Luca Stefanutti
email: luca.stefanutti@uni-graz.at

Cord Hockemeyer Dietrich Albert
email: dietrich.albert@uni-graz.at

Structuring and Merging Distributed Content

Keywords: distributed learning objects, knowledge structures, structuring content

A flexible approach for structuring and merging distributed learning object is presented. At the basis of this approach there is a formal representation of a learning object, called attribute structure. Attribute structures are labeled directed graphs representing structured information on the learning objects. When two or more learning objects are merged, the corresponding attribute structures are unified, and the unified structure is attached to the resulting learning object.

INTRODUCTION

In order to decide which object comes next in presenting a collection of learning objects to a learner, one might establish some order. Given a set O of learning objects, a surmise relation on O is any partial order ' ' on the learning objects in O. The interpretation of ' ' is that, given any two learning objects o and o in O, o o holds if a learner who masters o also masters o. The concept of a surmise relation was introduced by [START_REF] Doignon | Spaces for the assessment of knowledge[END_REF] as one of the fundamental concepts of a theoretical framework called Knowledge Space Theory. According to this theory the knowledge state of a learner is the subset K of all learning objects in O that (s)he masters. A subset K ⊆ Q is said to be a knowledge state of the surmise relation ' ' if o ∈ K and o o implies o ∈ K for all learning objects o, o ∈ O. Then the collection K of all knowledge states of ' ' is called the knowledge space derived from ' '. Knowledge spaces are used for representing and assessing the knowledge state of a learner (see, e.g., [START_REF] Doignon | Spaces for the assessment of knowledge[END_REF] and [START_REF] Doignon | Knowledge Spaces[END_REF] in this connection).

The construction of a surmise relation may follow different approaches. After a brief presentation of an existing approach based on vectors of components of a learning object, we extend this approach to a more flexible representation called attribute structure [START_REF] Albert | Ordering and Combining Distributed Learning Objects through Skill Maps and Asset Structures[END_REF]. The mathematical properties of attribute structures make it possible to compare distributed learning objects in terms of how much informative and how much demanding they are.

THE COMPONENT APPROACH

According to the component approach [START_REF] Albert | Component-based knowledge spaces in problem solving and inductive reasoning[END_REF][START_REF] Schrepp | Component-based construction of surmise relations for chess problems[END_REF], every content object o in O is equipped with an ordered n-tuple A = a 1 , a 2 , . . . , a n of attributes where the length n of the attribute n-tuple A is fixed for all objects. Each attribute a i in A comes from a corresponding attribute set C i called the i-th component of the content object. In this sense, given a collection C = {C 1 , C 2 , . . . , C n } of disjoint attribute sets (or components), each object o ∈ O is equipped with an element of the Cartesian product

P = C 1 × C 2 × • • • × C n .
Usually each component C i is equipped with a partial order ' i ' so that C i , i is in fact a partially ordered set of attributes. The partial order ' i ' is interpreted in the following way: for a, b ∈ C i , if a i b then a learning object characterized by attribute a is less demanding than a learning object characterized by attribute b. To give a simple example, it might be postulated that 'computations involving integer numbers' (attribute a) are less demanding than 'computations involving rational numbers' (attribute b). A natural order on the elements in P, the so-called coordinatewise order [START_REF] Davey | Introduction to lattices and order[END_REF], is derived from the n partial orders ' i ' by

x 1 , x 2 , . . . ,
o o ⇐⇒ f (o) f (o )
for all o, o ∈ O. The mapping f can easily be established even when the learning objects are distributed (see, e.g., [START_REF] Stefanutti | Derivation of knowledge structures for distributed learning objects[END_REF]).

ATTRIBUTE STRUCTURES

An attribute structure is used to represent structured information on a learning object or an asset and in this sense it represents an extension of the attribute n-tupel discussed in Section 2. From a mathematical standpoint attribute structures correspond to the feature structures introduced by [START_REF] Carpenter | The logic of typed feature structures[END_REF] in computational linguistics. Let C be a set of components and A a collection of attributes, with A ∩ C = ∅. An attribute structure is a labeled directed graph A = Q, q, α, η where:

• Q is a set of nodes of the graph;

• q ∈ Q is the root node of the graph;

• α : Q → A is a partial function assigning attributes to some of the nodes;

• η : Q × C → Q is a partial
function specifying the edges of the graph.

As an example, let C = {picture, topic, subtopic, text, language} be a set of components, and

A = {PICTURE1, TEXT1, ENGLISH, MATH, MATRIX INVERSION}
be a collection of attributes. Suppose moreover that a simple learning object is described by the asset structure

A 1 = Q 1 , q1 , α 1 , γ 1
, where Q 1 is the set of nodes, q1 is the root node, and α 1 and γ 1 are defined as follows: node can be reached from this node following some path in the graph. The root node is the entry node in the asset structure of the learning object, and the edges departing from this node specify the main components of the learning object itself. Thus, in our example, the learning object represented by A 1 is defined by three different components: picture, text and topic. The values of these three components are the attributes given by α 1 (η 1 (0, picture)) = PICTURE1, α 1 (η 1 (0, text)) = DESCRIPTION, α 1 (η 1 (0, topic)) = MATH.

α 1 (0) is not defined, α 1 (1) = PICTURE1, α 1 (2) = TEXT1, α 1 (3) = MATH, α 1 (4) = ENGLISH,
Observe, for instance that node 5 can be reached from node 0 following the path picture, topic, subtopic . The fact that, in this example, each node is reachable from the root node through some path is not a coincidence. It is explicitly required that every node in an attribute structure be reachable from the root node.

4th International LeGE-WG Workshop: Towards a European Learning Grid Infrastructure Progressing with a European Learning Grid

COMPARING AND COMBINING ATTRIBUTE STRUCTURES

Attribute structures can be compared one another. Informally, an attribute structure A subsumes another attribute structure A (denoted by A A ) if A contains at least the same information as A. In this sense an attribute structure can be thought as a class of learning objects (the class of all learning objects represented by that structure), and ' ' can be regarded as a partial order on such classes. Formally, an attribute structure A = Q, q, α, η subsumes another attribute structure A = Q , q , α , η if there exists a mapping h : Q → Q fulfilling the three conditions (1) h(q) = q ;

(2) for all q ∈ Q and all c ∈ C, if η(q, c) is defined then h(η(q, c)) = η (h(q), c);

(3) for all q ∈ Q, if α(q) is defined then α(q) = α (h(q)).

In Section 2 the attribute sets were assumed to be partially ordered according to pedagogical criteria and/or cognitive demands. Similarly we assume now that a partial order ' ' is defined on the set A of attributes so that, given two attributes a, b ∈ A, if a b then a learning object defined by attribute a is less demanding than a learning object defined by attribute b. Then the subsumption relation ' ' is made consistent with ' ' if condition (3) is replaced by ( 4) for all q ∈ Q, if α(q) is defined then α(q) α (h(q)).

According to this new definition, if A

B then A is either less informative than B or less demanding than B or both.

