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Skills and Competencies Monika Pilgerstorfer 5 April 2005

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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  1. Skills and CompetenciesMonika Pilgerstorfer5 April 2005

  2. 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

  3. 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)

  4. 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.

  5. Skill function • assign to each problem the skills required for solving this problem • Competencies = sets of skills sufficient to solve a problem

  6. Problem Competencies a {1,2,4}, {3,4} b {1,2} c {3} d {3,5} Example: skill function

  7. 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

  8. 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

  9. 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}}

  10. 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.

  11. 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

  12. Competence-Performance Approach • Extension: competence structure on a set of skills

  13. Competence-Performance Approach • Performance: observable solution behaviour • Competence: underlying construct explaining performance

  14. Competence-Performance Approach • Performance structure (A, P) A ... finite, non-empty set of problems P ... family of subsets of problems A

  15. Competence-Performance Approach • Competence structure (E, K) E ... finite, non-empty set of elementary competences K ... family of subsets of elementary competences E

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

  17. Representation function assigns to each competence state the set of problems solvable in it

  18. Problems given: a = 5 cm, c = 8 cm area A = ? given: b = 3 cm, c = 9 cm area A = ?

  19. Elementary competences

  20. Surmise function • Subsets of competencies • Extract subsets that are minimal concerning the subset relation • Minimal: not subset of each other

  21. 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

  22. Interpretation function

  23. e e a b d c b d c a

  24. Representation function

  25. e e a b d c b d c a

  26. Exercise Find the competencies that are necessary for solving following tasks:

  27. Exercise - competencies Suggested competencies:

  28. 5 4 3 2 1 Exercise Find the possible competence states and the competence- structure for the following surmise function!

  29. 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}

  30. 5 4 3 2 1 Exercise Find the Interpretation function for task A-G!

  31. 5 4 3 2 1 Exercise - Interpretation function

  32. Exercise Find the surmise function on the problems, based on the information of the Interpretation function!

  33. Thank you for your attention!

  34. 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.

  35. 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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