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Skills and Competencies Monika Pilgerstorfer 5 April 2005. Knowledge Space Theory. Knowledge : solution behaviour Knowledge state : subset of problems a person is able to solve Knowledge space : set of all possible knowledge states. Extensions of Knowledge Space Theory.

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Skills and Competencies Monika Pilgerstorfer 5 April 2005

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Skills and CompetenciesMonika Pilgerstorfer5 April 2005


Knowledge Space Theory

  • Knowledge: solution behaviour

  • Knowledge state: subset of problems a person is able to solve

  • Knowledge space: set of all possible knowledge states


Extensions of Knowledge Space Theory

Latent cognitive structures underlying

knowledge spaces

  • Skills (Falmagne; Doignon; Düntsch & Gediga)

  • Components and Attributes, Demand Analysis (Albert & Held)

  • Cognitive Processes (Schrepp)

  • Competence-Performance Approach (Korossy)


Basics

  • Set S of skills that are necessary for answering certain problems.

  • For each problem q  Q there exists a subset f(q) S of skills that are sufficient for solving the problem.


Skill function

  • assign to each problem the skills required for solving this problem

  • Competencies

    = sets of skills sufficient to solve a problem


Problem

Competencies

a

{1,2,4}, {3,4}

b

{1,2}

c

{3}

d

{3,5}

Example: skill function


Problem function

  • Set of skills (S)

  • Set of problems (Q)

  • assigns to each set of skills the set of problems, which can be solved in it


Problem

Competencies

a

{1,2,4}, {3,4}

b

{1,2}

Competencies

Problems

c

{3}

{1,2,4}

{a,b}

d

{3,5}

{1,2}

{b}

{3}

{c}

{3,5}

{c,d}

{3,4}

{a,c}

Problem function


Competencies

Problems

{1,2,4}

{a,b}

{1,2}

{b}

{3}

{c}

a

d

{3,5}

{c,d}

b

c

{3,4}

{a,c}

Example: problem function

v

K = {, {b}, {c}, {a, b}, {a, c}, {b, c}, {c, d}, {a, b, c}, {a, c, d}, {b, c, d}, {a, b, c, d}}


Knowledge State

  • A subset K of problems is a knowledge state if and only if there is a subset M of skills such that K contains all those problems having at least one competency included in M and only those problems.


Special cases

  • disjunctive model:

    only one of the skills attached to a problem q suffices to solve this problem

  • conjunctive model:

    all the skills assigned to a problem q are required for mastering this problem


Competence-Performance Approach

  • Extension:

    competence structure on a set of skills


Competence-Performance Approach

  • Performance:

    observable solution behaviour

  • Competence:

    underlying construct explaining performance


Competence-Performance Approach

  • Performance structure (A, P)

    A ... finite, non-empty set of problems

    P ... family of subsets of problems A


Competence-Performance Approach

  • Competence structure (E, K)

    E ... finite, non-empty set of elementary competences

    K ... family of subsets of elementary competences E


Interpretation function

assigns to each problem a problem-specific set of competence states which are elements of the competence structure


Representation function

assigns to each competence state the set of problems solvable in it


Problems

given: a = 5 cm, c = 8 cm

area A = ?

given: b = 3 cm, c = 9 cm

area A = ?


Elementary competences


Surmise function

  • Subsets of competencies

  • Extract subsets that are minimal concerning the subset relation

  • Minimal: not subset of each other


Surmise function

B(K) = K, H, P,K, P,H, P,A, K,A, H,A,

K,Z, H,Z, P,K,T,A, K,H,T,A


Interpretation function


e

e

a

b

d

c

b

d

c

a


Representation function


e

e

a

b

d

c

b

d

c

a


Exercise

Find the competencies that are necessary for solving following

tasks:


Exercise - competencies

Suggested competencies:


5

4

3

2

1

Exercise

Find the possible competence states and the competence-

structure for the following surmise function!


5

4

3

2

1

Exercise – Competence states

{ }

{1}

{2}

{1,2}

{1,2,3}

{1,2,4}

{1,2,3,4}

{1,2,3,5}

{1,2,4,5}

{1,2,3,4,5}


5

4

3

2

1

Exercise

Find the Interpretation function for task A-G!


5

4

3

2

1

Exercise - Interpretation function


Exercise

Find the surmise function on the problems, based on the

information of the Interpretation function!


Thank you for your attention!


References

  • Albert, D., & Held, T. (1999). Component Based Knowledge Spaces in Problem Solving and Inductive Reasoning. In D. Albert & J. Lukas (Eds.), Knowledge Spaces: Theories, Empirical Research Applications (pp. 15–40). Mahwah, NJ: Lawrence Erlbaum Associates.

  • Düntsch, I. & Gediga, G. (1995). Skills and knowledge structures. British Journal of Mathematical and Statistical Psychology, 48 ,9-27.

  • Falmagne, J.-C., Doignon, J.-P., Villano, M., Koppen, M. & Johannesen, L. (1990). Introduction to knowledge spaces: How to build, test and search them. Psychological Review, Vol.97, No.2, 201-204.


References

  • Korossy, K. (1996). A qualitative-structural approach to the modelling of knowledge. Report of the Institute of Psychology, Universität Heidelberg.

  • Korossy, K. (1997). Extending the theory of knowledge spaces: a competence-performance approach. Zeitschrift für Psychologie 205, 53-82


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