical issues, or the medical GLI, in a user friendly way. The second objective is the establishment of a SCORM-compliant e-learning environment for social medicine education (SCORM stands for Sharable Content Object Reference Model) (ADL, 2007). The third objective is the setting up of a web collaboration environment for collaboration between health professionals. The ultimate condition encompassing all the above requirements is the integration of international standards such as SCORM, LOM (Learning Object Metadata), Healthcare SCORM (Smothers, 2007) etc. within our framework.

A starting point to meet the project objectives is the collection of statistical information for the regions involved. The selection of useful statistical data can lead to the design and creation of a database where this information and data will be stored. Further requirements are the creation of predefined data sets that will be given as final output, and finding of the appropriate Geographic Information System (GIS) that allows external connection to database and demonstrate the results. The framework component has to meet the latest technologies standards as well as SCORM for e-learning compatibility.

SOLUTION

In this paper, we propose as a solution a concept using different modules to create a useful visualization tool that will help health professionals improve their social medicine education. We created this system as a tool within the cross-border collaboration INTEREG IIIA project "CrossBorderHealth" (CrossBorderHealth, 2007), but it can be used as a tool in e-learning processes under any SCORM compatible collaboration platform or moreover under any e-learning platform.

In the framework of the INTERREG project between Greece and Bulgaria, one of the requirements has been the development of a dynamic tool that would accept inputs from different sources and show useful results to the end users. That information includes general statistics for the region as well as existing health units, their availability, capacity and some general health statistics such as the number of specialized doctors per field etc. The concept is built upon the combination of a database and a Geographic Information System that provides a tool that could be useful from many different aspects.

In addition, this concept can be broadened and also used to demonstrate other information that are of significant importance such as demographic statistical overviews, medical statistical information of epidemiological type or any other useful information.

ARCHITECTURE

The systems itself contains several components: the external database provided from Google that contains the tile images used to offer the map flexibility of panning and zooming, the database that contains all the statistical data, and a user interface that has two parts -the user interface for browsing and the user interface for inputting data. The first is used for anyone that is interested to see the results, while the second is used only by contributors and needs special access. The last component is the LOM Object that complies with SCORM standards and it is used to combine the user pages within an e-learning module.

A component diagram of the system concept

The Database has been created to fit the statistics needs, the gathered statistics and information about the border region.

The Google Maps API allows us to embed Google Maps in our application for our own purposes with JavaScript. The maps have been used to give the visualisation of the specific region and, furthermore, to present, with some adjustments, the gathered information in a dynamic form. With the usage of the Java Scripting Language we have been allowed to geocode locations of interest showing the statistics gathered and provide information accordingly.

As we have already mentioned there are two user interfaces for data manipulation. The first interface is accessible to any user that is interested in browsing in the border area between Greece and Bulgaria and finding the desired information to be used for specific purposes or even just for increasing his/her knowledge on social medicine issues only by looking at the results. The second part is restricted only to specific members, those who have the permission to add or modify the data. The page allows the user to modify the existing tables in the database, which can be updated later on the browsing page or can be removed for various purposes.

DEVELOPMENT

The system has been developed to be working within the web site of the project. Thus, PHP on a Linux server has been used as the developing language by having MySQL as a database. As a Geographic Information System Google MAPS and its API 2.0 has been used, which allows manipulation on existing elements tuned for our own purposes or moreover for showing the statistics gathered in a dynamic environment enriched with PHP and HTML.

The whole web portal is organized in three main parts, the first is the web portal on its own and the links for browsing the entire web site; the second part is where a dynamic map is shown having all needed elements for medical statistic visualization and the third, is the "insertion section" where the administrator or a responsible person can add/edit/update statistical data on the existing database. Figure 3 shows how the structure of the portal may be integrated through the existing e-learning platform, following the concept described above. To achieve the above, we have considered the following. As known, the SCORM package can be described by the Learning Object Metadata (LOM), which consists of 9 categories as illustrated in the Figure 4. One of the latter is the "Technical category", which is composed by elements such as "Size", "Location", "Requirements" etc. "Location" is a string and may be used to access the learning object; it usually represents its physical address (Figure 5). Therefore the connection between the e-learning environment and the user's pages could be easily customised through that connection.

Furthermore, this kind of Metadata can be associated with Assets providing suitable information about the Assets independently of learning content including the information of title, description, etc. The Asset Metadata can be applied both to <resource> elements (Asset resource) and to the <file> element which can be met as child element of <resource> within a Sharable Content Object (SCO). FIGURE 5. An XML extract of the connection between the "SCORM compliant" LMS and the geographical information system as a resource for social medicine education

DISCUSSION AND FUTURE WORK

The concept presented herewith enables the users to access a different way of gathering desired information or just informing themselves with the current cross-border situation in public health or health service provision. Learning or more specifically e-learning, has been designed using tools that involve the adequate educational strategies and methods, which, combined with this concept will provide a wide range of accessing and learning information in a more elegant, easy and visual way. The possibility for this system to be adjusted to any SCORM-compliant e-learning platform would allow existing e-learners to become part of it or new users to become members of the community.

As the title of the paper denotes, the whole development aims to enhance the crossborder collaboration between Greece and Bulgaria. Although not sufficiently evident at the moment, the system demands the collaboration of Greek and Bulgarian scientists at two levels. First, the input of statistical and health care data in the database is based upon mutual communication and collaboration at a database and policy level. Moreover, once the system is full of data, academics from both countries may utilise a web collaboration environment to collaborate on setting academic attributes such as the "aims and objectives", the "teaching strategies", the "cases" etc, in order to mutually enhance their teaching modules, or select teaching cases from a pool of already existing components developed by the other partner (this part has also been developed but it is not described here due to space limitations).

As an extension on what we have done by now, an additional component could be developed. The new component can be a third main page for the special users, allowing geocoding on new locations that are of special interest and include other vital information on that area. Google Maps API has a big contribution to the whole custom made development of such projects.

To conclude, this paper showed how ICT and its different tools can contribute to the improvement of education by empowering the learner with updated, dynamic context information. We have integrated different technologies and standards, in an effort/intention to enrich social medicine education and (ultimately) improve its practice across borders. Obviously, the overall success of the project endeavours is going to be judged by an actual evaluation study on the users of the system, which is something that has not been undertaken so far. However, the significance of the project's envisaged aims and objectives in the context of cross-border collaboration in South East Europe, as presented in this paper, cannot be simply overlooked.

FIGURE 2 .

 2 FIGURE 2. GLI visualisation result. nodes (light-bulb looking bubbles) indicate health care service provision points, while extended dialog bubbles provide detailed specific information

FIGURE 3 .

 3 FIGURE 3. The portal (web page) structure diagram integrated with the e-learning management system and with the provision to be utilised for social medicine education

FIGURE 4 .

 4 FIGURE 4. A detailed description of connecting the "SCORM compliant" LMS with the geographical information system as a resource for social medicine education

ACKNOWLEDGEMENTS

This work has been benefited from an INTERREG IIIA Greece -Bulgaria (Decision 300531/YD4388 01/11/2005; CrossBorderHealth project), as well as, from an INTERREG IIIA/ARCHIMED grand (Contract Number A.1.087; IntraMEDnet project) fund by the European Union and the Greek Government.


Ludger Thomas
email: thomas@iese.fraunhofer.de

Sonja Trapp
email: trapp@iese.fraunhofer.de

BUILDING RE-CONFIGURABLE BLENDED-LEARNING ARRANGEMENTS

Keywords: blended learning, re-configuration, customization, re-use

HAL is

INTRODUCTION

E-learning can be very much like learning from textbooks, especially if training contents are presented like book chapters with text dominance, for students learning in a selfpaced way. Usually, e-learning courses are not integrated in structured learning sequences: students work through the course units sequentially or arbitrarily, depending on their preferred way of learning, or they access the content in an encyclopaedia-like manner.

Traditional e-learning requires the capability to find one's own way in self-directed learning processes and it demands a high level of self-motivation. Studies on acceptance and usage of e-learning have shown self-learning competences and self-motivation as being the biggest challenge [START_REF] Keller | Blended-Learning-Projekte im Unternehmen[END_REF]. In order to evade loss of motivation and to enhance sustainability of learning, the training sessions need to be well organized and include a broad range of activities. In this respect, there is not much difference between traditional learning in a classroom (face-to-face communication) and with support from printed textbooks, and learning with online materials (e.g. SCORM packages) and computer mediated communication (e.g. Acrobat Connect, E-Mail). By including various methods and activity types other than mere self-paced learning, e-learning was turned into a more successful method called blended learning.

