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A Cognitive Approach for Modeling Lifelong Competence Development

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Lifelong competence development is a fundamental premise for an information society, as well as major aim and challenge. Facing the variety of learning programs and qualification measures, problems emerge in supporting lifelong learning. Efficient competence development necessitates providing learners with learning opportunities which are appropriate for their current knowledge and for their individual learning goals. A related problem is the comparison of learners' competencies when these have been assessed in very different situations, at different ages, and with different methods. This work discusses the advantages of formally modeling competence and performance, which enables determining learners' latent, unobservable competence states based on their observable performance on a set of assessment methods.
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A Cognitive Approach for Modeling Lifelong Competence
Development
Michael D. Kickmeier-Rust, Dietrich Albert, Christina M. Steiner
Department of Psychology, University of Graz, Austria
Key words:competence, performance, lifelong learning, learning path,
competence assessment
Abstract:
Lifelong competence development is a fundamental premise for an information
society, as well as major aim and challenge. Facing the variety of learning programs
and qualification measures, problems emerge in supporting lifelong learning. Efficient
competence development necessitates providing learners with learning opportunities
which are appropriate for their current knowledge and for their individual learning
goals. A related problem is the comparison of learners’ competencies when these have
been assessed in very different situations, at different ages, and with different methods.
This work discusses the advantages of formally modeling competence and
performance, which enables determining learners’ latent, unobservable competence
states based on their observable performance on a set of assessment methods.
1 Introduction
Lifelong competence development is a fundamental premise for an information society, as
well as major aim and challenge for research and development. Lifelong learning and
continuing acquisition of competencies are important factors for individual success and the
success of the whole society. There is little doubt that such factors will gain even more
importance in the future, especially in a society which assets are primarily based on
knowledge, competence, and know-how. Such viewpoint is emphasized, for example, by
efforts of the European Commission, e.g. by the campaign “2010 - ePortfolio for all”
(www.eife-l.org) or the IST1-project TENCompetence (www.tencompetence.org), which aims
at developing and establishing technology supporting efficient lifelong competence
development.
The concept of lifelong learning has been associated with four main purposes in the
literature: preparing individuals for managing their adult lives, distributing education
throughout individuals’ lifespan, fulfilling an educative function for the whole life experience,
and identifying education with the whole life (for an overview see [7]). Originally a universal
visionary concept; today, lifelong learning constitutes an integral part and central principle of
national and international policies [20]. As lifelong learning refers to the assumption that
individuals learn at all stages of their life, all levels of education and training need to
contribute for realizing a lifelong learning framework. For this, provision in education has to
be strengthened and diversified and universal access to learning needs to be ensured.
1 Information Society Technologies (IST) research framework of the European Commission
(http://cordis.europa.eu/ist/)
Kickmeier-Rust, M. D., Albert, D., & Steiner, C. (2006). A Cognitive Approach for Modeling
Lifelong Competence Development. In M. E. Auer (Ed.), Proceedings of Interactive
Computer Aided Learning (ICL 2006) – Lifelong and Blended Learning, September 27 -
29, 2006, Villach, Austria. Kassel: Kassel University Press.
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Strategies for realizing lifelong learning include increased involvement at the pre-school
level, instilling desire and ability to learn in compulsory education, broadening and
diversifying educational opportunities in secondary education, adapting higher education to
demand, and strengthening and updating adult education [20]. However, facing the variety of
existing curricula, learning programs, and qualification measures, problems emerge in making
lifelong learning and continuing qualification efficient and effective. Technology supporting
these aims should not only assist learners in orientating in the large body of learning
opportunities and in planning individual learning, it must also enable the comparison of
individual competencies. For realizing a framework of lifelong learning at the European level,
an individual should be able to freely choose among learning environments, jobs, and
countries for enriching his/her knowledge, skills, and competencies. Therefore, educational
qualifications, certificates, and diplomas need to be part of a coherent system for properly
evaluating and recognizing them [18]. In this way, comparableness between qualifications or
competencies acquired in different educational programs, institutions, and countries could be
ensured.
1.1 Planning individual competence development
Efficient and effective competence development requires providing learners with integrated
learning opportunities which are suitable and appropriate for their current knowledge and for
their individual learning goals. To give a very simple example, a JAVA developer who wants
to learn C# programming shouldn’t be provided with learning opportunities covering
programming basics but with such covering the differences between JAVA and C#.