As an example consider the three attribute structures depicted in Figure 2. Assuming that MATRIX PRODUCT MATRIX INVERSION, both mappings g and h fulfill conditions (1), ( 2) and (4), thus both attribute structures labeled by LO2 and LO3 subsume the attribute structure labeled by LO1. However there is neither mapping from LO2 to LO3 fulfilling the subsumption conditions, nor the opposite, thus these last two structures are incomparable to each other. The When two different learning objects are merged together, or when different assets are assembled into a single learning object, the corresponding attribute structures are unified, and the resulting attribute structure is assigned to the resulting learning object. On the other hand, the generalization operation is used to find the common structure of two or more learning objects or, stated another way, to classify learning objects. An example of the generalization operation applied to two attribute structures is shown in Figure 3. Here, the resulting structure shows that two learning objects have in common topic and subtopic. Generalized attribute structures can also be used e.g. for searching a distributed environment for all learning objects whose structure is consistent with a certain 'template' (for instance to find out all learning objects that are 'problems' involving, as cognitive operation, 'recognition' rather than 'recall').

and α 1 FIGURE 1 :

 11 FIGURE 1:The attribute structure A1 describes a simple learning object on 'matrix algebra'

FIGURE 2 :FIGURE 3 :

 23 FIGURE 2: Both LO2 and LO3 subsume LO1. However LO2 and LO3 are incomparable. derivation of a surmise relation for the learning objects parallels that established in section 2. If s : o → s(o) is a mapping assigning an attribute structure to each learning object, then a surmise relation ' ' on the learning objects is derived by o o ⇐⇒ s(o) s(o )


Fred Neumann
email: fred.neumann@fim.uni-erlangen.de

Rüdiger Geys
email: ruediger.geys@fim.uni-erlangen.de

SCORM and the Learning Grid

Keywords: eLearning Standards, ADL SCORM, Learning Grid MOTIVATION

The Sharable Content Object Reference Model (SCORM) is a profile of several elearning specification to ensure the reusability and interoperability of elearning content in web based Learning Management Systems (LMSs). Learning grids -learning environments built on the technology of grid services -are a promising new approach to enhance quality of elearning by overcoming the page oriented structure of the web. This paper investigates how SCORM can be used in conjunction with learning grids. After an introduction to the relevant aspects of SCORM two major scenarios are discussed: the use of grid enhanced content in a SCORM compliant LMS and the use of SCORM content in the context of a learning grid.

•

IEEE LOM for metadata describing learning objects (LOs), enabling the search for content • IMS Content Packaging to exchange LOs between authoring tools and learning environments • AICC for the run-time communication between the content and the learning environment

•
SCORM as a reference model to integrate the specifications above

For a certain period it seemed that especially the content packaging and run time environment are more adopted in commercial elearning applications for the use of commodity content modules available on the market. But meanwhile these specifications became also relevant in the academic scene, often after years of experiments with internally developed applications and contents using proprietary formats. As a consequence, tools with scientific origin are modified to support elearning standards. For example ILIAS, an open source LMS popular at German universities, is now being extended to handle SCORM compliant content. This is a remarkable step, because light-weight, open source solutions are especially important for smaller, non profit organisation who try to apply elearning for new target groups and cannot afford expensive commercial servers that support the current elearning standards.

Grid computing is a promising new technological paradigm but the concepts for a learning grid are at the very beginning. To get a further understanding of their potential they may be developed in an idealistic way and evaluated in dedicated test beds. But in the mean time the development of conventional web based elearning solutions and standards will continue and the investments will increase. Therefore it is essential for the success and acceptance of a learning grid development to provide a smooth migration path from current web based to grid based solutions. This can be accomplished by taking into account the current exchange and interoperability standards in the elearning domain to enable:

• the use of grid services in a wide range of web based LMSs, • the use of existing standard compliant content in a learning grid.

In this paper we will look at SCORM [START_REF]Sharable Content Object Reference Model (SCORM ® )[END_REF] for that purpose, as it provides an integrated view on a set of standards and specifications that focus on single aspects.

SCORM and the Learning GRID Towards a European Learning Grid Infrastructure: Progressing with a European Grid 1

SCORM OVERVIEW

In 1997 the US Department of Defense (DoD) launched the Advanced Distributed Learning (ADL) Initiative as a collaboration between government, industry and academia to specify a learning environment that permits the interoperability of learning tools and course content. ADLs major outcome is the Sharable Content Object Reference Model (SCORM), a "collection of specifications adapted from multiple sources to provide a comprehensive suite of e-learning capabilities that enable interoperability, accessibility and reusability of Webbased learning content." (www.adlnet.org).

SCORM is an application profile for the use of existing standards and not a specification or standard in itself. The underlying specifications are slightly amended to be suitable for the DoD's education and training needs. However, the interoperability promoted by ADL became attractive to the commercial e-learning industry in general. The following table may give a rough impression of the current situation. It is remarkable that more software vendors are certified or declare themselves as compliant to SCORM then to its major underlying specifications (counted The reference model is divided into three parts ("Books") to which we will have a further look in the next sections: the Content Aggregation Model (CAM), the Run-Time Environment (RTE) and the Sequencing and Navigation (SN) Book. SCORM defines both, requirements for an LMS and for the content. Especially in the RTE and the new SN model the minimum requirements are very much higher for an LMS to achieve than for the content.

CAM: Content Aggregation Model

The CAM defines how instructional components are described with metadata and how they are organized and packaged. A content package includes all needed physical files and an xml based file named imsmanifest.xml describing the content and its structure. The manifest is composed of the following sections:

• Meta-data describing the content package as a whole

RTE: Run-Time Environment

If we look for the applicability of SCORM in a learning grid then the most interesting part is the run-time environment which specifies how an SCO is launched and how it communicates with the LMS. This section introduces the main RTE characteristics that will be discussed for a combination with grid services later. Figure 1 shows the RTE architecture:

FIGURE 1: SCORM Run-Time Environment
The LMS uses the URL of an SCO defined in the manifest to launch the SCO by HTTP in the client's web browser, either in a child window or a child frame of the LMS window. Each SCO must be able to be launched this way.

After that the SCO has to search in the DOM hierarchy of its window parents for an API object provided by a runtime service of the LMS that resides in the browser. SCORM does not specify how the run-time service is implemented and how it communicates with the LMS. All it defines are the API functions, how the API is found locally and that it must be called by JavaScript. Every communication is initiated by the SCO. The SCO is responsible for starting the communication with an Initialize()and to end it with a Terminate() before it is removed from the browser. Between these calls it is able to read and write run-time data with GetValue() and SetValue(). Written data may be cached in the client by the run-time service. The SCO cannot check, whether data is cached but it may use Commit() to force the cached data being written back to the LMS. The remaining functions defined by the API are for error handling and diagnostic purposes.

The main interaction between SCO and LMS is done by exchange of run-time data according to a data model based on the IEEE draft standard with added requirements for the run-time behaviour. All data model elements are optional to an SCO but the LMS must provide them. Their initial values may be defined in the content package, by a learner registration process or by learner profiling requirements.

The data model elements have different purposes. Some are used to track status, scores and objectives of an SCO, some provide learner specific data and others have impact on the sequencing behaviour of SCOs. The runtime data is initialised at the beginning of a learning attempt which may span one or more learning sessions and can be suspended while keeping the actual values stored. Additionally a content package can define that the SCOs run-time data must be kept persistent over several attempts.

SN: Sequencing and Navigation

SCORM 2004 introduces the Sequencing and Navigation (SN) Book by applying the IMS Simple Sequencing specification to define how content objects may be sequenced through learner-initiated or system-initiated navigation events. For this purpose an organisation within a content package is derived into an activity tree for a learner. The leaf activities of that tree have content objects associated and the sequence of launched content objects builds an actual learning experience. The progression through learning activities may be sequential, nonsequential, user-directed or adaptive. It follows sequencing rules defined in the activity tree and takes the current RTE data into account. IMS Simple Sequencing 1.0 is a rather complex specification and the amount of changes done by ADL in its pseudo code indicates that there is still some flow in the specification process. Therefore it will take reasonable time until the whole SCORM 2004 will be implemented by a wide range of systems and in the mean time SCORM 1.2 will remain a state of the art that supports only a hierarchical content menu and a simple forward and backward navigation through the SCOs.

Learning Management System

SCO

SCORM AND GRID

Grid computing is a new technology for the flexible, secure and coordinated sharing of distributed resources and data. The Open Grid Services Architecture (OGSA) is built on web service technology and supports "transient services as named, managed entities with dynamic, managed lifetime" [START_REF] Foster | The Physiology of the Grid: Open Grid Services Architecture for Distributed Systems Integration[END_REF]. For elearning this allows the creation of learning grids -learning environments built on OGSA-compliant software and services. Learning grids promise to introduce a new quality of elearning by:

• enabling collaborative learning with peer-to-peer communication, • making computing-intensive visualisations or simulations available for the learners, • giving access to real-world data and resources like virtual laboratories.