For those who are experienced in building blended learning arrangements, it still remains difficult to create a reasonable mix of learning elements for each target group, especially if the learning material -which is still an important part within such scenarios, is presented in a rather static way. In most cases, the trainer cannot just cut out bits and pieces, add new material und combine it in order to create a new course or adapt the contents to the participants special needs. This would require highly flexible and modularized material, which is hard to develop with the current approaches. A study from the E-Learning Guild [START_REF]The eLearningguild: The Content Authoring Research Report[END_REF] showed that exactly this re-purposing of content is one of the features that are urgently demanded; nevertheless it is one of the least supported by common commercial authoring tools (e.g. Adobe Flash, MS Word etc.) [START_REF]The eLearningguild: The Content Authoring Research Report[END_REF].

In this article, an approach for developing re-configurable blended learning is presented. It is strongly based on the eduDocBook Format, which has been developed by Fraunhofer IESE within the Up2UML project. The article first presents an overview on blended learning concepts and underpins the need for re-configurable learning contents. Afterwards, the eduDocBook format as an approach to handle the problem of re-configuration of learning material and documentation is introduced. Based on this, IESE developed an online tool for the re-configuration of course material and course documentation, the CourseComposer. This approach is discussed in Chapter 4. The article ends with a conclusion and an outlook on future works.

BLENDED LEARNING CONCEPTS

Blended learning [START_REF] Trapp | Blended Learning Concepts -a Short Overview[END_REF] can be defined as the combination of multiple approaches to pedagogy or teaching, e.g. self-paced, collaborative, tutor-supported learning or traditional classroom teaching. Blended learning often refers specifically to the provision or use of resources which combine e-learning with other educational resources.

Some authors talk about "hybrid learning" [START_REF] Kerres | Online-und Präsenzelemente in hybriden Lernarrangements kombinieren[END_REF], "mixed learning" or "multi-methodlearning". However, all of these concepts broadly refer to the integration (the "blending") of e-learning tools and techniques with traditional methods. Computer-based learning is no longer regarded as an alternative to traditional forms of learning/teaching. It is integrated into a learning arrangement which combines those methods that have been selected for a specific learning purpose or environment.

Blended learning is not really a new concept. Teachers have always been using "combined resources". Basically, blended learning is just a combination of teaching or facilitation methods, learning styles, resource formats, a range of technologies and a range of expertise. It intends to take the best of both worlds. From classical classroom training, it takes the • teacher driven presentation and selection of relevant content,

• social interaction and • the dialogue between student and teacher.

Concerning e-learning, it benefits from the advantages of self-paced learning, i.e. • learning anytime everywhere;

• students can work through a specific task or problem as often as they want, until they reach their learning goal. In classroom training this would be impossible. It also requires stronger involvement of learners with the subject which might be one of the reasons why e-learning is said to be more effective and sustainable than face-to-face training.

If teachers or trainers want to provide or use different kinds of educational resources, they usually put up a plan, define a specific syllabus or plan learning sequences. Training plans or blended learning arrangements present ways of how to combine self-learning phases with synchronous or asynchronous online collaboration and cooperation, as well as with faceto-face training sessions.

When trainers make use of the educational content, they often select specific parts of the content, add their own material, with the aim of bridging the gap between theory and practice, they find ways of how to motivate learners, involve them in learning activities, give them tasks that can only be done in groups, etc. Due to the enormous costs of content development, organizations (e.g. universities) are usually not in a position to provide individualized courses for each trainer or target group, but provide generalized content to be used for course delivery. In general, online course material is rather static, and that is why trainer-specific custom-made learning arrangements are difficult to realize.

A solution to that problem is to build the content in a way that trainers can customize it to their particular needs, e.g., by building individual course arrangements. This assumes that as a result of content creation there should be concise and highly modular content units (cf. "microcontent", "microlearning", [START_REF]Microlearning: Emerging Concepts, Practices and Technologies after e-Learning[END_REF]), which then enable trainers to select different content elements, in order to recombine and mix them with other teaching and learning elements, like, e.g., project work, discussions, exercises, etc. Easy adaptation of learning materials to target group-specific domains is essential for any organization delivering high-quality educational settings.

RE-CONFIGURABLE BLENDED LEARNING WITH (EDU)DOCBOOK

DocBook [START_REF] Walsh | DocBook. O'Reilly[END_REF] is an XML dialect that was developed as an exchange format for (software) documentation in the early 1990s; it now has reached worldwide distribution. So far, it has served as a successful example for the development of structured formats for documents for XML developers. Thus the developers of the educational modeling language (EML) report that DocBook was the model for developing their XML-dialects [START_REF] Koper | Representing the learning design of units of learning[END_REF]. A wider, documented dissemination of DocBook in the area of learning media production has not been reported up to the present. eduDocBook as developed and used at Fraunhofer IESE is an extension and specialization of DocBook, which recommends the language especially for the educational sector. The currently available version of the eduDocBook format mainly allows fine-granular modeling of sequential-hierarchical learning content (book, chapter, section, reference etc). In particular it provides the following options:

• Markup of blended learning activities (e.g., online and offline activities)

• Markup of target group specific content (e.g. userlevel="novice") and content varieties (e.g. condition="course").

• Assistance of relations within documents (e.g. <eduRelationtype="isExerciseTo" linkend="nodeid"/>).

• Heavily modularized storage and reuse of learning content and course documentation.

• Build-tool based on open source software.

• All other additional options provided by DocBook: glossary, index, directories, function references, bibliographies.

The successful implementation in industry and higher education has shown that the eduDocBook format in combination with the accompanying tools enables the detailed markup of a number of formats and provides output in multiple configurations and media.

On a technical level the (edu)DocBook-based single-source publishing approach differentiates four consecutive layers which are passed successively for compilation and processing of learning content or course documentation [START_REF] Grützner | Systematische Entwicklung von Medien zur Benutzerunterstützung und -schulung mit einem XML basierten Single-Source-Ansatz[END_REF]:

Storage layer:

On this layer the components of the content are created in XML and retained for further processing. The components use the eduDocBook format, which separates content, structure and layout of documents, and hence provide great flexibility for future repurposing of the contents.

Composition layer:

This layer provides the aggregation of the components into a complete, valid DocBookdocument, which is used as the central foundation for further processing.

Transformation layer:

On this level the aggregated documentation is transformed into the desired output format. Currently various HTML and PDF formats are provided by eduDocBook.

Presentation layer:

This layer presents the formatted documentation to the user. Usually this can be done by using a CMS or KSM system.

FIGURE 1. A typical DocBook Production Process [9]

On the storage layer, which is responsible for creation and allocation of documentation, the authors will typically work with authoring tools such as an XML-editor or an IDE-tool such as Eclipse. The components are for example retained in a CSV/SVN repository for further processing. Using technologies such as xinclude, xpointer, xml catalogue, conref etc. enables an extensive modularization of information as well as the reuse on a technical level. An XSLT processor is the central tool on the composition and transformation layer. It transforms the validated XML-file, the so-called profiled intermediate file, to the desired output formats. In case of XSL-FO, the free Apache FO-Processor can be used to transform XSL-FO files into PDF files -although it only provides restricted possibilities. Professional results can be achieved using commercial products such as RenderX XEP or Antennahouse XSL Formatter. For presentation and allocation of the final documentation and media, a content management system (CMS) or, in case of educational software, a learning management system (LMS) can be used to import the produced SCORM packages. The relevant files for SCORM, the IMS Manifest, can be directly written from eduDocBook. The complete production process is largely automated and is controlled by a transformation wizard. The application initially queries the necessary data from the user and subsequently starts the transformation process for the wanted data and media formats.

Within the project "Upskilling to Object-Oriented development with the UML" (Up2UML) this form of content and course documentation production was widely adopted and further improved. In addition, specific output formats for eduDocBook with an attractive and functional interface were developed. Furthermore, eduDocBook was used to model documentation on blended learning activities -here called course documentation -and their relationships with content elements (e.g., X isExerciseTo Y). This allows not only the output of customized learning media for the students but also of the relevant documentation and support material for the trainer.

