The development of an Adaptive Educational Hypermedia System (A. E. H. S) presupposes a detailed user model, a complete observations model and a well defined adaptation component [13]

The development of an Adaptive Educational Hypermedia System (A.E.H.S) presupposes a detailed user model, a complete observations model and a well defined adaptation component [13]. Moreover, a fundamental issue is the creation and organization of a Learning Repository (L.R.), which serves the electronic educational activities. A L.R. is a database of various learning material forms: lectures, articles, presentations, and any digitalized resource aiming at educational use. In addition to characteristics which serve the needs of a specific A. E. H. S., it is crucial for the L.R. to have the characteristics of reusability and interoperability. To achieve the reusability it is necessary that the content of L.R. have modular structure and every essential part unit be self-consistent.

The term « Learning Objects (L.O.) » was used for the first time by Wayne Hodgins in 1994 [22]. The L.O. is a product of Domain Model ontology, which is originated in Intelligent Tutoring Systems (I.T.S.). “An LO is a reusable chunk of information, used as a modular building block of e-learning content” [1]. An important factor which facilitates reusability is the use of metadata. Information about LO developers, description of its meaning and its possible role are the main body of LO metadata. In this way the retrieval of L.O., is facilitated [12].

So far, different standardizations for metadata have been proposed. Among them, for the needs of the present article we adopt Learning Object Metadata ( LOM ) by ΙΕΕΕ Learning Technology Standards which is the most popular [17].

The variety of LO’s in terms of size and structure is enormous « A learning object could be a picture of the Mona Lisa, a document on the Mona Lisa (that includes the picture), a course module on da Vinci, a complete course on art history, or even a 4 year master curriculum on western culture.” [10]. Thus, the necessity to introduce a well-defined statement on LOs characteristic properties , becomes obvious. Such characteristic properties are the size and the structure of LO.

Today, educational metadata which describe the L.O., do not completely satisfy the educational community [24]. Moreover, they do not facilitate their identification in accordance to the learning style that is better served. In the present article we aim to facilitate LO search and retrieval according to the learning style of the learners. So the adaptivity may extend to the quality characteristics of the student as they are recognized by the system. In order to achieve this, we define the structure of the learning material, its properties and the accompanying metadata . The way of management of the LOs and their properties is also described.

In the I.E.E.E. standard Information about conceptual contents of the LO is given by the metadata of General Category as title description, and keywords. L.O.’s correspondence to a frame of concept relations of a specific knowledge domain is done within LOM standards by metadata category that is taxonomy. In some cases such taxonomy is already available. For example ACM Computer Classification System (ACM-CCS, 2002) is a ready taxonomy that can be used as a topic ontology in the field of computer science [9]. Whenever such concept taxonomy of the learning domain is not available, we have to consider a method for inferring concept relations. Furthermore, in the framework of this article a mathematical model of conceptual relations inference is given which allows the dynamic construction of the general concept map. The dynamic glossary construction of concepts and the concept map of the knowledge domain are done during the enrichment of the learning repository. The dynamic formation of a gnosion Map, tailored to the needs of each user, is described as personalized “view” of L.R.

The L.R. model which is described in the present article supports adaptivity. More specifically: 1) it facilitates the adaptive to the users’ interests and special needs content retrieval, 2) it facilitates adaptive presentation of educational contents with the use of adaptive hypermedia techniques i.e. content adaptation and adaptive navigation support [2]. In both cases the adaptivity results in the use of a database that includes information about the user within which the learning profile and style is recorded as it is observed and formed dynamically during the educational process. This paper has the following structure: in paragraph I we set the learning object’s properties and we also present a set of metadata which can be considered as an extension of the L.O.M. standard educational category. In paragraph II a brief description of metadata management is given. The metadata management has been planned in terms of each individual user’s specific needs i.e. on user’s cognitive characteristics and knowledge evaluation. In paragraph III the databases and a mathematical model for the formation of cognitive relations are described. Finally, in paragraph IV, a method for adaptive content retrieval of learning material, as well as a corresponding annotation for its comprehensiveness is given.

1. 
   Gnosion as a L.O
   

To start with , let us refer to the learning object basic determinant characteristics. We introduce gnosion as the learning object that satisfies the following properties:

1. Gnosion is elementary, can not be partitioned in subparts, and in case of being just a text it can not be smaller than a single paragraph.

2. 
   Its time length does not determine Gnosion.
   

2. 
   Gnosion is conceptually elementary and self-consistent i.e. deals with a) a concept and its properties or its aspects, b) a relation between concepts and c) a proof or a set of arguments supporting a thesis without links or cross-references.
   
3. 
   Gnosion is described by its metadata set, properly selected to reflect the contained information, in such a way as to be exploited in systems adaptation to user’s cognitive state and learning style.
   