This principle is the basis of many adaptive or personalized eLearning solutions,
however, on a small scale (e.g., limited to a specific domain of knowledge). Generally, these
adaptive eLearning systems, e.g. ALEKS (http://www.aleks.com), ELM-ART [29], or KBS
Hyperbook [22], attempt to compete the one-fits-all approach of traditional eLearning
[10][13], accounting for certain requirements and preferences of a learner. Primarily, adaptive
or personalized approaches provide adaptive navigation and adaptive presentation of contents
[3][5][9][13][14]. Adaptive navigation refers to guidance through learning objects by, for
example, a customized hyperlink structure or format. The degree of freedom granted within
such system is determined by a specific underlying learner model. Adaptive presentation
refers to a customized presentation of learning objects. On the one hand this might concern
the visual or auditory design; on the other hand this might concern the amount or grade of
details of presented learning contents.Whilst adaptive, personalized eLearning systems
already successfully provide adaptivity and adaptability regarding the learning objects and test
items of a specific limited domain and focused on a certain point in time, approaches to
facilitate lifelong learning in terms of efficiency and effectiveness must address the same
issues, however, based on a much larger scale of content (e.g., including job-specific
competencies) and on a much wider timeframe.
1.2 Assessing and comparing competencies
One of the most important indicators for (lifelong) learning processes and learning success are
assessments results; gathered in very different situations, at different ages, and with different
methods. Thus, questions for research, for example in view of a global labor market and
global competition, might concern cross-cultural aspects and how different learners’
competencies (e.g., the ones of a programmer graduated in Austria and the ones of a
programmer graduated in the UK) can be compared with each other. This comparison is
important in order to:
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(a) enable adaptive support of learners in planning individual learning paths,
(b) support learners in navigating through the large body of learning opportunities,
(c) support learners’ presentation of accredited achievements and competencies, and
(d) enable employers to identify persons fulfilling the requirements of a specific
position.
This comparison, however, is not a trivial problem because educational contents of curricula,
for example in computer science, and the focus of education often vary significantly between
different schools and universities, different countries, or different cultures. Even among
individuals with the same educational background differences may occur when those learners
have the possibility to focus on certain topics or to choose certain courses. Thus, when aiming
for facilitating lifelong learning by means of providing learners with appropriate learning
paths and learning opportunities, we have to break down competencies into a sufficiently fine
granularity and we need an underlying model that allows us to process this vast amount of
data.
1.3 Competence vs. performance
The concept of competence is a vital element of our society. From our point of view, a major
problem when considering individual competencies is the often unclear differentiation
between latent competence and observable performance. To date a variety of definitions of
competence exist (e.g., [6][26]). The American Heritage Dictionary of the English Language,
for example, states: “Competence means the state or quality of being adequately or well
qualified; a specific range of skill, knowledge or ability”. This and many other definitions
have in common that they describe competence as an abstract, latent, not directly observable
quality. For an adequate development and assessment of competence, however, latent
competencies must be associated with observable behavior or achievements. An early
distinction between latent competencies and observable performance was introduced by
Chomsky [12] in the framework of linguistic theory. He distinguished a speaker’s competence
to use and understand a language and the performance, which includes grammatical mistakes
and non-linguistic features like hesitations. Today, this distinction has a much wider
application, especially in the field knowledge and learning psychology. Still, in practice the
concepts of latent competencies and related observable performance often lack a thoroughly
differentiation, operationalizations are often one-two-one mappings of underlying
competencies and performance, and often the same labels are used for both concepts. From a
scientific point of view, this is not an utilitarian approach; it is fraught with difficulty as
demonstrated with following examples:
Imagine an exam in trigonometry. Students might be allowed to use a mathematical
formulary and a pocket calculator. If two students master a certain task of the exam, can we
conclude that these students do have the same competencies with regard to the task? We
cannot; one student might have the necessary competencies to master the task without using
the formulary, another student maybe mastered the task only by chance, incidentally choosing
the right formula from the formulary. Or imagine three other students who didn’t master the
task. One student might not have the competence to fully understand the task and its
formulation. Thus, it would not be efficient or successful to teach that student how to use a
formulary. Another student might fully understand the task and also might be able to choose
the right formula, but maybe this student is not able to use a required function of the
calculator. In this case it would not be efficient or successful to teach this student how to
understand trigonometry tasks. Finally, a third student might have the necessary competencies
to master the entire task but might have problems to concentrate on the tasks during an exam.
Thus, it would not be useful to teach this student math.
