Applying Competence Prerequisite Structures for eLearning
and Skill Management
(University of Graz, Austria
(Trinity College Dublin, Ireland
(Trinity College Dublin, Ireland
(University of Graz, Austria
Abstract: Several approaches for formalising prerequisite structures
on skills or competencies based on the psychological theory of knowledge
space have been suggested and applied for adaptive eLearning. In this paper,
we will discuss how these structures may be applied in skill management
in a broader sense. After introducing some formal structures for prerequisite
relationships between competencies, we will briefly present an example
of an adaptive eLearning system based on this approach (APeLS). Several
other aspects of the system which promise to be useful for advanced skill
management are discussed. In the final part of this paper, we will discuss
such broader applications of the model with respect to personal as well
as to organisational skill management.
Keywords: Skill management, eLearning, Personalised hypermedia
Categories: J.4, K.4.3, H.5.4
Several approaches for structuring a domain of knowledge through prerequisites
between skills (or competencies) within this domain have been developed
on the basis of the theory of knowledge spaces [Doignon
and Falmagne (1985)], [Doignon and Falmagne (1999)],
[Albert and Lukas (1999)]. While the original aim
of these approaches lay in testing knowledge, the focus has changed in
recent years to applying these structures for teaching knowledge in personalised
hypertext systems [Albert and Hockemeyer (1997)],
[Conlan et al. (2002a)].
These (and other) personalised eLearning systems based on knowledge
space theory share two limitations: (i) personalisation is limited in these
systems to personalisation toward the learner's current knowledge and (ii)
the support in learning and personal knowledge management is limited to
singular learning processes neglecting the need to update previously learned
knowledge to the current state of the art as well as neglecting the support
for repeating the previously learned contents in order to achieve a life-long
The latter point includes a shift in the interpretation of "life-long
learning" from "learning throughout the whole life" towards
"learning for the whole life".
In the sequel, we will first briefly introduce a formal model for competence
prerequisite structures and present an example for an personalised eLearning
system based on this model. Afterwards we will discuss how this model can
be applied for skill management on a personal as well as on a company level.
2 Competence prerequisite structures
2.1 Knowledge space theory
The model for competence prerequisite structures we use in our work
is based on the theory of knowledge spaces [Doignon and
Falmagne (1985)], [Doignon and Falmagne (1999)].
This theory models the response behaviour for knowledge tests on a behavioural
level, i.e. on the basis of prerequisite relationships between the items
in a test.
A basic notion in knowledge space theory is the surmise relation.
Two test items a and b are in a surmise relation (a
b) if, whenever a person has solved item b correctly, we can surmise
that this person is also able to solve item a correctly. From a mathematical
point of view, such a surmise relation is a quasi-order on the set of test
If we regard, on the other hand, a person's knowledge state as
the subset of test items this person is able to solve, we see that the
set of possible knowledge states is limited through the surmise relation.
The set of all knowledge states conforming to a surmise relation is called
(quasi-ordinal) knowledge space. A knowledge space conforming to
a surmise relation contains the empty set (i.e. knowing nothing) and the
complete set of test items (i.e. knowing all items) as knowledge states.
Furthermore, for any knowledge states K and K', their union
and their intersection are also knowledge states (called closure under
union and under intersection, respectively).
In practice, we often find test items which can be solved in different
ways. Doignon and Falmagne have defined a certain mapping, the surmise
system as a means to model this. A surmise system assigns to each test
item a family of subsets of items called clauses. Each clause is
a subset of prerequisite items corresponding to some way of solving the
test item. Knowledge spaces conforming to a surmise system are sill closed
under union but the are not necessarily closed under intersection.
This behavioural model for prerequisite structures has been applied
for eLearning, e.g., in the ALEKS (http://www.aleks.com)
2.2 Competence performance approach
Over the last decade, there have been a number of approaches to enrich
the theory of knowledge spaces by modelling not only the observable behaviour
but also the underlying latent skills or competencies [Albert
and Lukas (1999)]. Throughout this paper, we will focus on the competence
performance approach [Korossy (1997)], [Korossy
Korossy models a domain of knowledge through performances (i.e. test
items) and the underlying latent competencies. He derives a performance
structure from three sources: an interpretation function mapping
each item to the subset of competencies required for solving this item.