USING THE UP2UML COURSECOMPOSER TO CUSTOMIZE BLENDED LEARNING

The developed content modules on the UML2 were stored as largely independent modular information objects and enriched with meta-data. The overall goal was to enable future "reusers" of the components, such as trainers, publishing houses and course providers, to put together individual courses. A trainer may, for example, use the content developed in the project, for preparing a presence unit by using an online course on fundamentals of UML diagrams, and later on provide exercises together with a case study, handed out to the participants at the end of the workshop. The modular design within Up2UML supports the customization of existing blended learning concepts and the re-configuration of courses and help, for example, focusing on specific types of diagrams within UML.

The term re-configuration of content in this paper refers in general to the "authoring by aggregation" as described by [START_REF] Hoermann | Wiederverwendung von Lernressourcen mittels Authoring by Aggregation im ResourceCenter[END_REF]. Ultimately re-configuration describes the combination of content from existing content components (aggregation) or the change of this combination as well as transfer to different dimensions of reuse (re-configuration).

The creation process of learning media in Up2UML occurs in two steps: initially, the content is created and stored in a modular form. In the second step, these components, the socalled content objects, are aggregated into didactically meaningful arrangements, including various access support tools (e,g, an index or advanced organiser). A local solution was used as an aggregation tool as well as a tool for re-configuration of content tools. During that stage, the idea arose to apply the same processes to a web server and thus enable in the future a more comfortable combination and re-configuration of educational media. This application, called CourseComposer allows the users to comfortably develop or reconfigure didactically motivated arrangements of content objects -factually these are XML-files available in SVN in eduDocBook format. Subsequently, the combinations run through a number of transformations to be available for download in the desired output format, with the desired content (e.g. target group specific data).

FIGURE. 1. Schematic sequence of the re-configuration of educational Settings using the

CourseComposer [START_REF] Grützner | Building re-configurable multilingual training media[END_REF] Due to the use of Java-Script and Ajax libraries and technologies, the CourseComposer provides an intuitive interface. For example, it is possible to put together courses by drag and drop using the so-called "Arranger" in CourseComposer. It is also possible to move nodes, lectures, chapters etc. with the mouse. The so-called "Transformer" transfers the courses assembled with a few clicks into the desired format. After completion of the transformation, the courses can be made available to the students in different formats, WBT (HTML) and PDF, as well as in different languages.

DISCUSSION

The analysis showed that the possibility to reuse and re-configure learning content provides important stimulation of student motivation within blended learning arrangements, hence it contributes to the success of the approach. Furthermore, it represents an exciting area for the enhancement of e-learning, since similar technologies could be used to deliver truly personalized learning experiences. eduDocBook, as well as related tools provide solutions that enable the realization of numerous approaches. In contrast to the many proprietary solutions (e.g. LMML [START_REF]Learning Material Markup Language Framework LMML[END_REF], eEML [START_REF]Multidimensional LearningObjects and Modular Lectures Markup Language[END_REF], <Ml> 3 [START_REF]eLML -eLesson Markup Language[END_REF]), DocBook is an established standard, worldwide in use and with a very active user group, as well as numerous related technologies. Due to the distribution and use of standard technologies eduDocBook appears to be medium-term future-proof.

The described approach for creation and re-configuration of content has proven valid within an industry application and a research project with varying goals. It seems feasible that it is suitable for other topics, but this can currently not be fully documented. Even if the use of DocBook in social sciences and humanities is demanded sporadically [START_REF] Bunke | Schreibt strukturiert! XML und Docbook in Sozial-und Geisteswissenschaften[END_REF], we only have few experience reports about the suitability of the standard for the markup of corresponding texts, e.g. for medicine, law, etc. [START_REF] Merz | MedicCaseML: XML Austauschformat für CBT Systeme in der medizinischen Aus-und Weiterbildung[END_REF]. As a result of the flexible adjustment and specialization of DocBook -which increases further with the upcoming version 5 -it can be assumed that such solutions are possible. Generally eduDocBook has proven to be an applicable markup language in the mentioned contexts. Its low specialization in the area of educational media modeling is also a problem of eduDocBook: its ability to describe exercises in a semantically accurate way is limited. Complex didactical scenarios, often demanded, but rarely implemented in practice, can only be realized rudimentarily with the textbook logic implemented in eduDocBook. Furthermore, the feasibility of educational modeling with eduDocBook outside the described projects has to be examined. It is necessary to explore whether the techniques also work in the context of further blended learning projects and if the expected results can be achieved.

CONCLUSIONS

A perfect mix of media and methods adapted to the specific target group and optimized for the subject to be taught is one of the key factors for learning success. This has been true since the early days of adult education and it still remains true for blended learning. The creation of blended learning settings can be supported and facilitated by effective tools like the eduDocBook-based single-source publishing approach.

Within the Up2UML project a repository with learning objects and blended learning activities for UML2 was set up. It can be used by trainers, course providers and publishing houses to create their own learning products. To support re-configuration of educational media and corresponding course documentation, the tool CourseComposer was developed. It allows the assembly of modular information objects in the eduDocBook format and their transfer to multiple output formats.

ACKNOWLEDGEMENTS

The project "Upskilling to Object-Oriented development with the UML" (Up2UML) includes partner organizations from Bulgaria, France, Germany, Ireland and Romania and receives funding through the European program LEONARDO da VINCI 2005 -2007 (Project No. PP 146369).


Stathis Th Konstantinidis

Panagiotis D Bamidis
email: bamidis@med.auth.gr

E-LEARNING ENVIRONMENTS IN MEDICAL EDUCATION: HOW PERVASIVE COMPUTING CAN INFLUENCE THE EDUCATIONAL PROCESS

Keywords: continuing education, SCORM, Healthcare LOM, SCORM for Healthcare, POCKET SCORM, pervasive devices, PDA, mobile learning

HAL is

INTRODUCTION

During the last decade processes in medical education have started to become enriched with electronic learning and other Computer Science features and tools. In the meantime, pervasive computing has been gradually integrated in all facets of everyday life including the education process.

Lots of projects regarding the use of pervasive computing in e-learning have been developed. Some of them examine the exploitation of common devices such as projectors, microphones and cameras in order to record educational sessions in real time and to allow students to follow the educational process from a distance, trying to integrate the traditional activities within a classroom with the tele-education ones [START_REF] Abowd | Classroom 2000: An experiment with the instrumentation of a living educational environment[END_REF], [START_REF] Shi | The smart classroom: merging technologies for seamless tele-education[END_REF]. Furthermore, the use of mobile devices for e-learning entails the use of the appropriate E-Learning Environments in Medical Education… 292 standards, and the creation of an environment for self-motivated learning [START_REF] Chang | Design and implementation of ad hoc classroom and eSchoolbag systems for ubiquitous learning[END_REF], [START_REF] Lin | Pocket SCORM. Distributed Computing Systems Workshops[END_REF].

One of the problems that appeared as a result of embedding pervasive computing in medical education within e-learning, concerns the integration of the Sharable Content Object Reference Model (SCORM) for Healthcare into pervasive devices, the use of WEB 2.0 tools within pervasive Healthcare education environments, and the prerequisites for such endeavours.

To fill in the gap, we propose herein a framework that integrates standards like SCORM for Healthcare and the mobile SCORM equivalent, Pocket SCORM, into any pervasive device, allowing the reusability and the interoperability of learning context accompanied by Web 2.0 tools such as podcasts, vodcasts, blogs and wikis. The aim is to demonstrate the process of distance medical education can be influenced by the use of pervasive computing environments, but also to establish a set of directives in order to protect technical and human entities from potential malefic attacks.

The remainder of this paper is structured as follows. In Section 2 we provide a brief account on related work. In Section 3 the concurrent route of e-learning environments and pervasive computing is described, while in the following section the framework is introduced. The prerequisites for the existence of this framework are given in Section 5, followed by discussion on key issues of concern and future work.

