According to (Brusilovsky, 2003), the starting point of any adaptive systems is a structured DM that is composed of a set of small domain knowledge elements. Such elements are named differently in different systems: concepts, knowledge items, topics, knowledge elements, learning objectives, learning outcomes, but in all the cases they denote elementary fragments of the domain. Here, with the aim of working with a DM not just from a well-structured point of view but also from the pedagogical one, the notion of Learning Goal (LG) will be used. Also known as educational objectives, pedagogical goals and other denominations in different works, the LGs may be defined as statements that describe, in terms of observable behavior, the results that are expected from the teaching/learning process. Further information about this notion may be obtained in (Duque, 2009).
In order to structure the LGs, and therefore the DM, a collection of one or more Simple Directed Graphs (SDG) will be used. This approach was used instead of others more robust, ontologies for example, because it simplifies DM instantiation and its connection with the SM and TM as explained later.
A SDG is defined as a pair G = (V, A) with a set V, whose elements are called vertices or nodes, and a set A of ordered pairs of vertices, called arcs (also known as directed edges or arrows). In this case the vertices are the LGs, whereas the arcs represent decomposition operations, it means that there could be atomic LGs (a leaf) or composite (a vertex with at least one arc going out from it). Although according to this last description an LG could have only one “son”, the normal would be that it has at least two because such relationship represents a decomposition of the DM in terms of content instruction, rather than an actual content taxonomy. This however is just a recommendation because from de DM point of view as well as from the other models that are described later, it is not problem working with a LG without nay “brothers”.
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SDG graphs also have the following two properties: they do not have multiple nodes, which means that each vertex is contained only once and; they are acyclic, which means that in every possible arrangement represented by the graph, each vertex has a unique existence. Additionally to these two, there is another property for the proposed DM: just leaf LGs have actual content whereas the other ones are used only to build the structure domain knowledge. It does not mean that such “brunch” LGs does not play an important role in the system because in fact, as is described later in the SM and the TM, they are useful to represent student knowledge.
A DM general schema using the SDG approach is illustrated on figure 2.1. Notice that each LG has a unique identifier (it does not matter its format) that allows the verification of the two properties described earlier. A continuous arrow going out from LGi to LGj defines
a subdivision of LGi into LGj and may be interpreted as “LGi is divided in / is composed by
/ contains / has / ... LGj” or, in the other way, “LGj is a division of / is part of / is contained
in / ... LGi”.
Figure 2.1: DM general schema
This approach grants DM flexibility, allowing the definition of typical structures like the ones presented on figure 2.2, as well as other more complex that are just combinations of those, like the one presented on figure 2.1.
Figure 2.2: Typical DM schemas
(N-ary) Hierarchical tree structure
Non-structured LG2 LG3 LG1 LG4 LG5 LG Id6 LGK-2 LGK-1 LGK
…
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As stated in (Knutov et al., 2009) this type of DM, where all the elements may be fine grained and hierarchically structured, makes adaptive presentation and navigation support come into play. In fact, most adaptive systems embrace DM schemas similar to the one presented here, the differences lie basically in the name of the elementary fragments, in the connections restrictions or in the hierarchy depth. For example the study presented in (Hatzilygeroudis & Prentzas, 2004) proposes a four levels hierarchical structure composed by concept groups, concept subgroups, concepts and course units, these last ones constitute the learning material to be presented to the students in the form of Web pages. In (Jiménez, 2006) the author proposes two levels called learning basic units and instructional goals. In the work presented in (Arias et al., 2009) the DM may be seen as an extension of the previous one adding two more levels with which the whole structure is defined as learning basic units, topics, instructional goal and activities, these last ones contains the learning material which in this case refers to LOs.
Many other works agree with this proposal in the sense of using not a fixed but a N- levels structure using the notion of composite fragments. For example, in (Cristea & Aroyo, 2002; Cristea & de Mooij, 2003; Cristea & Calvi, 2003) they define such fragments as concepts, similarly to the work presented in (Dagger et al., 2005), whereas in (Motz et al., 2008) they are called topics.
Considering such approaches, the main contribution of the proposed DM is that it is general and flexible enough to cover most of such possibilities and therefore author decisions about domain knowledge structure going from independent items to simple sequential items, typical book-like structures, hierarchy trees with or without semantic meaning, etc.