A correct solution to an item is interpreted in such a way that the person's
competence state contains at least all those competencies assigned
to this item. On the other side, a representation function assigns
to each subset of competencies the subset of items solvable by a person
who has these (and only these) competencies. This function denotes how
the unobservable competencies are represented visibly through item solving
behaviour. Furthermore, there may also be defined a prerequisite structure
on the set of competencies.
From these three entities (interpretation function, representation function,
and optional competence structure), a structure on the set of performances,
the performance space can be derived. Thus, we obtain an item structure
based on theoretically analysing the items in the regarded field of knowledge.
A similar approach was applied to eLearning in the RATH system [Hockemeyer
et al. (1998)]. RATH uses a knowledge space which was, however, developed
through a demand analysis of test items [Albert and
3 Personalised eLearning based on competence structures
Based on an extension of Korossy's competence performance approach,
an eLearning application based on APeLS (Adaptive Personalised eLearning
Service) [Conlan et al. (2002b)] was developed as
a first step towards metadata based reuse of adaptive eLearning resources,
[EASEL (2000)]. We will first describe the competence
learning structures forming the psychological basis of APeLS
and then the system itself.
3.1 Competence learning structures
The original intention behind Korossy's competence performance approach
was to develop a solid basis for knowledge structures obtained through
theoretical analysis of the respective domain of knowledge. Applying this
approach to personalised eLearning with an additional attitude towards
reusability of adaptive resources through standardised metadata led to
an extension of Korossy's model.
A domain of knowledge be described through a set of learning objects
(e.g. lessons) and a set of competencies. We define two mappings t
and r which assign to each learning object the subsets of competencies
taught within the learning object or required to be able to understand
the learning object, respectively [Hockemeyer (2003a)].
From these mappings, we can also derive a third function l assigning
to each subset of competencies (i.e. competence state) the subset of learning
objects which can be understood by a person having exactly that competence
From the mappings t and r, we can also derive a surmise
system on the set of competencies and, thus, also a competence space. Similarly,
also a prerequisite structure on the set of learning objects can be derived.
This approach works fine for lessons and other learning objects oriented
towards teaching (see Section 3.2). In the case of
test items, however, this approach is not able to model different ways
of solution although the prerequisite relationships are described through
a surmise system as the mapping r defines one set of required
competencies for each object.
The surmise system in the original knowledge space theory, however,
models alternative sets of prerequisites for a certain test item (i.e.
For this reason, the more general concept of competence testing structures
was developed [Hockemeyer (2003b)]. First of all,
in the case of test items, the distinction between taught and required
competencies is replaced by a distinction between competencies to be actually
(intended to be) tested with the test item and other required competencies.
A test item about dividing two fractions, e.g., might intend to actually
test the knowledge that the quotient of two fractions can be computed as
the product of the nominator and the reciprocal value of the denominator.
However, solving the item would furthermore require the knowledge how to
multiply two fractions. This would then be a required but not actually
tested competence. The shift from taught to actually tested competencies,
however, is only a shift in the interpretation of the model.
In order to model also different ways of solving an item (which might
involve different sets of prerequisites), one needs also an extension of
the competence learning space approach: Each solution path may involve
different subsets of required and of actually tested competencies. In the
competence testing structure approach, each object is, therefore,
mapped to a set of pairs of such subsets of required and of actually tested
competencies. From such a mapping, again a surmise system on the set of
competencies can be derived.
3.2 Adaptive Personalised eLearning Service (APeLS)
applies the competence learning space approach for personalised eLearning
in the context of metadata based reuse of adaptive eLearning resources
[EASEL (2000)]. This approach is achieved in APeLS
by the following three steps which are explored further in this section.
- Developing a mechanism to model the learner, both in terms of capturing
their prior knowledge and in capturing the knowledge they acquire through
using the personalized course
- Creating an appropriate narrative [Conlan et al.