Do SCORM and a learning have much in common? Looking at the core aims of SCORM (accessibility, adaptability, interoperability and reusability), they seem partially similar with the aims of grid technology. However, SCORM is focussed on the exchange and delivery of instructional content in web based LMSs, while grid technology is concerned with sharing of any resources in a distributed environments.

First we have to clarify what a learning grid will look like compared to a web based LMS. Will it be an infrastructure hidden behind a "portal" with conventional web access or will the learner's device be an active resource on the grid? Both architectures have their justification depending on the target group of learners. In the first case the grid functionality can be designed in any way, as long as the interaction with the user is done through HTML pages. But if a learning grid intends to overcome the page oriented design of the web then it must bring dynamic functionality to the learner's client. For best applicability this should be done in a transparent and system independent way, e.g. without the need for an extra installation, and requires an execution technology that is widely available in common browsers which currently means to use Java applets.

In [START_REF] Pankratius | Towards E-Learning Grids: Using Grid Computing in Electronic Learning[END_REF] Pankratius and Vossen propose an elearning grid architecture that consists of two major parts: an LMS that is internally based on web services and a core grid middleware. They also introduce the concept of a grid-enabled learning object (GLOB) that includes conventional learning resources as well as an application layer for the use of grid services. Figure 2 is a simplified illustration of their concept without showing the detailed internal services. At the initial login to the LMS the fabric layer of the grid is delivered to the learners device as a Java applet. The login service of the LMS is able to authentify the user and his device against the grid and may also be trusted to create or delete grid users. The LMS will request a TGT (ticket-granting-ticket) from the grid middleware and deliver it to the client. If a GLOB is delivered to the learner's device it is able to use the fabric layer and the TGT initially provided by the LMS to further request session tickets and directly access the grid services.

FIGURE 2: A proposed Learning Grid Architecture [START_REF] Pankratius | Towards E-Learning Grids: Using Grid Computing in Electronic Learning[END_REF] The proposed architecture describes a loose coupling between LMS and grid middleware with little requirements for the LMS: the call of a few operations from a grid login service and the delivery of a grid enabling applet to the client at login time. Therefore it seems possible to enhance nearly every web based LMS this way, regardless of whether the LMS is already internally built on web services or not. However, sometimes it will not be possible to introduce grid support by extending an LMS, for example in the following scenarios:

• An elearning content provider wants to offer grid services in conjunction with his content. To not restrict possible customers he must support as many platforms as possible.

•

A lecture chair wants to offer grid based applications for a virtual course but has to use a campus-wide LMS that can't be modified.

There are many possible scenarios in which grid services can be integrated into a learning content: database searches, exercises, simulations, virtual laboratories or visualisations. For that we could ask whether it would be possible to realize GLOBs as grid enabled SCOs and use them in an LMS without the need to modify it.

Grid enabled SCORM content

In the following we assume that the whole functionality needed to access the grid is implemented by a Java applet ("grid applet") and included in a SCORM compliant content package. Depending on the learning purpose the applet may implement the whole fabric layer of the grid to include the learner's device as a resource on the grid or it may be just a client to access the grid via an ordinary web service. The most important aspect to clear is how to provide a single-sign-on from the LMS -that means how to authentify the LMS user for the desired service and how to transmit user related information between LMS and the grid.

For this purpose we have to take a look back to what the SCORM run-time-environment specifies. The grid applet must have access to the JavaScript API of SCORM for the exchange of data. The following data elements provided by the RTE are of special interest:

• launch_data is taken from the content package and is read-only • learner_id is provided by the LMS and read-only • learner_name is provided by the LMS and read-only

•
interactions are used to store the results from interactive exercises • suspend_data can be anything up to 4000 characters to be stored between sessions

Figure 3 shows a possible implementation. First the LMS launches the SCO containing the grid applet and the normal initialisation process is done. Now the applet has to authentify with the grid service. For this purpose it requests the launch_data from the LMS and extracts an included static key which is created by the vendor of the learning grid. The key is stored in the imsmanifest.xml of an SCO and may be set individually for an LMS or a course. Additionally the applet may determine its own origin with a getCodeBase() call. Due to JavaScript security restrictions in modern browsers the applet must come from the same domain as the API and so the code base helps to ensure that the applet is delivered from an LMS which is allowed to use the grid functionality [START_REF]Cross-Domain Scripting Issue[END_REF]. The learner is identified by ID and the grid login is done with a combination of static key, code base and learner ID. The grid may log this data e.g. for billing purposes. A session ticket provided by the grid can be stored in the suspend_data element of the SCO's run-time-data.

FIGURE 3: Using Grid enhanced SCOs

How secure is the proposed implementation? This questions is about preventing the grid from being misused (e.g. for stealing computing power) and preventing user accounts from being misused (e.g. for faking their activity). The communication between LMS and run-time-service is not specified and may have lower security than the grid provides, e.g. it may not be encrypted. Security is then determined by the weakest part -the LMS. Theoretically it is also possible to simulate an SCO session, extract the authentication from the LMS and to store and recompile the grid applet. Then a "cracked" standalone applet can be created for the use of a grid service with the ID of another user. However, this will mean a reasonable effort and will leave traces if both LMS and grid service log their accesses, so we can assume a medium security level. The problem comes from the fact that the authentication is based on static information (key and learner_id) delivered from the LMS to the client. Solutions to overcome this weakness may be applicable in special scenarios:

•
The LMS is able to create session-tickets and deliver them to the SCO, e.g. in an extended run-time data model element. However, this would require the inclusion of a grid client on the LMS server and a modification of the LMS.

•

In an Intranet the learners device may already be a resource on the grid. Then the grid applet in the SCO can use the local host and user for an authentication.

•

The learner has to manually authentify for the grid at least once and receives a ticket that is stored in the suspend_data. Subsequent authentication may be necessary after time-out of the ticket. A grid enhanced SCO may be designed to support all scenarios with priority for the most advanced authentication method but a cascading fallback mechanism to the others.

Aside from security issues, a content oriented solution will not be appropriate for all purposes of grid enhanced elearning. A learner will work on content, but also use content-independent communication and collaboration facilities, e.g. for getting tutorial support or working in groups. A grid solutions for general supporting tools shouldn't be embedded in an SCO that is only accessible on a table of contents. SCORM can't be a help for this purpose and therefore the LMS has to be extended. An introduction of grid support may follow the architecture described in [START_REF] Pankratius | Towards E-Learning Grids: Using Grid Computing in Electronic Learning[END_REF] but with the grid applets being directly embedded in the user interface of the LMS.

SCORM Content in Learning Grids

The obvious requirement for a SCORM compliant learning grid solution is to handle existing SCORM compliant content, at least to import it as content packages and to launch and track the SCOs for the learner. The question is how this content can be seamlessly integrated in a highly collaborative, grid-enabled environment. At present the reusability of SCOs prohibits a tight coupling of content with additional functionalities provided by an LMS like forums, conferences, or advanced tele-presence tools available in a grid infrastructure. The IMS Simple Sequencing provides minimal hooks for the invocation of so called "Auxiliary Resources", however SCORM does not yet define their further behaviour and ADL recommends content developers and LMS vendors to use them with extreme care to ensure future interoperability [1: SM-5-11]. The other direction is of equal interest: how may content objects easily be used by the learners as references in communication messages? SCORM requires that each SCO must be launched by its URL, but it may not be possible to simply copy it from the browser location into a message because it is hidden or includes user-specific parameters.

The conceptual relationship between content and collaboration is intensively addressed by the IMS Learning Design [START_REF]IMS Learning Design Version 1.0 Final Specification[END_REF] which specifies an XML based language to describe complete learning scenarios including group work or collaborative learning. It formalizes the definition of actors and their roles in a learning scenario, its activities and the use of learning objects or services in an activity. IMS Learning Design is not included in SCORM and it is open whether it will be in the future. But a learning design may be integrated in a content package and SCOs may be used in a Learning Design. A learning grid designed to support both may enable pedagogically well defined collaborative learning with the use of widely available content. Learning Design is a conceptual model and does not define the technical implementation and the process of instantiating the activities. IMS provides a best practice guide with suggestions for developing a runtime environment but these are not normative. This gives freedom for the design of a service oriented learning grid architecture, especially in the decision which services should run locally on the learner's device or will be called remotely and whether the collaborative actions will behave in a peerto-peer or server mediated manner.