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These examples demonstrate that it is not only necessary to break down certain types
of competencies [11] to a certain level of granularity, but also to separate competencies from
performance and to adapt learning to individual needs. This is especially true for lifelong
learning when the aim is to have a continuous model of competence development, to track the
development during a long time span, and when competencies are assessed with many
different instruments (e.g., observations, tests, achievements).
Such aims require a clear and probably standardized, definition of competencies in a
given domain and a cognitive framework that allows distinguishing latent competencies and
observable performance and, further on, that provides a formal model of competencies and
their interrelations. A sound framework to achieve such goals might be the Competence
Performance Approach (CPA).
2 Competence structures
Knowledge Space Theory (KST) [1][2][16][17], is the basis for several approaches to
competence structures, which provides a set-theoretic framework for organizing a domain of
knowledge and for representing the knowledge based on prerequisite relations. A knowledge
domain is represented by a finite set Q of problems. The knowledge state of a learner is
described by a subset of problems that s/he is able to master. Due to prerequisite relations
among the problems of a domain, not all subsets of problems are possible knowledge states. If
two problems a,b
Q are in a prerequisite relation aeb, we can assume from mastering
problem b a mastering of problem a. To give an example, image five problems of the domain
of basic algebra, an addition, a subtraction, a multiplication, a division, and an equation. For
five problems the set of all possible knowledge states is 25; if we assume that addition,
subtraction, multiplication, and division are prerequisites for solving equations, not all 32
knowledge states will occur, because it is highly improbable that a student will be able to
solve equations but no addition problems.
The collection of possible knowledge states corresponding to a prerequisite relation,
including the empty set and the whole set Q, is called a knowledge structure K. To account
for the fact that a problem may be solved in different ways and thus may be associated to
different sets of prerequisites, the notion of a prerequisite function has been introduced,
which, as a generalization of a prerequisite relation, associates a family of subsets of Q with
each problem.
In its original formalization, KST is rather behavioral, focusing on the observable
performance without referring to the competencies that underlie that performance. Among
others [15][18], one extension, which incorporates explicit reference to the competencies that
are required for mastering the problems of a domain is CPA by Korossy [23][24]. The basic
idea of CPA is to assume a basic set E of abstract, cognitive competencies that are relevant for
mastering the problems of a domain. The competence state of an individual is the collection
of all available competencies of that person, which is not directly observable but can be
uncovered on the basis of the observable performance on the problems representing the
domain. As in KST, prerequisite relations are described on the set of competencies
establishing a competence structure C, which contains all possible competence states.
Utilizing interpretation and representation functions, families of subsets of competencies
(competence states) can be mapped to problems, which can be mastered with the given
competencies and vice versa. By the assignment of competencies to the problems of a
domain, also a “problem structure” – which may be a surmise relation or a surmise function -
on the set of problems is induced.
To illustrate this approach, assume a knowledge domain that is represented by a set of
four problems (e.g., test items), Q={a, b, c, d}. Consider the set E={V, W, X, Y, Z} of
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Figure 1. Panel (a) displays the AND/OR-graph for a prerequisite function among five competences
(V to Z). The bended line below competence X indicates a logical or. Panel (b) shows the competence
structure established by the prerequisite function. The bold line indicates a valid learning path.
competencies that are relevant for solving these problems. A prerequisite function that might
exist among these competencies is demonstrated by the And/Or-Graph in Figure 1a. Thus, if a
student has competence Xwe can assume that this student also possesses either competence V
or W or both; if a student possesses competence Y we can assume that this student at least
possesses also competence W. The prerequisite function establishes a competence structure
(Figure 1b), which includes only thirteen possible competence states from a total of 25 states.
Table 1 lists an interpretation function, which associates competence states that are adequate
for mastering a given problem. This means, for solving problem aone of the two competence
states {V, X} and {W, X} is necessary or sufficient; a student that is in one of these two
competence states (or a superior one) will be able to master this problem. Given the
interpretation function, the representation function specifies the subset of problems that can be
solved in each competence state.
Table 1. Interpretation function.
Problem Competence states
a {V, X}, {W, X}
b {W, Y}
c {V, W, X}, {W, X, Y}
d {W, X, Y, Z}
The outlined approach entails several advantages. Given the performance, i.e. the
subset of problems a student could master, the latent cognitive competencies underlying that
problem solving performance can be identified. Due to the utilization of representation and
interpretation functions no one-to-one mapping of performance (e.g., responses to test items)
to competencies is required.