(2002b)] that generically describes how the theory of knowledge space
may be implemented
- Creating appropriate metadata describing the candidate eLearning resources.
Specifically this involves creating metadata describing the conceptual
relationships between candidate content groups and the eLearning resources
within them [Dagger et al. (2003)].
3.2.1 Modelling the Learner
The modelling of the learner occurs in two stages in the eLearning application
developed - (i) Initial modelling of the learner's prior knowledge. (ii)
Continuous monitoring and updating of their knowledge as they use the personalised
courseware. By adopting the first approach of initial modelling, the competencies
of learners can be assessed before they approach the learning material
enabling the learners of different abilities to start at different stages
of the eLearning material.
This initial learner model forms the basis upon which the first personalised
offering is created. With respect to the theory of knowledge spaces the
competencies that exist as learner prior knowledge may be considered as
prerequisites for any material that may be presented.
The second, continuous, stage of learner modelling through monitoring
involves keeping track of the pages that learners access. More specifically,
it involves keeping track of the competencies taught by the learning resources
on these pages. If the learner has been successful in their learning then
these competencies taught become competencies the learner has acquired.
In order to ensure the learner had control of their learning experience,
new competencies learned did not immediately impact upon the personalised
course, i.e. the navigation structure of the course did not shift as the
learner browsed from page to page. Instead the learner was given the ability
to initiate a re-personalisation of the course, i.e. an adaptation
of the course contents based on the current learner model. This re-personalisation
involved interpreting the narrative based on the most current competencies
the learner had learned.
The approach taken to providing personalised eLearning solutions in
APeLS revolves around reusing not only the eLearning resources through
metadata, but also reusing, where possible, the adaptive narratives that
describe how the personalization occurs. In the case of the personalised
eLearning applications based on the theory of knowledge spaces the role
of the narrative was to embody the principles of this theory. Narratives
in APeLS are capable of accessing metadata and modelled information and
reasoning upon it. In this instance the narrative can access the competencies
the learner has learned and the competencies required to understand a given
concept. The narrative also determines the structure in which concepts
will be presented.
The narrative does not, however, refer directly to the eLearning resources
to be taught. Rather it refers to them abstractly through a candidacy architecture
[Dagger et al. (2003)]. This enables reuse of the
narrative as it is not tied directly to the resources used to teach the
material. A use of this may be in applying the theory of knowledge spaces
to material in different languages while reusing the narrative and the
teaching approach embodied in it.
One of the fundamental components to the approach to adaptivity and
personalisation taken in APeLS is appropriate metadata. In the case of
the eLearning application based on the theory of knowledge spaces described
here the metadata described the competencies required to understand an
eLearning resource and the competencies the learner would gain upon learning
the resource [see Albert et al. (2001)]. In developing
this metadata a conceptual structure must exist that details how learning
concepts in the domain being taught are related, in particular the prerequisite
relationships. This structure is used to place the learning resources (abstracted
through candidacy [Dagger et al. (2003)]) into a
knowledge space. The domain structure is not used directly in the adaptation
process, but is inferred through the descriptive metadata.
As such, the individual learning resources remain reusable and independent
from the eLearning application, as they are not tied directly to the implementation
of that application.
This section has briefly described APeLS and an eLearning application
based upon it highlighting the importance of appropriate learner modelling,
narrative and metadata. For further details on APeLS and the multi-model,
metadata driven approach please refer to [Conlan et al.
4 Applying competence models for skill management
In the previous section, we have shown the applicability of competence
models and competence structures for personalised eLearning. In this section,
we will take a broader and more programmatic view on the application of
competence models for skill management in general [see Ley
& Albert (2003)].
In the sequel, we look at applying competence modelling for skill management
first on a personal and afterwards on an organisational level. Finally,
we will also look at other elements of the APeLS system ant their applicability
to skill management.
4.1 Applying competence modelling for personal skill management
A central issue in research as well as in strategic planning on eLearning
is the concept of life-long learning. Traditionally, this term denotes
supporting learning throughout a person's life. Especially with respect
to the professional life, it is nowadays not any more sufficient to learn
in school and university before starting to work. Instead, we have to acquire
new knowledge in parallel to our work. Taking a view of personal skill
management here means that everybody takes over responsibility for themselves
to acquire new knowledge whenever it is needed.