T_gnosion as a physical entity can be anyone of the following: text , video , animation , graph, simulation , slide , table , diagram, figure, in any digital format, developed in a way that serves its role to teach concepts , concept relations e .t. c. as aforementioned in property 4.

An A_gnosion is a fundamental self-contained question along with its correct answer and the corresponding feedback to the learner (bound in an XML file)

The set of metadata, we use to identify gnosion, is compatible with the IEEE-L.O.M . Educational category in this standard consists of the following fields:

Let us make now a comment on the LOM-metadata field: “LEARNING RESOURCE TYPE ”. Based on the proposed Value Space of this field the machine recognizes the identity of the learning object as an A_gnosion when this certain field takes one of the following values: exercise, problem statement, or questionnaire. As we consider gnosion TYPE a fundamental identifying gnosion’s entry, we assign the responsibility of giving this characterization to the educator who introduces the gnosion. An additional reason for this is the fact that we adopt the IMS Question & Test Interoperability standard (I.M.S. , 2000) in structuring Α_gnosions to the purpose of retaining interoperability.

As learning procedure takes place simultaneously with assessment one recognizes the importance of feedback. Proper feedback not only encourages learner at his/her efforts to learn but also informs him about his/her learning state and leads him to develop his/her metacognition during learning process. Feedback results in a range of suitable statements addressed to the learner that supports his/her efforts. The feedback statements can be just information on his/her answer correctness (Question Feedback=0) or has one of the forms: either a short paragraph (Question Feedback = 1) or a detailed paragraph (Question Feedback=2). In both cases the learner is supplied with additional information about his/her answer (see table 1). Question Feedback value is selected according to user’s style. For example, an “accommodator” who likes to proceed quickly, should be satisfied if he/she is succinctly informed on his/her answer correctness.

TcontentParameter takes the value: Technical, or nonTechnical. This characterization turns to be an advantage in interdisciplinary knowledge fields, referring to technical or theoretical knowledge background correspondingly. Let us now consider three learner stereotypes referred to interdisciplinary knowledge subjects: those who have theoretical background (social sciences, humanities e. t. c.)-(SH), the ones who are familiar to scientific disciplines except social sciences and humanities-(SD), and a last category of general info seekers (IS). Table 4 presents possible selection combinations for these three user stereotypes.

• 
  G: data base containing gnosions
  
• 
  M data base of gnosions metadata
  
• 
  C data base of learning concepts
  
• 
  U data base of user’s profile, history and performance.
  

Database G includes gnosions that is the learning material itself. G is related to database M of the metadata. Each gnosion corresponds to one metadata set which describes this gnosion. Through metadata the gnosion identification is attempted by the system. The gnosion metadata description may not be unique; Thus, M is separated from G.

A

Figure 1

set of keywords is used to match gnosions and the concepts it refers to. The concepts, as well as their relations, constitute the contents of C.

The set of concepts, together with their relations and the wide range of their explicit or implicit presentations (expressions), consist ontology [11]. An ontology may not be unique to a given knowledge domain. In the present article we present a model of concept map dynamic formulation , as L. R. is enriched with gnosions.

For every gnosion in G database used by the learner, for this learner appropriate pieces of information are recorded to U database. That is : a) the Uniform Resource Identifier (URI) of the gnosion which is used , b) the score achieved (if there is any) c) the set of gnosion ’s keywords .

C* is part of the user’s database U. Elements in C^* are ordered pairs (x,y) where xC and yIR (IR the body of real numbers) resulted as combination of the achieved evaluation scores and the number of LO he/she made use of. Thus, y indicates the degree of user awareness of concept x.

The set of users preferences is also recorded in U .The relation between U and M refers to the correspondence between the various fields of those databases. Part of this correspondence has been discussed in paragraph II.

Next we adopt the following terminology:

Let X and Y any two objects which belong to any one of the above data bases . Let moreover A: XY be a map of X onto Y, given by the relation A(x,y).

A	Domain X	Range Y	(Notation)
R2M	G	C	R2M(gn,ci)
R2S	G	C	R2S(gn,ci)
C_prereq	C	C	C_prereq(ci, cj)
G_prereq	G	G	G_prereq(gi, gj)
DcontentParameter	G	MDM MD={definition , Detailed, nonDetailed)	DcontentParameter(gn,MDi) Where MDi is one of the three elements of MD

Table 5
As for the relation A, for the following we consider specific relations as appear in table 5.

Let us consider a gnosion g_m that refers to concepts c_i and c_j. Through relation C_prereq two concepts c_i, c_j are related as c_i being the prerequisite of c_j. The prerequisite relation concerns concepts’ ordering. It also orders gnosions that refer to relevant concepts in the gnosions map. The map of gnosions is subject to an up to date reordering as long as G is enriched with new gnosions. Therefore, whenever a concept c_i is prerequisite to a concept c_j, there exists at least one gnosion in database G which refers mainly in c_i while it uses c_j and for which DcontentParameter has value “definition” . This leads to the logical two ways implications,

Last implication expresses that the knowledge of gnosion g_l is prerequisite to the knowledge of gnosion gm which means α) these gnosions refer mainly to concepts c_i, c_j with the c_i being prerequisite of c_j, or β)gnosion g_m refers mainly to c_j ,which cj is used by g_l .