3 Applications
As mentioned, CPA might be a promising approach for modeling lifelong competence
development and making it more efficient and effective. In the following, several areas are
outlined within which CPA was successfully applied.
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3.1 Longitudinal observations
With regard to lifelong learning, it is important to keep track on individual development of
competencies over a long period of time. CPA allows the mapping of a variety of different
assessment instruments of a certain domain to one competence structure. This means that it is
possible to identify the actual competencies of a person once with a school exam and many
years later with a different instrument, e.g. achievements at the workplace.
This strength of CPA was applied, for example, in the domain of children’s
understanding time, distance, and velocity concepts, as a tool for modeling the developmental
course [4] including misconceptions. In recent work learning paths are utilized to analyze
longitudinal data in this domain.
3.2 Competence development
Besides identifying competencies, a further major advantage of CPA is that it allows
determining a person’s current competence level by personalized, adaptive competence
testing. Furthermore, individual learning paths can be defined on the competence level. Due
to the prerequisite relations between competencies the development of competencies cannot
occur along arbitrary paths. Referring to the example presented before, a student who is in the
competence state {W, Y} cannot directly proceed to competence state {V, W, X, Y, Z} because
competencies V,X, and Z are lacking (Figure 1b demonstrates a valid learning path for this
example). Thus, CPA allows very detailed planning of competence development along
learning paths and adapting teaching to individual needs with regard to learning objectives. If
a student is, for example, in competence state {W, Y} it would be most efficient to teach this
student competence X instead of V in order to reach competence state {W, X, Y, Z}, which
allows the student to master problem d.
3.3 Technology-enhanced Learning
During the last years, the approaches of KST and CPA were increasingly integrated into
adaptive eLearning systems [21] such as the research prototypes APeLS (http://css.uni-
graz.at/demos/apels) or RATH (http://css.uni-graz.at/rath), as well as the successful
commercial eLearning platform ALEKS (www.aleks.com). Moreover, this formal,
computational approach contributes and contributed in the past to state-of-the-art eLearning
projects under the IST1-framework, e.g., EASEL (css.uni-graz.at/projects/easel/easel.htm),
EleGI (www.elegi.org), iCLASS (www.iclass.info), or ELEKTRA (www.elektra-project.org).
These approaches to eLearning attempt to adapt to the learner’s knowledge state or
competence state respectively by providing personalized navigation support and personalized
presentation of contents on the basis of a learner’s performance in adaptive assessments.
3.4 ePortfolios
A further example to demonstrate the importance of clear definitions of competencies and
their separation from assessment instruments are ePortfolios. During the last years ePortfolios
gained more and more importance and attention. These portfolios are dynamic collections of
authentic and diverse evidence that represents which competencies a person has acquired over
time [8]. They provide (a) profiles of competencies, (b) opportunities for learners to document
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their competencies in different contexts, (c) opportunities for reflection in different contexts to
integrate learning experiences, and (d) opportunities for a more holistic approach to learning
[25]. ePortfolios’ gain of currency is fostered, for example, by the European Union’s initiative
“2010 - ePortfolio for all” (www.eife-l.org). Another example for the importance of
ePortfolios as a platform for recording, tracking, and presenting individual competencies is
CampusCanada (http://campuscanada.ca), which aims at bridging the workplace and
academic opportunities by permanent and accredited individual records.
To achieve such dynamic, comparable, and sound collections of competencies it is
necessary to develop standardized competence databases, which clearly define competencies
of certain knowledge domains. Moreover, competencies must be related to performance and
achievements and, in a next step, possibilities for the (self-) assessment of competencies
might advantageously be integrated. Only if the competencies of a person from one part of
Europe assessed with a school test are directly comparable to the competencies of a person
from another part of Europe assessed by an evaluation at the workplace, these attempts can be
a substantial gain and progress. The framework of CPA presented in this paper is able to
provide a sound starting point for future steps in this direction.
4 Conclusion
CPA, as an extension of KST, is a sound and well-elaborated psychological framework,
which can be utilized to model competencies and their interdependencies and, furthermore, to
assess latent competencies by observable performance. A major advantage of CPA is its
formal mathematical nature, which can easily be implemented in computational systems, such
as adaptive tutorial systems.