SETTING THE SCENE

Pervasive computing was initially discussed as a new way of thinking about computers [START_REF] Weiser | The computer for the 21st century[END_REF] taking into consideration the human world and giving the opportunity to computers to be hidden in the background while being an integral but invisible part of people's life. Three concerns were firstly issued for pervasive computing: (i) low cost and low-power computers with equally convenient displays; (ii) software for pervasive applications and (iii) networks that act as platforms of intercommunication among all [START_REF] Dritsas | Protecting privacy and anonymity in pervasive computing: trends and perspectives[END_REF], [START_REF] Langheinrich | A privacy awareness system for ubiquitous computing environments[END_REF].

Low-power computers were firstly replaced by mobile devices and then by wearable and pervasive devices consuming low energy and having high autarchy extended with invisibility. The software for pervasive applications has taken the bun of classical graphical user interfaces and implicates natural human forms of communication such as handwriting, speech, pen-based or free-form interaction [START_REF] Fitzmaurice | Bricks: Laying the foundations for graspable user interfaces[END_REF] and sensors attached to computational devices so as to provide management and manipulation in physical ways [START_REF] Harisson | Squeeze me, hold me, tilt me! An exploration of manipulative user interfaces[END_REF], [START_REF] Abowd | Charting Past, Present, and Future Research in Ubiquitous Computing[END_REF]. Communication and collaboration of the heterogeneous and different environments that interfere in pervasive computing has been also a major issue when demanding ubiquity, invisibility, interconnectivity and co-operation between pervasive devices, as well as, memory affiliation.

As pervasive computing is incrementally integrated with all facets of everyday life, it is reasonable to expect influences on educational activities as well. Numerous efforts within projects were made to create environments that capture as much of the university classroom experience as possible by automating the production of online lecture notes with electronic whiteboards and other gadgets and tools such as, embedded microphones, cameras and projectors in the ceiling during the real-time lessons [START_REF] Abowd | Classroom 2000: An experiment with the instrumentation of a living educational environment[END_REF]. Then a Smart Classroom by the use of Smart Space and similar means gave the teacher the opportunity to be away, bridged the gap between tele-education and traditional classroom activities in terms of teacher's experience and seamlessly integrated these two separate educational practices [START_REF] Shi | The smart classroom: merging technologies for seamless tele-education[END_REF]. In another project [START_REF] Chang | Design and implementation of ad hoc classroom and eSchoolbag systems for ubiquitous learning[END_REF], a wireless platform was developed where an ad hoc classroom accompanied by the eSchoolbag system was built, allowing the communication between teachers' and students' with devices such as desktop PCs, laptops and PDAs in order to create a self-motivated learning environment. Electronic subsystems were also created such as PowerPoint broadcasts, text transmissions, voice and Image transmissions etc so as to complete the application ranges required for all kinds of devices.

In the mean time, e-learning environments undertook a crucial part in the educational process by means of collaborative tools for synchronous and asynchronous communication such as chat, forum, e-mails, as well as, document exchange tools, file management, etc.

Furthermore, international standards of learning material were specified in order to meet the portability and interoperability between the different e-learning platforms. SCORM (SCORM, 2004) adapted requirements regarding accessibility, adaptability, affordability, durability, interoperability, and reusability. It was based on widely accepted technology standards such as XML and JavaScript and it was adopted by a large number of providers, institutions and corporations worldwide. The standard was initially organized by the Advanced Distributed Learning Initiative (ADL), but several other studies proposed extensions or changes in order to fit in special needs of every educational process. In order to fulfil the needs of medical education, the MedBiquitous Consortium -which is the ANSIaccredited developer of information technology standards for healthcare education and competence assessment -proposed a specification called SCORM for Healthcare [START_REF] Smothers | SCORM From Healthcare Specifications and Description Document[END_REF].

SCORM for Healthcare extended the Learning Object Metadata (LOM) standard in order to provide custom vocabularies for some metadata elements. That LOM profile was called Healthcare LOM [START_REF] Smothers | Healthcare Learning Object Metadata Specifications and Description Document[END_REF]. SCORM for Healthcare was actually a version of SCORM implementing Healthcare LOM. The requirements for medical education that were not included in the existing LOM have been addressed by extending the LOM standard by a Healthcare Metadata category using custom vocabularies. To incorporate the use of mobile devices in the e-learning purposes, a modification of SCORM, called Pocket SCORM [START_REF] Lin | Pocket SCORM. Distributed Computing Systems Workshops[END_REF], was designed and tested on Pocket PCs; its main focus was on connection mechanisms, courseware import and export and learning records buffering.

The latest collaborative and e-learning tools which are frequently met in the e-learning platforms are wikis, blogs, podcasts, vodcasts and blikis. These are called Web 2.0 tools and they increasingly interfere in the educational process. They use RSS (Really Simple Syndication) and the users can easily access them through Internet Explorer (version 7 and above) or Mozzila without the need of using a special program. Consequently, they can be easily embedded or added in existing e-learning environments. In medical education they have been well received due the sternness of their features. As Boulos et all [START_REF] Boulos | Wikis, blogs and podcasts: a new generation of Web-based tools for virtual collaborative clinical practice and education[END_REF] conclude in their paper "if they are effectively deployed, they could offer a way to enhance students', clinicians' and patients' learning experiences and deepen levels of learners' engagement and collaboration within digital learning environments". All these tools facilitate the collaboration on the Web through suitable Web Collaboration Environments. Furthermore, Mobile learning, taking place across different locations by the use of portable devices and technologies, derived from the evolution brought about by mobile computing. Portable devices such as laptops, Pocket PCs, Personal Digital Assistants (PDAs), smart phones, or just simple mobile phones advance the e-learning operability and enhance its use in everyday life. International standards ensure portability and organization of learning material, while standardization of learning object metadata provides the context for an effective and flexible e-learning environment which can be adjusted for various needs and requirements.

FIGURE

Pervasive computing meeting e-learning for medical education: standards, tools, and issues of concern Figure 1 illustrates the above issues in an attempt to merge the developments in elearning and pervasive computing within the field of medical education.

Finally, we have to mention that one of the most critical points in advancing e-learning is the audience itself. Medical doctors compose one of the most demanding audiences in the educational process, as the nature of their education necessitates a considerable combination of theory/knowledge and clinical practice.

THE RATIONAL AND THE FRAMEWORK

The majority of e-learning environments provide the necessary features for theoretical education. More advanced technologies, such as podcasts and vodcasts, wikis, blogs, blikis, and real time conferencing tools and Web Collaboration Environments contain features that advance interactivity and enable the fulfilment of more practical education targets. Such technologies also provide the ability to the user-teacher to constrain the role of the userstudent so as to avoid "information vandalisms" thereby imposing barriers for the deterioration of information quality. But how can such options become integrated with the SCORM standard and more specifically to SCORM for Healthcare by the simultaneous use of pervasive devices?

All mobile and pervasive devices with some computational power and a manipulated interface can be easily adjusted to use Pocket SCORM [START_REF] Lin | Pocket SCORM. Distributed Computing Systems Workshops[END_REF]). As the modifications on SCORM do not influence the elements of SCORM that exist on the Server, the only requirement is the installation and configuration of (i) the Pocket SCORM run-time environment (RTE) into pervasive devices, (ii) the PC Dock -which is a layer between Pocket SCORM RTE and the SCORM LMS server -so that a connection with the local LMS server can be established, and (iii) of the local LMS Server so that all the course material can be stored (in a Data Repository), when the connection is unavailable.

When the standard SCORM for Healthcare is used on a wired PC, it allows Web 2.0 tools to be embedded as Metadata by the use of Healthcare LOM. Metadata can be associated with Assets such as images, documents or video and audio streams providing suitable information about the Assets independently of learning content including the information of title, description, etc. and allow external search. The Asset Metadata can be applied both to <resource> elements (Asset resource) and to <file> element which can be met as child element of <resource> within an Sharable Content Object (SCO) (Figure 2).

FIGURE 2. Asset Metadata for Web 2.0 tools in SCORM

The Healthcare LOM includes all the categories of LOM, therefore the "Technical category" as well. The Technical category is composed by some elements including Size, Location, Requirements etc. Location, is a string and may be used to access the learning object; it usually represents its physical address. SCORM for Healthcare on the web server side can cooperate without problems with Pocket SCORM on the pervasive devices' side because it uses the same basic functions as SCORM (Figure 3). Regarding podcasts or vodcasts as Healthcare LOM, once a stream of data is initialized they will start to be loaded into the wired PC, and be projected through a suitable software. In case of wikis, blogs and blikis the page will be loaded and used in a dynamic mode. The same procedure could be followed in case of a wired pervasive device, with only one difference; the data would be initially loaded into the local LMS server and then to the Pocket SCORM RTE, so as to be viewed through the software viewer of the device.