On the other hand, if it is intended to include SCORM content in a learning grid, the architecture must take care of the requirements for a SCORM run-time environment. SCORM proposes that an LMS has a service based architecture, but it doesn't define anything of it, even not whether the services are real or just internal functionalities of a monolithic system. If we look at the run-time architecture in figure 1, a first step towards an integration of SCORM and grid technology would be to specify the proprietary communication between LMS and the run-time service as a web or grid service. The API functions defined by SCORM must be translated to service operations. An SCO should have the choice whether to use the JavaScript API or whether to directly communicate with the service, for example, if it is launched from a different content server. In this context the following statement from the SCORM specification is of special interest:

"There are ongoing research and development efforts investigating alternative methods (e.g., as a Web Service) for LMS vendors to provide SCOs access to the API Instance. (...) Future versions of SCORM may introduce other communication protocols that support the fundamental requirements defined by the IEEE standard." [1: RTE-3-26]

The current SCORM API service may be one of a set of services for a content to LMS communication and we could imagine a suite of conformance levels with the SCORM API as the lowest common denominator and other services as extensions. Once the communication between LMS server and run-time service is specified, generic run-time services can be implemented as a bridge between service oriented LMSs and API oriented content. The JavaScript API may also wrap the extended services so that content developers can use them in a familiar way. This may be done by the introduction of new API functions or by the extensions to the run-time data model, e.g. with information on user groups and shared data for collaborative work.

To give a practical example, one extension could be the support for collaborative annotations. The editing and storage of annotations would be implemented by the LMS but their appearance must be rendered by content specific functions. The content must be adaptive to enable or disable this feature depending on what conformance the LMS provides and it must be able to invoke the editing function. We could also imagine that the annotations may be extended with presence indicators showing whether the originator is currently online (or logged in to the LMS) and allowing to start a synchronous communication. Again, this information is provided by the LMS, but rendered in the content, if available.

SCORM and the Learning GRID Towards a European Learning Grid Infrastructure: Progressing with a European Grid

CONCLUSION AND DISCUSSIONS

Using grid services in a SCORM compliant LMS may be possible without modification as long as the grid functionality can be wrapped by learning object in a didactically reasonable way and as long as a medium security is acceptable. Otherwise the LMS has to be extended with grid functionality. Using SCORM in a learning grid may not just mean to "simple implement it" but will lead to extensions of the run-time-environment defined by SCORM if a real integration of content and communication facilities is intended.

We see that many aspects need a further investigation and many issues are still open, both in the SCORM and the grid world. However, the main open question is: how relevant will SCORM be in the future? Will it be the dominating model for content sharing at the time when a learning grid infrastructure is ready to use? Critic voices argue that SCORM is pedagogically poor while at the same time being too complex and too difficult to implement. How high is the benefit for a learning grid to have access to existing SCORM compliant content and how large will this pool be? Should a learning grid have its own reference model with a different set of supported specifications, e.g. with IMS Learning Design instead of Simple Sequencing? It would be a considerable effort to repeat the integration and profiling work already done by ADL.

A strategy may be not to rely on SCORM for the core architecture of a learning grid but to check for each concept how it harmonizes with SCORM content. In parallel, providing pluggable SCORM compliant, grid-enhanced content packages and creating small and smart learning grid applications with guidelines on how to integrate them in any LMS will raise the attention of the elearning world. This may create the "critical mass" for a broad acceptance of a learning grid architecture that will lead to its inclusion in the main standardisation process for elearning.


Toshio Okamoto
email: okamoto@ai.is.uec.ac.jpkayama@isc.senshu-u.ac.jp

Mizue Kayama

The Model of Collaborative Learning GRID to Activate Interactivity for Knowledge Building

Keywords: Collaborative Learning Ecology, Knowledge Building, Collaborative Learning GRID, Collaborative Memory, Social Computing

The purpose of this study is to support the learning activity in the Internet learning space. In this paper, we examine the GRID technology as the knowledge management for supporting "collaborative learning" / "collaboration in learning" (CL). RAPSODY-EX (REX) is a distributed learning support environment organized as a learning infrastructure. REX can effectively carry out to support collaborative activities in asynchronous/synchronous learning mode. The mixed distributed learning environment is utilized as a new learning ecology, where individual / collaborative learning environment with audio/visual channel (like as a videoconference) are performed on the multimedia communication network. In this mixed distributed learning environment, people can arrange, modify and integrate educational information for the purpose of investigating, decision making, planning, problem solving, building knowledge and self development. Diverse information in the educational context is referred and reused as knowledge which oneself and others can practically utilize. We aim at constructing the growing digital portfolio database for learning knowledge management in Internet environment. In addition, we explore the GRID technology of activating human-interactivity for knowledge mining/discovering.

Introduction

The society is changing along with the explosive growth of Internet. This growth is so closely, tightly, and widely that everyone even feels the power of the information evolution. Education certainly is riding on the waves. Internet is becoming the catchphrase in the world of school education, which makes the distance education possible to anybody at anytime and from anywhere. As such, a new learning style 'e-Learning' emerged under the umbrella new concept of "Learning Ecology and Pedagogy", where Internet raises the level of communications and collaborations among people via technology.

Nowadays, the word/system of "e-Learning" is rapidly spreading out according to popularization of Internet. As for advantages of Internet, people can communicate each other for anyone, anytime and anywhere. Moreover people can share, rebuild, stock and reuse the various kind of information. Here, it seems that the concept of "e-Learning" gets the citizenship in the society instead of CAI (Computer Assisted Instruction). Along with this stream/trend, we recognize the necessity of construction to new learning society such as learning individuals, learning organization and learning community. Above mentioned, we can say that Internet is a kind of "Treasure Island" of educational resources from the world wide stance, though it includes much harmful information.

In asynchronous learning, the transformer of knowledge and the transformee of knowledge communicate with a time lag. In such a situation, more positive support is required to realize an effective and efficient learning activity. We need to build a learning infrastructure with learning spaces with various functions.

Recently, the thought of GRID technology in e-Learning are introduced, which means conceptual and technical aspects of electronic learning. Furthermore, this concept is being extended toward knowledge GRID, GRID Intelligence, and distributed artificial intelligence for effective knowledge communication/ building/management. We investigate the mechanism of transmission and management of knowledge for the development of the knowledge community in the learning space, within the educational context. In this paper, we discuss about the technology the knowledge management and the knowledge representation of the learning information for the CL support in consideration of GRID technology under the context of e-Learning.

Collaboration in Learning

Some Definitions

In terms of [START_REF] Roschelle | The construction of shared knowledge in collaborative problem solving[END_REF], they defined "collaboration" to be "a coordinated, synchronous activity that is the result of a continued attempt to construct and maintain a shared conception of a problem". [START_REF] Dillenbourg | Collaborative learning, -Cognitive and Computational Approaches[END_REF] takes up the following 4 points as the features of CL, which are a situation, interactions, process(learning mechanism) and effects. Cowie & Rudduck(1988) defined that collaboration in leaning is the opportunity to learn through the expression and exploration of diverse ideas and experiences in cooperative company. It is not about competing with fellow members of the group and winning, but using the diverse resources available in the group to deepen understanding, sharpen judgment and extend knowledge".

In consideration of those views, [START_REF] Okamoto | Towards Intelligent Media-Oriented Distance Learning and Education Environments[END_REF] pointed out that CL should emphasize as follows:

1) Process/situated context 2) Individual learning achievement such as knowledge acquisition, skill formation and concept formation, learning set 3) Versatile cognition for both of holistic and serialistic thinking schema 4) Understandings of objective relationship among self/you/he or she 5) Effects of observation learning (reflection/self-monitoring) CL doesn't depend on place and time. Especially, In Internet environment, the type of asynchronous ecology of CL is more useful rather than the synchronous one (such as a Videoconference). Moreover, in the process of CL, individual learning may be sometime embedded based on a certain curriculum in schools and vise versa. Collaboration in learning and/or collaborative learning often happens during ordinal educational situation. In this study, CL is thought as a fundamental and essential learning activity.