Thus, this approach gives the edge to set up a detailed model of competencies of a
domain. Learners’ competence states can be determined by different methods and at different
ages. On this basis, learners can be provided with learning opportunities that are appropriate
and suitable for their competence states. At the same time this approach enables the flexibility
of different learning paths to reach a certain individual learning goal. Moreover, the
competencies of different learners, at different ages, and further on from different countries
can be compared by detailed competence and performance profiles and learners can present
their competences in a corresponding way, for example with ePortfolios.
Even if such demands are rather visionary, a road map for future developments is to
establish a standardized catalogue or database of competencies in certain domains of
knowledge / competence. For instance, such catalogue might be based on ontologies and
might include information about the mapping of performance to certain competence states.
This enables incorporating the advantages of CPA in technological approaches to lifelong
competence development (e.g., semantic web technologies).
Still, major challenges exist, which are addressed by recent and future research. For
example, it’s necessary to model errors, which likely occur in empirical responses to test
items (i.e., careless errors and lucky guesses [15][27]). This requires the extension of
deterministic competence-performance models by probabilistic components. Another major
issue is the validation of prerequisite relations among competencies and the resulting
competence structures. Currently, various coefficient-based methods to compute the “fit” of a
proposed knowledge or performance structure to a given set of empirical response data exist
[28]. The question challenging research is how unique the relationship between a set of
competencies and a set of performance indicators (e.g., test items) is. In a next step goodness-
of-fit measures can be developed. This is no trivial task because already performance
structures might be difficult to validate, thus, attempting to distend validations to the latent
competence level is even more difficult.
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Even if future work must address existing problems, CPA provides a promising
cognitive and methodological basis for the requirements of modeling and assessing lifelong
competence development and for making another step towards a more effective, efficient, and
satisfying lifelong learning.
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Author(s):
Michael D. Kickmeier-Rust, M.Sc.
University of Graz, Department of Psychology
Universitaetsplatz 2 / III, 8010 Graz, Austria
michael.kickmeier@uni-graz.at
Dietrich Albert, Prof. Dr.
University of Graz, Department of Psychology
Universitaetsplatz 2 / III, 8010 Graz, Austria
dietrich.albert@uni-graz.at
Christina M. Steiner, M.Sc.
University of Graz, Department of Psychology
Universitaetsplatz 2 / III, 8010 Graz, Austria
chr.steiner@uni-graz.at
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Suppose that Q is a set of problems and S is a set of skills. A skill function assigns to each problem q i.e. to each element of Q — those sets of skills which are minimally sufficient to solve q; a problem function assigns to each set X of skills the set of problems which can be solved with these skills (a knowledge state). We explore the natural properties of such functions and show that these concepts are basically the same. Furthermore, we show that for every family K of subsets of Q which includes the empty set and Q, there are a set S of (abstract) skills and a problem function whose range is just K. We also give a bound for the number of skills needed to generate a specific set of knowledge states, and discuss various ways to supply a set of knowledge states with an underlying skill theory. Finally, a procedure is described to determine a skill function using coverings in partial orders which is applied to set A of the Coloured Progressive Matrices test (Raven, 1965).
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The concept of a knowledge space is at the heart of a descriptive model of knowledge in a given body of information. Another model explains the observed knowledge of individuals by latent skills. We here reconcile these two underlying approaches by showing that each finite knowledge space can be generated from a skill assignment that is minimal and unique up to an isomorphism. Some more technicalities are required in the infinite case. Part of the results reformulate theorems from the theory of Galois lattices of relations.
Chapter
In Chapter One “Lifelong Learning: Concepts and Conceptions” David Aspin and Judith Chapman note that, although the term “lifelong learning” is used in a wide variety of contexts and has a wide currency, its meaning is often unclear. It is perhaps for that reason that its operationalisation and implementation has not been widely practised or achieved and such application as it has had, has been achieved primarily on a piecemeal basis. They show that “Lifelong Learning” has been the subject of a range of various attempts at analysis, exploration and justification for some time now - since the publication of the UNESCO 1972 Report of the Fauré Committee, to further analysis and exploration in the Report of the UNESCO Delors Committee in 1996; and the Reports of the OECD, the European Parliament and the Nordic Council in the later 1990s. Since then policy-makers in countries, agencies and institutions have urged that a "lifelong learning" approach should be promoted in education policies to provide a strong foundation to underpin continuing education and training, social inclusion and individual opportunities for personal growth and emancipation. However the meanings and values implied by policy-makers’ use of and commitment to such ideas and values of “lifelong learning” remains ill-defined and unclear.