The case of wireless devices, such as most pervasive devices, is much more complicated. Podcast and vodcast require a stream of data to be sent to the device in-real time and the capacity of memory to be high enough for the transaction to be successfully established. While the wireless pervasive devices are on-line the problem is solved because the speed of data transfer is suitable for this operation. In case of non-connectivity the data should be stored earlier in the Data Repository of the device. Furthermore, the amount of stream data does not allow the whole stream to be stored, but only the first part. The solution to this problem is the break of the stream into parts by the external WEB LMS server before retransmitting it to the pervasive device and sending the parts in a chain until the device sends a message of full memory. When the user finishes viewing a part, it is being deleted from the Data Repository and in the first online chance a message is sent so that the following parts that are waiting to the web LMS server are transmitted one by one.

Regarding wikis, blogs, and blikis, the process is easier. The pervasive device requests through the Healthcare LOM one of the above tools and when the connectivity is available, the page is stored into the Data Repository. If any changes occur only the added or changed content is transmitted to the web LMS server, which is responsible to add the content in the tool and retransmit it, including the changes so that the user of the device takes a feedback.

FRAMEWORK REQUIREMENTS

The prerequisites of this framework can be dealt within two different dimensions. The first one is the technical and the second depends on the individual person's privacy and anonymity.

Technical prerequisites are set due to the features of the devices that are used. Mobile devices or pervasive devices in general need a "pervasive SCORM". In case of mobile devices a Pocket SCORM has been proposed [START_REF] Lin | Pocket SCORM. Distributed Computing Systems Workshops[END_REF], which can be also applied in the pervasive devices the user uses with few modifications. For example, if we have sun glasses with computing power and a screen on the glass and want to provide a vodcast, the pervasive device should support Pocket SCORM or a similar architecture with some navigation controls which may be in the rim of the sun glasses.

Furthermore, pervasive devices (including mobile devices) have limitations on computation power, memory resources and energy. All of the three limitations/constraints are elaborated daily and their operability advances. In the proposed framework, the download of learning objects and learning object metadata follows the prototype of Pocket SCORM, stores all the necessary data in the pervasive device when the wireless connection is available, and uses them along user demands. To this extend, special cases of LOM which need high bandwidth and a lot of memory, such as podcasts and vodcasts will follow the same protocol and will be stored in the device, but they have to be separated into smaller entities in order to fulfil the preconditions.

On the other hand, for the data that are spread throughout pervasive devices and include for example patients' sensitive data, one has to ensure that no leak would occur and the anonymity and privacy will be retained or kept within the specific e-learning community. E-learning platforms' designers make a strong effort to ensure that the sensitive data will remain within the e-community. They use the RBAC model in software design and Hyper Text Transfer Protocol Secure (HTTPS) in order a different default port (443) and an additional encryption/authentication layer between HTTP and TCP to be used in addition to cryptographic protocols: Transport Layer Security (TLS) and Secure Sockets Layer (SSL) which provide secure communications on the Internet for such things as web browsing, email, Internet faxing, and other data transfers.

In addition, human entities should be protected by the malefic attackers and secure their privacy and anonymity about their personal data, such as their IP address, their location etc. There exist many protection mechanisms [START_REF] Lederer | A conceptual model and a metaphor of everyday privacy in ubiquitous computing environments[END_REF], [START_REF] Lessig | The architecture of privacy[END_REF], [START_REF] Adams | The implications of users_ privacy perception on communication and information privacy policies[END_REF]) [START_REF] Langheinrich | A privacy awareness system for ubiquitous computing environments[END_REF], [START_REF] Jendricke | Pervasive privacy with identity management[END_REF], [START_REF] Muhtadi | Routing through the mist: privacy preserving communication in ubiquitous computing environments[END_REF], [START_REF] Beresford | Location privacy in pervasive computing[END_REF], [START_REF] Beresford | Mix zones: user privacy in location-aware services[END_REF], [START_REF] Nguyen | Privacy mirrors: understanding and shaping sociotechnical ubiquitous computing systems[END_REF], [START_REF] Jiang | Modelling privacy control in context-aware systems[END_REF] in the form of an abstract context, a protocol or a technology proposed for this issue, but most of them were not clearly designed for pervasive devices, resulting to the lack of full anonymity and privacy. Nevertheless, Dritsas et all [START_REF] Boulos | Wikis, blogs and podcasts: a new generation of Web-based tools for virtual collaborative clinical practice and education[END_REF] refers to the privacy threats that were identified in a pervasive environment and presents a set of principles for ensuring privacy in this context (Notice, Choice and consent, Proximity and locality, Anonymity and pseudonymity, Security, Access and Resource).

DISCUSSION AND FUTURE WORK

The framework presented herein enables the use of SCORM for Healthcare in pervasive devices. It provides the use of WEB 2.0 tools in all kind of pervasive devices giving the opportunity to the medical learners to learn and study while being away from the class and take advantage of the time pressures and the time they are "on the move". What is more, it enhances the medical learning procedure concerning the medical doctors being in rural areas where the chances for enhancing the knowledge acquisition are limited.

The theoretical framework that sets the use of pervasive computing along the special needs and requirements of medical education utilising e-learning environments can boost the knowledge and advance the willing of e-learning participation with the selection of learning contexts that fulfil the learner's interests. However, the framework could be demolished unless appropriate prerequisites are set corresponding to the simultaneous development of pervasive computing and e-learning environments. The protection of privacy and anonymity are prominent issues, and despite of the numerous protection mechanisms that have been proposed, there is a clear design lack in the case of pervasive devices. Nevertheless, the use of such mechanisms is essential in order to reassure the security of personal data such as name, location, etc and patients' data that are used for educational purposes in web e-learning platforms, as well as, in pervasive learning environments.

In conclusion, our ultimate intention is to implement a system based on this framework so as to be able to research the practical problems and difficulties that may arise during the implementation. Of course, the feedback of the learners themselves will judge where the actions undertaken by the framework and its implementation will assist in reorganising the learning process suitably well, while at the same time meeting the real needs that arise during the medical educational process.

FIGURE 3 .

 3 FIGURE 3. Integration Scheme for SCORM for Healthcare, Pocket SCORM and WEB 2.0 tools

ACKNOWLEDGEMENTS

This work has been benefited from an INTERREG IIIA/ARCHIMED grand (Contract Number A.1.087; "IntraMEDnet: A Mediterranean Research and Higher Education Intranet in Medical and Biological Sciences") fund by the European Union and the Greek Government.


Matan Cohen

The proof of Goldbach's Conjecture

come

The complete proof of Goldbach's Conjecture

Introduction

Goldbach's Conjecture states that every even number greater than 2 is the sum of two primes. That is: ∀2m ∃p 1 ,p 2 : 2m = p 1 +p 2 , m ∈ ℕ. This paper uses a binary tree to provide a complete proof to Goldbach's Conjecture.

Definitions and Formulas

Definition 1 The following structure is called a Binary Tree. In some parts of the proof, it is simply called tree.

The above tree consists of 4 levels, and contains natural numbers up to 15. Our goal is to proof Goldbach's Cojecture for an infinite amount of even numbers, For this reason, let us assume that the above tree is unlimited and contains all natural numbers.

Definition 2

The symbol V represents an arbitrary vertex in the tree.

Definition 3

∀V ∈ tree, the right child of V is an even number and the left child of V is an odd number.

Definition 3

The Barracuda of the tree is the group {V ∈ tree : V = 2 k , k ∈ ℕ}.

Definition 4

The level k of the tree contains 2 k vertices Formula 1 ∀k ∈ ℕ 2 0 +2 1 +2 2 +....+2 k = 2 k+1 -1

Definition 5

The sub-tree which consists of the levels 0,1,2,...k contains 2 0 +2 1 +2 2 +....+2 k vertices. According to Formula 1, that is 2 k+1 -1 vertices

Definition 6

the Offset of V is the number of vertices that exist in the level of V and are located to the right of V. The offset of V always includes V as well.