Technological /Functional Conditions to Encourage CL

In general, we can divide the activities on collaborative learning into two classes. The social activities and the cognitive activities are estimated. Table 1 shows these classes. Based on these activities, the resources required in CL environment are taken up as follows:

・ Technologically mediated dialogue channel ・ Shared workplace for a group ・ Personal workplace ・ Learning materials/ learning tools ・ Analyzing tools of Data/Information ・ Repository/Memory for data /information revealed in CL ・ Reference channel for the collaborative repository ・ Modeling tools for monitoring the process of CL To encourage the CL, we implemented the RAPSODY-EX.(REX) REX is a learning framework with above resources. This system can store all leaning activities log in the digital portfolio holder and participants can review those data in order to diagnose/evaluate their achievements. Also, the participants can refer the flow/stock of knowledge for an arbitrary situation of collaborative learning. The repository-module in the REX can work to analyze/manage knowledge that each of participants revealed /found in the process of collaborative learning. .

The Schema and Functions of Learning GRID

In this study, the information/knowledge processing is considered as a process of the knowledge management in the learning context. Knowledge management is defined like follows [START_REF] Davenport | Working Knowledge[END_REF]). The knowledge management is "the systematic process of finding, selecting, organizing, distilling and presenting information in a way that improves an employee' s comprehension in a specific area of interest."

Here, we propose the functions of Learning GRID as the knowledge management between learning environments (like as a set of the REX). It guarantees the mutual interactivity among learners and activates knowledge building. In some sense, GRID means the role of exchanging knowledge or artifacts in a set of marketplaces that can stock the various kind of information. At the same time, learners need the value of sense with sharing/re-using manners. We have developed GRID technology as knowledge mining in collaborative learning process. REX plays as a marketplace in the GRID world.

Figure 1 shows the meaning of Learning GRID which plays roles of the set of the marketplaces for knowledge transmission, transformation and exchange. Moreover, the function of Learning GRID is in charge of bring about building and discover of knowledge through assimilation/ accommodation , differentiating/ integrating occurred in collaborative learning. We aim to realize this mechanism as social computing by active collaborative memory (CM).

Learning GRID we intend plays roles of encouraging collaborative learning. Figure 2 shows the framework of learning GRID technology. From participants' performance information and learning resource information. Learning GRID has the functions of modeling the situation of collaborative learning and perturbing a learner's behavior for knowledge exchanging, transforming and acquiring by distributed collaborative agents in order to facilitate knowledge building.

Learning GRID provides adhesive fundamentals for social computing which has also the function of collaborative filtering with recommendation function. So, we can regard this as a conductor in a marketplace and a kind of negotiation-circulation engine for knowledge management. Every agent is embedded in every Learning GRID in Internet space, each agent tries to communicate, exchange need-information among Learning GRID. In some cases, plural agents behave collaboratively or competitively for taking well knowledge negotiation along with participants' requirement. Therefore, the agent's roles become to be quite important within/among Learning GRID. We set up two kinds of agent who are 1) Learning GRID agent (LGgent), 2) Knowledge Messenger agent(KMgent) for investigation, collaboration and whole-watching in the GRID world.

Knowledge Management and Collaborative

Memory in the GRID World

The Management of Learning Information

The abstract mechanism of the management of learning information developed in this study is shown in figure 3. The processing mechanism consists of two components. The first one is a module that offers the learning environment. The second one is the CM that controls various information and data produced from the learning environment.

In the learning environment, 2 types of functions are offered. One is the monitoring function for the learning progress. The other is the tool/application for the CL. The former function controls the learning history/record of individual learners and the progress of the collaborative group learning. The latter tool/application becomes a space/workplace for collaborative synchronous /asynchronous The CM offers 2 types of functions. One is the knowledge processing function, and the other is the knowledge storage function. In the former, input learning information is shaped to the defined form. In the latter, for the formatted information, some attributes related to content are added. The complex information processing takes place in the CM.

The Collaborative Memory

The CM consists of two parts. One is a information and knowledge processing/management mechanism, which integrates and organizes the stored learning information and knowledge based on the purpose of usage and/or reference them. The other is a structured memory space, where diverse information and knowledge on learning are stored. In the CM, information generation / arrangement / housing / reference / visualization are the management processes of expressive knowledge in the learning space. REX is a learning environment, which possesses a knowledge management mechanism. This function works soundly with CM. In this environment, the following functions are realized in the learning space.

1) the review of the learning process, 2) the summarization of the problem solving process 3) the reference of other learners' problem solving method Learning information is expressed by a unified format. Then, that information is accumulated in the CM. This information becomes the reference object of the learner. The generation and the management of the information on the learning performance and the portfolio of the learner and group are main objects of the knowledge management. In this study, learning information is obtained from the application tools for the CL. It is necessary to control the learning record, the reference log of the others' learning information and the log of problem solving and learning progress. To realize this control not only techniques based on symbolic knowledge processing approach, but also techniques based on sub-symbolic knowledge processing approach are used.

The CM consists of two layers. One is the information storage layer and the other one is the management layer of the stored information. At the information storage layer, 4 kinds of information are mainly processes.

1) Learning information, 2) Information on the learner, 3) Information on the setting of the learning environment 4) Information on the learning result.

At the information management layer, the reference/ arrangement/integration of learning information are processed. The individual learner profile information is composed of information following the IEEE Profile information guidelines (IEEE 2000). The group information is expressed by the expansion of the individual learner profile information. The conversion from the learning log data to learning information is necessary to develop this profile database. The information, which should apply in learning information, is as follows:

・ Information and/or data on its learning context and/or learning situation ・ Information about the sender and the sendee of the information ・ Significance and/or outline in the educational context ・ Information on the relation structure of the learning information ・ Reference pointer to individual learner and group who proposed or produced the information ・ Relation with other material

Pedagogical Agents in the GRID

By adding above-mentioned information, the learning information is arranged into an unique form. If a learner requires some information related to his/her current learning, the learning market, like as a REX, shows the estimated/desired information to the learner. Figure 4 shows a communication scheme in the GRID. Two types of agent are in the GRID world. The learning GRID agent (LGgent) and the knowledge messenger agent (KMgent). These agents work for investigation, collaboration and whole-watching in the GRID world.

LGgent are organized by three types of agents. They are existed in the learning market. In the case of REX market, these agents perform each mission with user (user-RAPgent), each CL tool (application-RAPgent) and the CM in REX server (CM-RAPgent). Communication protocol between RAPgents is defined based on the FIPA ACL communicative act. The missions of each RAPgent are to transform information adaptively to create group portfolio, to maintain learning contexts in the group member and to let refer information in CM. To realize the knowledge management in REX, application-RAPgents develop some learning contexts by using learning information in the CM. Then they refer the suitable learning information for the collaborative tool/application.

The Learning GRID Technology in REX

The knowledge management in educational context is defined as follows: "the systematic process of finding, selecting, organizing, distilling and presenting information in a way that improves a learner' s comprehension and/or ability to fulfill his/her current learning objectives." The information of learning entity contains the expressed knowledge by learners. This overt knowledge can be represented by natural language as verbal information. So, we can regard this knowledge as one that would be elicited from the learner' s tacit • Who are the subjects of our knowledge management work? Learners and the persons who support the learners are our subjects. Learners' task is to acquire the ability/skill for the problem solving. On the other hand, supporters' tasks are to support for acquisition of ability/skill of the learner, and to support of the problem solving by the learner. Supporter means a facilitator/tutor/coach/ organizer etc.

• What are the knowledge resources in the learning group? For learners, the knowledge for the effective and efficient problem solving is their knowledge resource. On the other hand, for the supporters, the knowledge on problem setting and activity assessment is their knowledge source.

• What is the gain for the learning group?

The gains for learners are to acquire the ability in which to effectively and efficiently solve the problem, and to acquire the metacognition ability. For supporters, the acquisition of the ability of supporting the ability acquisition of the learner is their gain.