We propose to extend the idea of personal skill management to cover
not only life-long learning but also life-long retention,
i.e. it is not sufficient to learn any new things coming up but, at the
same time, it is also important to keep active what we have learned before.
Ecological memory research [see Bahrick (2000)] has
investigated models and methods for this purpose. However, so far this
work has been focused on basic research and has not yet found its way into
applications, e.g. in eLearning.
For a true personal skill management, however, it is important not to
regard life-long learning and life-long retention as isolated goals. Instead,
we have to connect these two sides, e.g. distinguishing between previously
learned knowledge that should be repeated to support long-term retention
and previously learned knowledge that is obsolete and needs an update due
to new developments, for example in technical areas. The competence model
in such an integrated system could then help identifying (i) deprecated
competencies that should be replaced or updated, (ii) seldom needed but
nevertheless important competencies that need a refresh, and (iii) often
used competencies that are already implicitly refreshed regularly by daily
work. The latter two aspects need, of course, also a strong integration
to organisational skill management, e.g. by assigning competencies to work
tasks within a company [see Stefanutti & Albert (2002)].
4.2 Applying competence structures for organisational skill management
A central area for skill management is still given on the organisational
level, i.e. companies etc. need an identification of needed as well as
of available competencies within their staff. A central issue organisational
skill management here is the identification of competencies required for
certain tasks as well as the identification of competencies available within
the staff in general but also within each single staff member [Stefanutti
& Albert (2002)]. The results of such a competence modelling are
an important information basis for building project teams based on the
competence demands of the tasks and the competencies available among the
staff [see Hoppe (1995)]. On the other side, the
results of such an analysis are an important basis for demand-oriented
further education of staff members, in an integration with the aims of
personal skill management mentioned above.
4.3 A system for the support of skill management based on the ideas
underlying the APeLS system
In the description of the APeLS system, we have mentioned three important
aspects, learner modelling, narratives, and metadata. While we have discussed
the application of the learner modelling mechanism, i.e. the competence
modelling, in the previous subsections, we will now focus on the other
The narratives of the APeLS system can be regarded more generally as
strategies to teaching. Transferring this to skill management, it means
that the system clearly separates the content and domain related issues
from general, transferable issues. A skill management support system based
on the ideas underlying APeLS would support the transfer of successful
skill management strategies between different departments of an organisation
or between different organisation sin general. Since these strategies are
contained in one system, its users could switch between different strategies
at any time.
Metadata usage in APeLS goes beyond the normal usage as a means to describe
objects. In APeLS, metadata connect the concrete objects to abstract concepts
(in this case competencies) and, thus, serve as a means for realising adaptivity.
An important point is here the usage of fixed vocabularies in order to
avoid ambiguities [see Albert et al. (2001)].
In a skill management support system, metadata would be used to describe
the skills and competencies of the organisation's members. In order to
integrate skill management and eLearning, such metadata should be oriented
towards existing learner metadata schemas [see IMS (2003)].
From these metadata, information about the competencies of groups, departments
and whole organisations could be derived. However, also groups to be built
could be described using the same schemas as for existing groups. Competence
metadata here would describe the competencies the group should have, e.g.
in order to be able to solve a certain task. Afterwards, the aforementioned
general strategies could be applied to find the appropriate persons for
the to-be-built group.
We have introduced structures for modelling prerequisite relationships
between competencies within a certain domain of knowledge. Such prerequisite
structures have been used to provide personalised eLearning in an efficient
and flexible way.
Approaches to broaden these ideas for skill management in general have
been discussed. The methods use in the APeLS system promise to be similarly
efficient and effective in this broader application as they have proven
in eLearning. However, further research and development is necessary to
find out how various existing methods for skill management could be incorporated,
e.g. as strategies, into such a system and, thus, lead to an integration
of different methods.
Part of the work described in this paper was financially supported by
the EC through the EASEL project (Grant No. IST-1999-10051).
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