Definition 7

In every level of the tree, the offsets of even numbers are odd.

Definition 8

In every level of the tree, the offsets of odd numbers are even.

The Proof

Theory

Goldbach's Cojecture is correct

Proof of the Theory Lemma 1

Goldbach's Conjecture is correct for every vertex outside the barracuda, which is even and greater than the number 2. Proof 1. Since the tree is unlimited, Every even number greater than 2 can be found in the tree.

2. Let us choose an arbitrary vertex X in the tree. so that X = 2m, m ∈ ℕ, m > 1 3. Let Y be the level of X. Let R be the intersection between Y and the Barracuda.

4. Let T be a sub-tree, with a root that connects X and R together. For example, if X = 10 then R = 8 and T will be the following tree: 5. Let A be the offset of vertex X in level Y of the tree T.

6. Let B be the difference between the number of vertices in Y and A, that is: B = 2 y -A Theorem 1.1. Either A is prime or B is prime.

Proof of Theorem 1.1:

1. 2 y is even. According to definition 7, A must be odd. Therefore, B must be odd as well.

Theorem 1.2:

X -p 1 is prime.

Proof of Theorem 1.2:

1. Since X is even and p 1 is prime, the term X -p 1 is odd. According to Definition 8, the offset of X -p 1 is even. Let 2m be the offset of X -p 1 .

2. Because of Definition 5, X -p 1 = 2 k -1+2m

3. Let us assume that X -p 1 is a composite number. If so, it can be divided by an odd number greater than 2. Let's call that number -1+2m 4. It follows that:

5. The number 2 k only has 2 as a prime factor, while odd numbers never have 2 as a prime factor. So 2 k and an odd number will have no prime factors in common. For this reason, the number 2 k cannot be divided by an odd number.

6. From step 4 and step 5, it follows that the term:

is not a natural number, that is, the odd number X -p 1 cannot be divided by an odd number. So X -p 1 is prime. 7. Q.E.D 8. From Theorem 1.1. and Theorem 1.2. it follows that Lemma 1 is proven. 9. Q.E.D

Lemma 2

Goldbach's Conjecture is correct for every vertex in the Barracuda (except of the vertex 2).

Proof of Lemma 2

Let 2m be an arbitrary even number, so that {2

x ≠ 2m > 2 k : m ∈ ℕ, k ∈ ℕ, x ∈ ℕ, x > k}. It is easy to see that: {∃n ∈ ℕ : 2m = 2 k + 2n , 2n ≠ 2 x }
Because 2n ≠ 2 x , the number 2n is outside the Barracuda. Hence, according to Lemma 1, Goldbach's Conjecture is correct for the number 2n, so 2n = p 1 + p 2 . It follows that:

2m = 2 k + p 1 + p 2
For the same reason, Goldbach's Conjecture is correct for the number 2m. It means that the weak version of Goldbach's Conjecture must be correct for the number 2m. According to the weak version of Goldbach's Conjecture, every odd number is the sum of 3 primes. Therefore, the number 2m is the sum of 4 primes.

It follows that 2 k + p 1 + p 2 is the sum of 4 primes, so 2 k is the sum of 2 primes, thus Goldbach's Conjecture is correct for 2 k .

In other words, Goldbach's conjecture is correct for every vertex inside the Barracuda.

Q.E.D

Proposition 1

If Goldbach's Conjecture is correct for every vertex outside the Barracuda (which is even and greater than 2) and Goldbach's Conjecture is also correct for every vertex inside the Barracuda (except of the vertex 2) , then Goldbach's Conjecture is correct for every even number greater than 2.

Proof of Proposition 1

Let OUT be the group of all vertices that are outside the Barracuda (and are even and greater than 2).

Let IN be the group of all vertices that are inside the Barracuda (except of the vertex 2).

According to Lemma 1, Goldbach's Conjecture is correct for OUT According to Lemma 2, Goldbach's Conjecture is correct for IN It is easy to see that the union OUT ∪ IN is the group of all even numbers greater than 2.

Q.E.D.

The proof of Proposition 1 results in the proof of the Theory.

Q.E.D

Examples:

2.

  Given that A and B are odd, Let us assume that both A and B are composite numbers. That is, A and B can be divided only by odd numbers. It means that {∀* : A ≠ 2 * } and {∀& : B ≠ 2 & }. Therfore {∀* ∀& : A + B ≠ 2 * +2 & }, and it follows that {∀* ∀& ∀y : 2 * +2 & ≠ 2 y }. Contradiction! 3. Because of the contradiction in step 2, at least one of the two numbers (A and B) must be prime. 4. Q.E.D 7. Let p 1 be a prime number which is equal to either A or B. Let us evaluate the term X -p 1 .

Does the number 10 satisfy Goldbach's Conjecture? Does the number 6 satisfy Goldbach's Conjecture? Does the number 14 satisfy Golbach's Conjecture? Does the number 12 satisfy Golbach's Conjecture?


Miroslav Trajanovic
email: miroslav.trajanovic@fit.edu.yu

Dragan Domazet
email: dragan.domazet@fit.edu.yu

Biljana Misic-Ilic
email: biljana.misic@fit.edu.yu

DISTANCE LEARNING AND FOREIGN LANGUAGE TEACHING

Keywords:

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

For the past two years the Faculty of Information Technologies (FIT) in Belgrade has been organizing, along with the traditional academic program, the distance learning program for its students from Serbia and other European countries as well. The technological platform for the distance learning system is the Oracle iLearning system. The system has proved itself in practice as robust and very suitable for most of the academic courses. However, the common practice of foreign language teaching and learning poses a series of specific requirements for the distance learning system which are difficult or almost impossible to implement.

The paper first gives a short description of the distance learning system and English language teaching at FIT. Then follows the overview of the problems encountered in teaching materials preparation and course distribution. The final sections of the paper show and discuss some solutions and the results achieved in this kind of teaching.

METHODOLOGY 2.1 Technological platform of the e-learning system

The technological scenario for the e-learning system is shown in Figure 1. It means that all the participants in the process are connected to the Internet and that they can communicate among themselves via the Internet. The participants of the distance learning process are: Teachers, whose role is to prepare the teaching material, follow the students' activities throughout the semester, provide support for the students and assess them. Teachers can perform their activities at the FIT premises or at some distant locations.

•

Distance learning system administrator, whose task is to process and publish teaching materials, administer the users and maintain the system.

•

Students, whose task is to study using the teaching material and on-line tutorials in the synchronous and asynchronous regime. Moreover, students have to complete homework assignments, knowledge tests and examinations. Both traditional students and elearning students can use this e-learning system.

The raw teaching material prepared by the teachers consists of lecture texts, figures, presentations, audio recordings, video recordings, the list of external web locations, quizzes, tests and exam tasks. All these components comprise the input into the production system, whose task is to produce the teaching material in the form suitable for publication at the distance learning system. The schematic representation of the functioning of the production system is shown in Figure 2. The completed teaching material is stored at the database and is available to all the authorized users (students, teachers, and administrators).

FIGURE 2. Production system

During the production of the teaching material it should be constantly kept in mind that is has to be designed in such a way that a distance learning student does not notice that s/he is not in the classroom. This can be achieved only with the adequate combination of audio/video content. The main result of the production is the audio/video recording of the lecture, which is, upon students' request, emitted at the time most suitable for them. Unlike students in traditional education, the distance learning student has the option to go forward and backward through the lecture and repeat it as many times as s/he needs to learn the material.

Communication between the teachers and the students is also done via the Internet. (Figure 3). They have synchronous and asynchronous methods at their disposal. Synchronous methods include chat, VoIP, and video conferencing. Among the asynchronous methods only e-mail and forum are used. The production of the same audio/video recording can be done in various qualities, corresponding to various transmission speeds. Although it is possible to work with lower bandwidth, the minimum recommended bandwidth should be 64 Kb/s. Technically this can be achieved if all the users have ISDN or, even more common, ASDL connection with the ISP.

