Skills and competencies monika pilgerstorfer 5 april 2005
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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 competencies monika pilgerstorfer 5 april 2005

Skills and CompetenciesMonika Pilgerstorfer5 April 2005


Knowledge space theory

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

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

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

Skill function

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

  • Competencies

    = sets of skills sufficient to solve a problem


Example skill function

Problem

Competencies

a

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

b

{1,2}

c

{3}

d

{3,5}

Example: skill function


Problem 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 function1

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


Example 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

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

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


Skills and competencies monika pilgerstorfer 5 april 2005

Competence-Performance Approach

  • Extension:

    competence structure on a set of skills


Skills and competencies monika pilgerstorfer 5 april 2005

Competence-Performance Approach

  • Performance:

    observable solution behaviour

  • Competence:

    underlying construct explaining performance


Skills and competencies monika pilgerstorfer 5 april 2005

Competence-Performance Approach

  • Performance structure (A, P)

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

    P ... family of subsets of problems A


Skills and competencies monika pilgerstorfer 5 april 2005

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

Interpretation function

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


Representation function

Representation function

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


Skills and competencies monika pilgerstorfer 5 april 2005

Problems

given: a = 5 cm, c = 8 cm

area A = ?

given: b = 3 cm, c = 9 cm

area A = ?


Elementary competences

Elementary competences


Surmise function

Surmise function

  • Subsets of competencies

  • Extract subsets that are minimal concerning the subset relation

  • Minimal: not subset of each other


Surmise function1

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 function1

Interpretation function


Skills and competencies monika pilgerstorfer 5 april 2005

e

e

a

b

d

c

b

d

c

a


Representation function1

Representation function


Skills and competencies monika pilgerstorfer 5 april 2005

e

e

a

b

d

c

b

d

c

a


Exercise

Exercise

Find the competencies that are necessary for solving following

tasks:


Exercise competencies

Exercise - competencies

Suggested competencies:


Exercise1

5

4

3

2

1

Exercise

Find the possible competence states and the competence-

structure for the following surmise function!


Exercise competence states

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}


Exercise2

5

4

3

2

1

Exercise

Find the Interpretation function for task A-G!


Exercise interpretation function

5

4

3

2

1

Exercise - Interpretation function


Exercise3

Exercise

Find the surmise function on the problems, based on the

information of the Interpretation function!


Thank you for your attention

Thank you for your attention!


References

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.


References1

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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