• How are the knowledge resources controlled to guarantee the maximum gain for the learning group? By the information processing to relate common knowledge of the CM and learning context, we try to manage the knowledge in the CL. To create the collaborative portfolio between individual and group learning, extension of acquired knowledge of learners, knowledge extraction from learning history under the problem solving and making outline of problem solving process.

REX as a Learning Market

Learning GRID with REX

A learner group that guaranties the smooth transmission of knowledge can form a community (the knowledge community) by sharing and reusing common knowledge. The image of collaborative/ group learning with REX is shown in figure 5 Learning activities that occur within this group are as follows: ・ Achievement of learning objectives as a group; ・ Achievement of the learning objectives of each learner; ・ Achievement of the learning objectives of the learner group, which consists of multiple learners. REX supports the transmission of knowledge in the learner group and the promotion of the learning activity. It is indispensable that REX has the following functions:

1) Function which controls learning information for the individual learner and the group.

2) Function, which manages learning information of the learner for mediation. The learner and group information are produced from the learning space. This information will be stored in the collaborative memory (CM). This information is defined as learning information. We also define the method of information management of such information and the structure of the CM.

Examples of the Knowledge Management in REX

Figure 6 shows the window images of the collaborative applications on REX. Two types of applications are loaded. One is a chat tool for the text communication among the group member. Another application is a collaborative simulator for the . Each application has each application-RAPgent. By the functions of these RAPgents, learning history data at this session is stored in the CM and formulates a set of the group portfolio.

The examples of knowledge management at this session are shown in the figure 6. A log data of this dialog is visualized by three kinds of methods. These results are produced by three application RAPgents. The first method is visualization of the dialog structure (figure 6 (a)). The dialog layers are reasoned based on the dialog proceeding model [START_REF] Inaba | Negotiation Process Model for intelligent discussion coordinating system on CSCL environment[END_REF]) and the utterance intention information that were given to the dialog log. The result is shown as tree structure. The second method is visualization of transition of the contents of a dialog (figure 6 (b)). An appearance of the important term that is in a dialog is searched for using the term dictionary about the current discussion/learning domain [START_REF] Chiku | A dialog visualization tool : Gijiroku[END_REF]. This result and the timing connection of each utterance are considered to detect a transition of the contents of a dialog. The result is shown as graph structure. The third method is visualization of transition of problem solution process (figure 6 (c)). One utterance can be unified as meaningless unit for the problem solving process from the first and the second processing result and an educational mentor' s expertise/educational intentions. The result re-constituted as problem solution process is shown with the structure that imitated the dendrogram.

[Figure 2 :

 2 Figure 1 : The Concept of Collaborative Learning and Learning GRID

Figure 3 :Figure 4 :

 34 Figure 3 : The Mechanism Scheme of the Knowledge Marketplace (i.e. REX)

Figure 5 :Figure 6 :

 56 Figure 5 : Collaborative Learning on the REX with Two Types of Collaborative Applications < a text chat tool and a collaborative simulator for the nutrition treatment >

Table 1 :

 1 Activities on Collaborative Learning

Evaluation and Conclusions

Based on these concepts, we examined the feasibility, implementability and effectivity of our GRID world. The learning GRID was constructed by some collaborative applications (Collaborative simulator for the nutrition treatment / the company management/economical control ), some communication tools (text/audio/image) and the REX as a knowledge marketplace (Kayama 2002-a, Kayama 2002-b).

The purpose of this study is to support the learning activity in the Internet learning space. We examine the knowledge management and the knowledge representation of the learning information for the CL support. REX is a distributed learning support environment organized as a learning GRID technology.

In this paper, the management of learning information in REX is described. REX is an integrated distributed learning environment and the GRID technology for supporting tools/ applications for the CL. Also, in this paper, the knowledge management mechanism in the educational context is showed. The details of GRID technology as knowledge management and for connecting different soft wares is exploring by using the semantic web approach and it will be integrated with the current learning support environment.

Our Grid technology is focused in the center of connecting various information among learners' profile, log-data in learning process and learning resources as information Grid for the purpose of sharing with interoperability of applications/tools used in collaborative learning process.


Jürgen Heller

Cord Hockemeyer Birgit Mayer

Dietrich Albert

Competence-based Knowledge Structures for Personalised Learning: Distributed Resources and Virtual Experiments

Keywords: adaptive eLearning, personalisation, learning Grid, knowledge structures, competencies

The ELeGI project focuses on integrating technology-enhanced learning methodologies into a pedagogy-driven and service-oriented architecture based on Grid technology. It aims at a system that is capable of realising personalised, adaptive, and experiential learning. This requires to have available a framework that, on the one hand, allows for representing existing domain knowledge, and, on the other hand, provides a representation of the learner's current state of knowledge. It is shown that a competence-based extension of Knowledge Space Theory provides a representation of the conceptual organisation of a domain that not only allows for an adaptive assessment of an individual's knowledge, but also for generating personalised learning paths. The discussion of this framework emphasizes its application within an open distributed service model, and in the context of Virtual Scientific Experiments.

INTRODUCTION

Personalisation, which became one of the key concepts in current education, reacts to the fact that students come to school with different knowledge and skill bases as well as varying learning preferences, interests, and aptitudes. Personalised learning presupposes high quality teaching that is adaptive to the different ways students achieve their knowledge and skills. Therefore, the teaching courses, curricula, and school organisations have to be designed in a way to reach as many students as possible with diverse needs and experiences for as much of the time as possible. Personalised courses actively engage the learners by providing teaching strategies and materials that appeal to the learners' knowledge and preferences etc. Since it would be costly and unfeasible for teachers to produce personalised courses that meet all of these requirements, hypermedia learning systems are of prime importance for education. Such systems allow for delivering information outside the traditional bound of a classroom situation, where learners are taught by a static one-fits-all approach. An educational system that responds to individual needs by creating a personal learning path enables individual students to experience excellence in his or her learning. Among the various benefits of a personalised learning environment that are mentioned is the fact that the time taken to learn is reduced, and that the learner's retention is improved.

The European Learning Grid Infrastructure (ELeGI) project sets out to develop an adaptive technology-enhanced learning system that integrates a new pedagogy paradigm concentrating on active, experiential, contextualised, and collaborative learning processes. Thus, the system should behave like a private teacher, who adapts the training to the individual learner. Learning paths allow the learning system to describe alternative ways from an individual starting knowledge state to the selected goal state by instructional interventions. The system should also provide a method for adaptive knowledge and skill assessment. A central aspect here is to uncover a learner's state of knowledge in the frame of an efficient questioning by selecting the problems in a way that takes into account the previous answers of a learner. All of these features have high technical requirements, which in ELeGI are addressed by building on the open distributed service model evolved as part of the Grid technology. Grid computing supports coordinating and sharing computing, application, data, storage, or network resources across dynamic and geographically distributed virtual locations. An eLearning system based on Grid Technology also provides an open learning environment, where educational content related to specific knowledge domains can be changed, added or deleted in local as well as in remote repositories. To ensure adaptivity, the technological aspects have to be complemented by pedagogical and psychological principles as well as by the knowledge of a domain expert to guarantee that the educational material is presented in an adequately structured way. All these requirements demand to have available a framework for representing the existing domain knowledge as well as the learner's current state of knowledge. Knowledge Space Theory is suggested as a formal framework that satisfies these needs. An extension of the originally behaviouristic approach that incorporates the underlying cognitive skills and competences can serve as a basis for implementing personalised learning into a technologyenhanced learning system.

The following section introduces the basic notions of Knowledge Space Theory, and illustrates its potential for an efficient adaptive assessment of a learner's knowledge. Subsequently, this framework is extended by incorporating cognitive skills and competencies, which are to be derived from the ontological structure of the considered domain. This forms the basis for generating personalised learning paths, and assessing the learners' competencies. Finally, we address some aspects that are especially relevant for ELeGI. This includes the integration of the approach into a Grid-based learning system, and discusses its application to Virtual Scientific Experiments.