English language courses at fit

The FIT curriculum specifies three English courses, English 1, 2 and 3, in the first, second and third semester, respectively. Content-wise, these courses are the combination of general English and English for special purposes (ESP for IT), with ESP content progressively increasing to 80% in English 3. The first level is intermediate, while the final is upper-intermediate with elements of advanced ESP for IT. The aim of these courses, specified by the faculty authorities, on the basis of IEEE recommendations, is to train the students for oral and written communication in professional and academic settings. The teaching goals, defined in this way, suggested as the best choice the task-based and student-oriented teaching approach instead of the text-based or teacher-oriented one.

FIGURE 3. Communication inside the e-learning system

The starting point in designing and creating these three courses were some basic issues concerning course development, especially of a university language course [START_REF]The Impact of Information and Communications Technologies on the Teaching of Foreign Languages and on the Role of Teachers of Foreign Languages[END_REF] .

These basic parameters are: • to determine the level and proportion of general language and ESP • to focus on all four language skills (listening, speaking, reading, writing) and their integration • to include additional elements, specific for academic purposes, such as basics of academic reading, writing and oral presentation • to select and/or create appropriate teaching materials Additional tasks, stemming from specificities of FIT and the fact that the course has to be the same for both traditional and distance learning students are:

• to co-ordinate these two different teaching and learning media (the traditional one, in the classroom, and the e-learning one) • to provide approximately the same options and tasks for both categories of students, taking care that e-learning students do not get deprived of some usual communication activities.

In the following part of the paper we discuss how we dealt with these issues as well as with some other conceptual and practical problems and tasks.

The primarily pedagogical issues of course design and materials selection are of less importance for this paper, so we focus on questions primarily related to e-learning. It should be just mentioned that the primary teaching materials include the coursebook, practice book and audio CD pack Language to go, Intermediate and Upper intermediate (Longman) for general English and Oxford English for Information Technology (Oxford University Press) for ESP.

Due to the specificities of the dual distribution of the courses, the option we have chosen for our e-learning mode is a hybrid course. Theory defines it as: "Hybrid systems usually comprise a collection of materials made available on CD-ROM or on an institutional intranet, with links to the Web and regular contact with tutors by email, telephone or videoconferencing." (Walker, 2007). In our case all basic teaching materials are available offline -coursebooks, practice material, some audio materials, answer keys for all the tasks. Some of the noted advantages of a hybrid course include:

• no need for the student to be constantly online, thus avoiding potential technical problems

• all the students have the same teaching materials, in this case high quality coursebooks

• hybrid courses in recent literature on CALL (Computer Assisted Language Learning) are recommended as the optimal solution -"in order to be efficient, Web-based courses should be blended or hybrid", (Wolff, 2003) The key issue in the realization of a hybrid course is how to convey at the distance the existing teaching materials and activities, especially the instructions. As mentioned before, all the classes are planned in great detail in advance, carried out and recorded in Power Point as slides and as narration. Everything that the teacher says, asks, or explains in the classroom s/he anticipates and records in the Power Point presentation. Having the narrated recording, which is richer than just the text on the slides, is very important for several reasons. Primarily, it gives the student the sense of a 'real' teaching session. For foreign language teaching in particular this is essential because the student both sees the text and hears the pronunciation, which is not possible if lectures are given only in the written pdf. or ppt. format. The narration explains and elaborates the slides, but also addresses the students directly, inviting them for further communication, and serves both as the instruction and listening comprehension activity. When working with the coursebooks, the students are very precisely directed to the pages in the coursebooks, with very detailed instructions and explanations. It is important to note that the students can pause the narration to complete the task from the coursebook, and then go on to the next activity/task at their own pace, unlike the students in the classroom, who have to follow some average pace of the group. The e-learning students, unlike classroom students, can also repeat the slides/narration as many times as they want, thus having more time for listening to the lectures/activities. The Power Point slides and recorded narration are accompanied by the lecture texts (mostly the more formal and structured explanations of grammar, vocabulary, learning and problem-solving strategies, homework tasks and mini-project assignments) in the pdf. format. Together with the coursebooks and recorded classes, for all the activities in class, all tasks and practice materials, there are additional pdf. files with the answer keys and model/suggested answers. The audio CD, which is a part of the cousebook pack, is available only online, but, of course, as the commercial CD, it can be bought together with the coursebook. Naturally, if the students need or want to, they can always check their answers with the teacher, via e-mail. A student can also record her/his comments and send them via e-mail as the audio file. What is especially significant and needs special emphasis is the fact that there is a very strong support segment for the e-learning student from the teacher, who regularly communicates with them vie e-mail, mostly in English, but if necessary also in their mother tongue. Moreover, the students can also communicate among themselves, via e-mail, forum or chat. From the point of view of the teacher, such classes, as well as course management as a whole, request much more demanding and more detailed preparation, engagement and organizational skills, as well as a considerable level of technological skills.

One of goals of English 1, 2, and 3 courses is to develop, improve and practice the language skills of listening, speaking, reading, and writing, as well as skills integration. Due to the very nature of e-learning, with the lack of face-to-face interaction, it is the speaking component which makes the greatest problem, but this does not mean that this component has been totally neglected, as is the case with many CALL and language e-learning systems. Our solution has been to provide learning options for and assess one particular mode of oral communication -the oral presentation, which will be dealt with in greater detail soon. Table 1 presents the typical language teaching/learning tasks and the materials and methods used for completing them both in the traditional and distance learning mode, together with the used and suggested tools for distance learning.

Knowledge assessment at FIT is in accordance with the Bologna declaration. This means continuous assessment of knowledge, and, in case of English, performance and proficiency. A student gets 60% of the final mark through pre-exam activities and 40% as the final written test mark. In case of English 1, 2 and 3, the final exam is primarily the assessment of grammar, vocabulary and language functions, while the mastery of language skills is mostly assessed in pre-exam tasks and activities. This gives the e-learning students more time for preparation, and in a way, lowers the stress. The pre-exam tasks include:

• Progress test (grammar, vocabulary and use) This is a two-page test given around mid-semester, covering only the learned material. This test has a dual function. It should indicate the student's progress and identify the problem areas which need remedial action. Moreover, it serves as the model for the final exam, which has more or less the same form but is considerably longer and covers the material from the whole course. This test is given as the word document, for traditional students to do it in the classroom, while the e-learning students have a set, limited time to do it and submit it via email to the teacher.

• Listening comprehension test This is a short 15 minute test with 10-multiple choice and fill-in the blanks questions, distributed at the set time as the e-learning test, for both traditional and e-learning students. The system records the answers.

• Homework writing assignments They are related to lectures and mostly practice functional writing according to the given model, with the length and demands progressively increasing. In English 3, half of the tasks are group problem-solving integrated skills activities, where a group of 3-4 students, produces a joint short written report.

• Home reading and writing.

In each course students have to read a book simplified at the corresponding level and complete the given tasks related to language study, text study and essay writing. The significance of extensive reading in the foreign language of texts which are not exclusively professional is widely accepted in foreign language teaching2 .

• Oral presentation Traditional students do the oral presentation alive, in front of their colleagues, whereas elearning students record it as an audio or video file. Using the given presentation model, the students talk on professional, specified topics. Unfortunately, this is the only formal and obligatory mode of oral communication and presentation. These oral presentations recorded by e-learning students can be posted at the FIT forum. This can not only increase the student's awareness of public speaking in English, but also invite other students to provide feedback, thus promoting communication. Nevertheless, this is not the only oral communication mode -once a month there are audio conference classes, on a given topic and with activities announced in advance, where both traditional and e-learning students can take part. Since these are not obligatory, only the students who want to do it, participate. There are, however, several problems with such realtime classes. It is often difficult for the e-learning students to manage their time in order to take part [START_REF] Hampel | Towards an effective use of audio conferencing in distance language courses[END_REF] . Moreover, sometimes the broadband connections do not work properly and fast enough, which causes unpleasant interruptions and delays. Also, the discussion groups larger than five participants (the teacher included) can not work properly, so the students have to be divided into several groups, with the teacher joining alternatively each of them for a short period of time. Recent literature on CALL describes several attempts to include the oral communication component into e-learning (Kötter, Shield & Stevens, 1999, Humpel & Huck, 2004, Volle, 2005). The main common feature of these attempts is that they combine realtime and recorded communication, the number of students is rather small, and, most importantly, it is the students who primarily take the initiative and are in charge of the communication activity, with the teacher acting primarily as a facilitator, and less as a moderator or assessor. Unfortunately, our experience is that students, despite claiming they need oral communication, are very reluctant to take part and hardly take any responsibility, even when one of them is assigned the role of the group moderator.