Let G_l be the set of gnosions g_l which are either refer mainly to , or simply use the concept c_j , that is :

.

(3)

Let moreover, G_k be the set of g_k which are either refer mainly to , or simply use the concept c_j, that is :

(4)

Where:

(5)

Let us define the Closeness between two concepts as the measure p: CXC →[0, 1) which represents the concepts relevancy. This measure is crucial to the formation of the concept map. It is worthy to mention that the more gnosions are in the data database G, the more accurate the measure of the closeness is. The relation gives closeness:

(6)

Where, cardX is the cardinality number of the set Χ.

If two concepts are closer than a given number, then most possibly they will be mentioned together to at least one gnosion. Obviously, the more than two gnosions refer to a pair of concepts, the larger the measure of their closeness is.

Prerequisite relation implies closeness relation. The reverse of this implication does not hold. Using the prerequisite and closeness relations, the concept map graph is dynamically reformed for as long as database G is enriched with new gnosions. As far as the closeness relation is concerned, the graph of the concept map becomes a weighted -but not oriented- connected graph. However, referring to the prerequisite relation one can see that the graph of gnosions is not a connected one, as independent streams of concepts are formed. Each one of its connected subgraphs, forms an oriented graph.

Every edge in the concept map graph connects two vertices, which represent two concepts. Edges are marked due to the closeness relation. Thus, p(c_i ,c_j ) serve as the graph’s weights for all i and j.

4. Management of parameters and relations towards presentation development.
In an AEHS the concept map can be represented by certain oriented and weighted graphs. In the case in hands, the AEHS concept map is dynamically formulated and is subject to change as G is enriched with new gnosions.

For any given learning goal there is a set of concepts C_TARGET={c_Ti} to be learned. For each of them, the Inference engine formulates a broader set of concepts C_TARGET⁺ which consists of those concepts c_j for which :

(7)

Number T_p is the threshold determined by a two variables function, namely the user evaluation and user profile. Therefore, T_p value affects the speed of teaching as long as it affects the number of adjacent vertices (concepts) to the vertex of the target concept. As the concept map remains the basic tool with which the learning material is presented as a sequence of gnosions, relation (7) becomes a criterion with added value to the adaptivity of the system.

Concept map affects also the data mining in G. The concepts relevance affects the presentation order of learning material. The filtering of gnosions to be presented uses the criterion

(8)

Where T_R is a dynamically specified threshold and is the set of concepts to which gnosion g_m is referred, i.e. C_gm={c_i:R2[.](g_m,c_i) according to notation (5). In case where is an empty set, then the following criterion allows the proper selection of gnosions to be presented.

(9)

Gnosions selected as above, are presented to the user as a row of learning material. The presented gnosions are ordered considering G_prereq relation. They are also annotated on how proper they are for a given user to study at the given time. We can infer a gnosion ’s appropriateness to one user at his/her current learning state, the gnosions Comprehensiveness. The gnosion’s Comprehensiveness is estimated as follows:

(10)

Here .

In user interface we can consider two choices: either all gnosions selected using relations (8) - (9) to be active links annotated according to their comprehensiveness to the specific user (adaptive link annotation) or just those of gnosions for which comprehensiveness exceeds a certain threshold value allowed to be presented (adaptive link generation) according to criterion:

(11)

Value T_k is dynamically adapted to user learning style. For example: this threshold must be considerably small for the accommodator which prefers to be guided in what he must study .

Besides the concept relations and the learning objective, the succession of the presented to the user material depends upon the educational scenario which is adopted by an A.E.H.S.
Conclusions

In the present paper we have used the concept of the learning object and have given to it the identity of the essential knowledge concept, gnosion. Adopting the standard of metadata description of the learning object IEEE –LOM , we have added subfields so that the role of learning object at the learning process is recognized, as well as the learning style to which the gnosion fits better. We have indicated the way of development of metadata fields to the adaptable search and retrieval of the learning objects according to the special characteristics of the user.

We described a database model to store and to annotate learning material in a way that its correspondence to user’s learning state and style is easily deducible.

We have given a mathematical model of conceptual relations: prerequisite and closeness according to which the main part of the Knowledge Domain of conceptual map is constructed. Finally we have described a method of adaptive content retrieval of learning material, as well as a corresponding annotation for its comprehensiveness. The above data base model has been designed as a part of the Aptitude Treatment Training by Adaptive Instruction (Α.Τ .Τ .Α .ΙΝ) system. Α.Τ .Τ .Α .ΙΝ [8] is an ongoing project at the Department of Electrical and Computer Engineering in Democritus University of Thrace .

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