KNOWLEDGE SPACE THEORY

Basic Notions

Knowledge Space Theory [START_REF] Doignon | Spaces for the Assessment of Knowledge[END_REF] provides a set-theoretic framework for representing the knowledge of a learner in a certain domain, which is characterised by a set of assessment problems (subsequently denoted by Q). In this framework the knowledge state of a learner is identified with the set of problems this learner is capable of solving. Due to mutual (psychological) dependencies between the problems not all of the possible subsets of the set Q are plausible knowledge states. If a correct solution to a certain problem can be inferred given another problem is mastered then each knowledge state will contain the first problem whenever it contains the second one (i.e. the first problem may be considered a prerequisite to the second).

The notion of a surmise relation was introduced to capture the relationships between problems of a specific knowledge domain Q. A collection of knowledge states of a given knowledge domain Q is called a knowledge structure, whenever it contains the empty set ∅ and the set Q. The knowledge structure induced by the surmise relation depicted in

K = {∅, {a}, {c}, {a, c}, {a, b}, {a, b, c}, {a, b, d}, {a, b, c, e}, {a, b, c, d}, Q}.
The resulting order on this collection of knowledge states, based on set-inclusion, is shown in Figure 2. Two main features of Knowledge Space Theory can be discussed with reference to this knowledge structure, namely the realisation of personalised learning paths and adaptive knowledge assessment.

As can be seen from Figure 2, there are various ways to move from the naive knowledge state (empty set ∅) to the knowledge state of full mastery (set Q). One of the possible learning paths is indicated by the upwards-directed dashed arrows. This path describes the possible steps of a learning process in the frame of a psychological learning theory. According to the given knowledge structure in the first step the content related to problems a or c should be learned. Dependent on the current knowledge state the next content is to be selected accordingly. It is not a viable alternative to start with, for example, learning content related to problem b, because b has a as a prerequisite.

Aside from providing different learning paths supporting personalisation, based on a knowledge structure an efficient adaptive procedure for knowledge assessment can be devised. It allows for uniquely determining the knowledge state by presenting the learner with only a subset of problems. Supposing that the knowledge structure shown in Figure 2 has been obtained, in the beginning of an assessment phase all of these states may correspond to the knowledge state of an individual learner. According to a deterministic procedure, the assessment starts by selecting a problem that is contained approximately half of the states of this structure and by posing this problem to the learner. Dependent on the learner's previously given answers, the next problem will be selected. For example, if the learner is capable of solving problem b, then only the knowledge states containing problem b are still feasible. This reduces the number of still possible knowledge states from ten to six alternatives (for details see Table 1). If subsequently problem e is solved, states {a, b, c, e} and {a, b, c, d, e} remain. The learner's knowledge state is uniquely identified after presenting problem d. For instance, state {a, b, c, e} results if problem d cannot be solved by this learner. Thus, for a set of five assessment problems, the presentation of only three problems allows for identifying the knowledge state of a learner. Formally, the knowledge state of a learner is determined in about ld (│K│) questions. Once the knowledge state of a learner has been determined it may serve several purposes. Based on the learner's current state the learning material to be presented next can be selected according to the learning paths. Given the assessed state {a, b, c, e} of the knowledge structure shown in Figure 2, in the next step content related to problem d have to be selected. If previously learned material has to be reviewed then the content related to problem e seems to be a natural choice. To provide another example, assume that the learner's knowledge state is {a ,b, c}. In this case in the next learning step material related to problem d or e can be presented. Since it is not known whether content associated to problems b or c has been learned in the last step of the learning process, content related to problems b and c have to be selected when previously learned material has to be rehearsed.

∅ { a , b , c , d } { a , b , c , d , e } { a , b, c, e} { c } { a , c } { a , b , c } { a } { a , b } { a , b , d }
So far Knowledge Space Theory is discussed from a deterministic point of view. For practical applications it seems reasonable to assume that knowledge states may occur in a population with different frequencies, and that a learner sometimes may be careless in solving a problem or may guess the correct answer. To integrate this approach into a probabilistic framework the notion of a probabilistic knowledge structure was introduced [START_REF] Doignon | Knowledge Spaces[END_REF]. It assumes a probability distribution on the knowledge states in a given knowledge structure and uses the wellknown assumption of local stochastic independence to relate the conditional probability of observing a response pattern given a knowledge state to problem-specific probabilities of a careless error, or a lucky guess, respectively. Notice that in this approach the knowledge state is a latent construct that is distinguished from the observable response pattern.

Competence-based Extensions

Although there is a commercial learning system that is based on Knowledge Space Theory, which is the ALEKS system (http://www.aleks.com), this approach suffers from its limitation to a purely behaviouristic perspective. Knowledge Space Theory focuses completely on the observable solution behaviour, and does not refer to both learning objects and skills or competencies that are to be taught. Moreover, an open learning environment should enable teachers to assemble new learning courses from existing ones and from material in local and remote repositories as well as to change or add new educational content.

In the ALEKS system the procedure to assess the knowledge state of a learner is based on the dependency relations defined on the problems. Enlarging the set of problems is not straightforward in case of such a problembased system. Whenever the problems in a knowledge domain are changed, added or deleted, all the prerequisite relationships between these problems will change and, therefore, the prerequisite information attached to each of the problems will have to be revised. This issue can be resolved by assigning skills to the problems that are relevant to its solution. This skill assignment to a particular problem is independent of the skills associated to other problems. Adding new problems to a knowledge domain then does not require revising all the problems, it only calls for a re-computation of the knowledge structure. When implementing this approach the assignment of skills to problems has to be reflected by the metadata assigned to them.

Thus, Knowledge Space Theory has to be extended so that it incorporates explicit reference to learning objects and underlying skills and competencies. The subsequent consideration is based on previous work by [START_REF] Falmange | Introduction to Knowledge Spaces: How to Build, Test, and Search Them[END_REF], [START_REF] Doignon | Knowledge Spaces and Skill Assignments[END_REF], [START_REF] Düntsch | Skills and Knowledge Structures[END_REF], [START_REF] Korossy | Extending the Theory of Knowledge Spaces: a Competence-performance Approach[END_REF], [START_REF] Albert | Establishing Knowledge Spaces by Systematical Problem Construction[END_REF], [START_REF] Hockemeyer | Competence-based Adaptive e-Learning in Dynamic Domains[END_REF], [START_REF] Hockemeyer | Applying Competence Prerequisite Structures for eLearning and Skill Management[END_REF]. It not only integrates these different contributions, but also derives the implications for implementing a personalised learning system, and clarifies the approach's relation to domain ontologies.

Besides assessment problems there are learning objects (LO), which impart the knowledge and skills associated with the educational material. Therefore, extended Knowledge Space Theory deals with three different sorts of entities, which are

• the set Q of assessment problems • the set L of LOs, •
the set S of skills relevant for solving the problems, and taught by the LOs.

Notice that the skills in the set S are meant to provide a fine-grained, low-level description of the student's capabilities. Usually, it is a whole bunch of skills that is tested by an assessment problem, or taught by a LO. Each of these basic sets is assumed to be endowed with a structure, which we conceive as a collection of subsets of the respective set. In particular, we consider

• a knowledge structure on the set Q of assessment problems, • a learning structure on the set L of LOs, • a competence structure on the set of skills S.

The knowledge structure forms the basis of the problem-based assessment of a student's competency. The learning structure together with a student's current competence state (subset of available skills, element of competence structure) is used to generate a personalised learning path. Learning and competence structures are defined in complete analogy to the knowledge structure introduced above. The main goal is to identify the pieces of information that are needed for establishing all those structures.