It should be noted that one of the ideas in the design of these three English courses was to provide opportunities for realistic learning situations, in particular to enable the students to learn and use English in tasks related to and facilitating their study of other, IT-related courses at FIT. Homework writing and oral presentations are the areas of the most pronounced collaboration between English, and other, IT-related courses. Especially in English 2 and English 3, the tasks are set in such a way to include the content covered as assignments or projects in professional courses. This not only enables the connecting of the professional knowledge and language knowledge in a meaningful way, but also promotes peer and collaborative learning in a realistic environment, which is one of the key methodological recommendations in contemporary foreign language teaching (Vygotsky, 1978, Salaberry 1996, Rüschoff, 2001). A typically successful example is that the seminar papers and project tasks for some IT courses, for which the students have to use resources both in English and in their mother tongue, are presented orally, in an appropriately adapted version in English, and graded as the oral presentation.

RESULTS

The described system for distance learning of English has been already used for three semesters. The following Table 2 shows the results scored by traditional and distance learning students. We would like to note that these exam results should be taken tentatively, as a tendency rather than as a compelling evidence. It should be noted that the marks need not be taken as an absolutely reliable indicator of one mode of teaching being superior to another (as it may seem that the distance mode is superior to the traditional one!). It is common that the students enter the faculty with very different language levels, and some distance learning students have work experience with foreign companies, which can explain their better exam scores. A more interesting indicator is that distance learning students, on the average, tend to gather more points for pre-exam assignments than the traditional students. It seems that they, to compensate the lack of direct contact, put more effort into pre-exam task. Another possible explanation, and a rather unfavourable one, could be that distance learning students have someone else, very proficient in English, who completes their tasks. Our conviction, however, is that it is not the case, because their final test results roughly correlate with their pre-exam results.

On the other hand, the fact that distance learning students do not score worse than the traditional ones is a clear indicator that our distance learning course is indeed a viable, workable alternative, with satisfactory results. Needless to say, there is always room for improvement, about which we would comment in the following section.

DISCUSSION

In this section we would mention some potential and noted problems and advantages of applying the e-learning model to the teaching of English, as well as our observations after three semesters.

Typical general distance learning systems do not have installed systems to support synchronous and asynchronous communication, and as such they are not quite suitable for foreign language learning. By using additional tools such as Google Talk, Skype, various forums, whiteboards, etc. these problems can be overcome.

The next problem is the computer-aided verification of students' answers to tests other than multiple choice. Even the simplest fill-in tasks, reduced to a single word can be counted as incorrect because of spelling errors or even blank spaces. For more sophisticated fill-in tasks, multiple matching, sentence transformation, and the like, which are so typical for language study, this system could not be used at all. Some specialized distance learning systems are capable of solving some of these problems, but not all. An even greater problem is the automatic pronunciation checking.

Another problem is the motivation of distance learning students. In case of English courses, which do not aim only at acquiring knowledge but also some skills, including communication skills, this problem seems to be the greatest. An extremely significant task of the teacher in preparing the material and implementing the course is how to retain a high level of interaction in the teaching (virtual) environment despite the limited direct contact. The key problem for the students, however, remains the lack of opportunities for direct oral peer communication as well as with the teacher. To alleviate this potential feeling of isolation of distance learning students and strengthen their sense of belonging to the group and the institution, sometimes they are given group problem-solving tasks, and the complete e-mail or chat correspondence is sent to the teacher. This is the area which will be given more attention in the future.

It should be noted that the statistic results clearly indicate that distance learning students on the whole score higher than the traditional ones. As noted above, there are many possible reasons for this. Of course, it cannot be straightforwardly claimed that distance learning is superior to face-to face learning, but we would like to note that this fact leads to the conclusion that, to say the least, distance learning students are not too much underprivileged by being absent from classroom classes. Audio-video streams and various methods of synchronous and asynchronous communication manage to compensate the shortcomings stemming from their absence from the class.

CONCLUSIONS

The application of distance learning system to foreign language teaching is a great challenge. The greatest problem is the lack of face-to-face communication with peers and the teacher. The paper shows that by using state-of-the-art tools for synchronous and asynchronous communication this problem can be overcome. Our experience is related to the English language study only, but the similar method is applicable to the foreign language teaching in general.

Our observations, after initial apprehensions, are very positive, but we are aware that we are facing a lot of additional work to improve the courses, modify them, make better multimedia presentations, and, in particular, enhance interactivity. We believe that by applying the combination of pedagogical insights and modern technologies it is possible to realize a successful foreign language distance learning course.

FIGURE 1 .

 1 FIGURE 1. Technological scenario of the e-learning system

TABLE 1 .

 1 Difference between traditional and distance learning method

	Teaching/learning	Traditional	Distance learning	Distance
	task			learning tools
	Home reading and	Books and typed	Pdf documents, word documents	e-mail
	writing	documents	submitted via email, feedback
			from the teacher
	Oral presentation	Oral presentations in	Audio/Video clip	Microphone, Web
		front of the colleagues		cam, Skype
	practice	Pair/group work,	Students open audio conference VoIP, Google
		students talk and listen		Talk, Skype
	Grammar and	Written and oral tasks,	Very detailed answer key,	e-mail, forum
	practice,	Immediate feedback	suggested/model answers,
	checking and	from the teacher, for	additional and remedial
	correction	simple tasks written	and explanations upon
		answer key	student's request
	Writing practice	Paper, correction	Hypertext comments, real email	e-mail, forum
			communication with teacher and
			peers
	Problem-solving	Books and web	Books and web resources	e-mail
	activities	resources available,	available, written report
	(individual)	notes and oral/written
		reports
	Problem-solving	Communication direct,	Communication by email or	Circulating
	(group)	face-to face, various	chat, voice over IP (recorded	document with
		resources available,	and submitted to the teacher),	comment, chat,
		paper note-taking for	various resources available,	forum
		brain-storming	note-taking as hypertext,	Writing, different
			comments added	students add their
				comments
	Feedback from the	Direct, oral,	Usually written, delayed	e-mail, chat,
	teacher	immediate, real-time		Skype
	Presentation of	Teacher's live oral	Recorded teacher's presentation,	Audio-video
	content,	presentation	slides and narration	stream
	instructions for	Written material	Written material	pdf
	activities	Teacher reacts directly	anticipates the possible
			questions and problems and
			provides instructions
			accordingly
	Listening	Live communication,	Recorded presentations and	CD, audio-video
	comprehension	audio coursebook pack	instructions by the teacher,	stream
			audio coursebook pack
	Listening	Audio CD, cassette,	Audio recording at the system,	Media player, e-
	comprehension test	paper test note taking	test at the system	learning system

TABLE 2 .

 2 Students enrolled at English courses and their examination results

	Type of students		English 1	English 2 English 3
		Students (total)	83	18	23
		Total enrolled	22	4	7
		Exam taken	20	4	6
	Traditional students	Passed Failed	19 1	4 0	5 1
		Pre-exam points (average)	46,00	48,12	43,20
		Mark (average)	7,70	7,75	7,00
		enrolled	61	14	16
		Exam taken	34	14	7
	learning	Passed	34	14	7
	students	Failed	0	0	0
		Pre-exam points (average)	49,41	50,20	45,50
		Mark (average)	8,22	8,70	8,60

Miroslav Trajanovic, Dragan Domazet, Biljana Misic-Ilic

According to Graves[START_REF] Graves | Teachers as course developers[END_REF] the process of course development includes needs assessment, determination of goals and objectives, content conceptualization, selection and development of materials and activities, organisation of content and activities, and finally, assessment, evaluation and modification of the course.

In case of these three English courses the books are contemporary novels/biographies related to IT: Bill Gates: The Road Ahead (intermediate Penguin Readers, Longman), Isaac Asimov: I, Robot, (upper intermediate Oxford University Press Bookworm readers), Bill Gates: Business @the Speed of Thought (advanced Penguin Readers, Longman

The suggestion that these classes should be only for e-learning students, and take place late at night, with the teacher working from home, has not been tested yet, since there was no interest from the students.