Let us first consider the assignment of skills to both assessment problems and LOs. The relationship between assessment problems and skills can be formalised by two mappings. The mapping s (skill function) associates to each problem a collection of subsets of skills. Each of these subsets (i.e. each competency) consists of those skills that are sufficient for solving the problem. Assigning more than one competency to a problem takes care of the fact that there may be more than one way to solve it. The mapping p (problem function) associates to each subset of skills the set of problems that can be solved in it. It defines a knowledge structure because the associated subsets actually are nothing else but the possible knowledge states. It has been shown that both concepts are equivalent, which means that, given the skill function, the problem function is uniquely determined, and vice versa. Consequently, only one of the two functions needs to be known in order to build the respective knowledge structure. Consideration is confined to the skill function, because it may be interpreted as representing the assignment of metadata to the problems. It follows that assigning (semantic) metadata to assessment problems puts constraints on the possible knowledge states that can occur. In principle, the skill function for a given set Q of assessment problems may also introduce dependencies between skills. These dependencies, however, may only crop up in the given set Q, and it remains unclear whether they are valid in general. If capitalising on incidental dependencies between problems is to be avoided then the constraints the skill function puts on the possible subsets of skills should be neglected.

The relationship between the set L of LOs and the skills in S is mediated by two mappings. The mapping r associates to each LO a subset of skills (required competency), which characterise the prerequisites for dealing with it, or understanding it. The mapping t associates to each LO a subset of skills (taught competency), which refer to the content actually taught by the LO. In a similar way as outlined above, the mappings r and t may be exploited to induce a learning structure on the set of LOs, which plays a central role for generating personalised learning paths. The pair of mappings r and t also imposes constraints on the competence states that can occur. Again, these constraints are tied to the given set L of LOs, and may not be valid in general.

The identification of skills and their relationships is a crucial aspect for generating competence structures. Identifying skills by only analysing LOs or assessment problems leads to specific skill sets associated to these LOs or problems, which is problematic in the context of an open learning system. Other sources for establishing competence structures have to be determined.

Structural information regarding skills may be provided by ontologies or concept maps related to a specific knowledge domain. On the one hand, ontologies may serve as a kind of lexicon including the relevant "vocabulary" (skills, concepts, …), for example, to facilitate the process of adding new content. On the other hand, ontologies may provide structural information regarding the relations between the concepts and skills relevant for solving assessment problems, for example. These ontological structures on skills or concepts can be based on curricula analysis, and therefore they are not restricted to a particular set of LOs. Moreover, these relations between skills have an impact on the corresponding knowledge structures.

DISTRIBUTED RESOURCES

Since the Grid technology is based on distributed services, in this context the concept of distributed skill functions [START_REF] Stefanutti | Derivation of Knowledge Structures for Distributed Learning Objects[END_REF] is of particular interest. In a Grid-based system learning objects can reside on different locations, where every location has access to both, local and remote learning objects.

As outlined above, a knowledge structure may be induced by a skill function. If several skill functions are available, they can be merged into a single skill function (distributed skill function), which then induces a knowledge structure. The notion of a distributed skill function thus entails a distributed representation of a knowledge structure.

As an example consider the skill functions s 1 and s 2 defined on Q 1 = {a, b, c, d}, S 1 = {x, y, z} and Q 2 = {a, b, e, f} and S 2 = {w, x, y}, respectively. The knowledge structure K 1 induced by the s 1 is given by Mild consistency criteria have to be met (e.g. in case of overlapping basic sets) for defining a distributed skill function. Notice that, in the above example, the knowledge structure K 1 is 'contained' in K (to be more precise,

K 1 = {Ø,
K 1 ⊂ K ∩ Q 1 ), while K 2 is not 'contained' in K (i.e. K 2 ⊄ K ∩ Q 2 )
. This shows that further research is needed to elaborate this approach in order to clearly understand the interrelation between the knowledge structure induced by a distributed skill function and those associated to its components.

APPLICATION TO VIRTUAL SCIENTIFIC EXPERIMENTS

Extended Knowledge Space Theory can also form the basis for representing the learning processes that occur in the context of Virtual Scientific Experiments (VSEs). VSEs represent a way of inquiry teaching, in which the educational material is explored by the learner. Extended Knowledge Space Theory knowledge can be applied to either a single VSE or various VSEs within a specific course. Establishing knowledge structures for VSEs follows the same procedure as for assessment problems or LOs outlined above. For each VSE the relevant skills and concepts for solving it have to be identified and assigned to it. The skills and their mutual relationships can again be derived from a domain ontology.

In a VSE learning environment, a learner has to perform several sequences of actions or manipulations. For instance, a learner may want to identify which of several variables (e.g. length, mass, angle) has an impact on the period of a pendulum. To solve this task the relevant parameters have to be manipulated and the respective effects have to be observed and recorded. Possible skills that are associated to this pendulum-VSE might be to know that `period does not depend on mass' or to know that `period does depend on length'. To accommodate with such a dynamic learning situation, Knowledge Space Theory has to be integrated into a dynamic framework.

In a VSE a learner navigates through a space of LOs (identified with single activities). Selecting from several alternative activities available at a point in time the learner creates an individual sequence of LOs. This individual learning path is directly observable. Analogous to this observable behaviour the existence of cognitive states is assumed. The cognitive states may comprise skills and competencies as well as preferences and prior knowledge. The observable sequence of actions or LOs is supposed to depend on these cognitive states. Conversely, the visited LOs and performed manipulations determine what can be learned, and thus change the latent cognitive state of the learner. The dependencies between the observable and latent learning paths may be captured in a stochastic process model (e.g. Markov Chain Model, [START_REF] Kemeny | Finite Markov Chains[END_REF]). The state of the dynamic system can be represented by a compound consisting of the currently chosen activity (or, LO) and the current knowledge or competence state. The specification of the transition probabilities between the compound states forms the core of a Markov chain model. It is an important advantage of this Markov chain model is that, given an initial assessment, the current knowledge or competence state of the learner can be inferred from observing the sequence of chosen activities or learning objects. It is not necessary to continuously assess the learner during his or her interaction with the virtual experiment.

CONCLUSIONS

This paper discusses the application of extended Knowledge Space Theory as a formal framework for the knowledge representation within a technology-enhanced learning system based on Grid technology. The mutual implications and relationships between assessment problems, LOs, and related skills or competencies are outlined. It is shown that this approach allows for generating personalised learning paths, and for an efficient adaptive assessment of knowledge and competencies, respectively. Moreover, it addresses various issues that are essential for an application of the approach. In particular, it discusses the question of how to integrate domain ontologies, the handling of distributed resources as required by the Grid technology, and how to represent the learning process that occurs in experiential learning through VSE.

Figure 1 FIGURE 1 :

 11 FIGURE 1: Example of a Hasse diagram illustrating a surmise relation on a knowledge domain Q.

Figure 1

 1 Figure 1 is given by

FIGURE 2 :

 2 FIGURE 2: Knowledge structure induced by the surmise relation of Figure 1. The dashed arrows represent a possible learning path.

TABLE 1 :

 1 Adaptive assessment procedure.

	Posed	Answer	Feasible	knowledge
	proble		state(s)
	m
	-	-	Q
	b	solved	{a, b}, {a, b, c},{a, b, d},
			{a, b, c, d}, {a, b, c, e},
			{a, b, c, d, e}
	e	solved	{a, b, c, e}, {a, b, c, d, e}
	d	not	{a, b, c, e}
		solved

  {b}, {c}, {b, c}, {a, b, c}, {b, c, d}, Q 1 }, while the knowledge structure K 2 induced by s 2 reads K 2 = {Ø, {e}, {f}, {a, e, f}, {b, e, f}, Q 2 }. Merging the skill functions s 1 and s 2 results in the following distributed skill function s defined on Q = {a, b, c, d, e, f}, S = {w, x, y, z}. The knowledge structure K induced by s is given by K = {Ø, {b}, {c, f}, {b, c, e}, {a, b, c, e}, {b, c, e, f}, {b, c, d, f}, {a, c, e, f}, {a, b, c, e, f}, Q}.

	s(a)	=	{{x, y}, {x, z}, {w, y}}
	s(b)	=	{{x}, {z}, {x, w}}
	s(c)	=	{{x}, {y}}
	s(d)	=	{{y, z}}
	s(e)	=	{{x}, {w, y}}
	s(f)	=	{{y}, {w, x}}

Competence-based Knowledge Structures for Personalised Learning Competence-based Knowledge Structures for Personalised Learning

Competence-based Knowledge Structures for Personalised Learning