Competence-based knowledge structures for personalised learning

1. Competence-based knowledge structuresfor personalised learning Jürgen Heller, Christina Steiner, Cord Hockemeyer, & Dietrich Albert Cognitive Science Section, Department of Psychology,University of Graz, Austria ProLearn-iClass Thematic Workshop3-4 March 2005, Leuven

2. Overview • Knowledge Space Theory • Competence-based Knowledge Structures • Skills and Skill Assignments • Deriving Skills from Domain Ontologies • Skills as Sub-Structures of a Concept Map • Component-Attribute Approach • Assigning Skills to Assessment Problems • Problem-based Skill Assessment • Assigning Skills to Learning Object • Conclusions

3. Knowledge Space Theory • knowledge domain: set of assessment problems a. ½ x 5/6 = ? b. 378 x 605 = ? c. 58.7 x 0.94 = ? d. Gwendolyn is 3/4 as old as Rebecca. Rebecca is 2/5 as old as Edwin. Edwin is 20 years old. How old is Gwendolyn? e. What is 30% of 34?

4. d e c a b Knowledge Space Theory • knowledge state of a learner: set of problems that he/she is capable of solving • mutual dependencies between problems • from a correct answer to certain problems we can surmise a correctanswer to other problems • captured by surmise relation

5. d e c a b Knowledge Space Theory • not all potential knowledge states (i.e. subsets of problems) will actually be observed • knowledge structure • collection of possible knowledge states • example K = {Ø, {a}, {b}, {a, b}, {b, c}, {a, b, c}, {b,c, e}, {a, b, c, e}, {a, b, c, d}, Q}

6. Knowledge Space Theory • knowledge structure

7. Knowledge Space Theory • key features of Knowledge Space Theory • adaptive knowledge assessment • determining the knowledge state by presenting the learner with only a subset of problems • representation of individual learning paths

8. Competence-based Knowledge Structures • Knowledge Space Theory in its original formalisation is purely behaviouristic • focus on solving assessment problems • Knowledge Space Theory needs to be extended to incorporate • underlying skills and competencies • learning objects

9. Competence-based Knowledge Structures • relevant entities • set Q of assessment problems • set L of learning objects (LOs) • set S of skills relevant for solving the problems,and taught by the LOs • relevant structures • knowledge structure on the set Q of assessment problems • learning structure on the set L of LOs • competence structure on the set S of skills • main goal • identifying the pieces of information that are needed for establishing those structures

10. Deriving Skills from Domain Ontologies • how to identify and structure skills? • e.g. cognitive task analysis, querying experts, systematic problem construction • utilise information coming from domain ontologies • ontology • specification of the concepts in a domain and relations among them • represent the structure of a knowledge domain with respect to its conceptual organisation • concept map • common way of representing ontologies • network representation

11. Deriving Skills from Domain Ontologies • skills as sub-structures of a concept map • a skill can be identified with a subset of propositions represented in a concept map • example: geometry of right triangles • skill ‚knowing the Theorem of Pythagoras‘

12. Deriving Skills from Domain Ontologies • skills as sub-structures of a concept map • a structure on the skills is induced, for example, by set-inclusion • if skill xis subset of skill y then skill x is subordinatedto skill y

13. Deriving Skills from Domain Ontologies • component-attribute approach • concept map represents results from curriculum and content analysis • basic concepts to be taughte.g. ‘Theorem of Pythagoras’ • learning objectives related to these concepts • include required activities of the learner • may be captured by action verbse.g. ‘state’ or ‘apply’ a theorem • skill: identified with a pair consisting of a concept and an action verb • e.g. ‘state Theorem of Pythagoras’

14. c1 a1 c3 c2 a2 c4 Deriving Skills from Domain Ontologies • component-attribute approach • concepts with their hierachical structure • e.g. `Theorem of Pythagoras´ prerequisite for `Altitude Theorem´corresponding to curriculum • order on the action verbs • e.g.: `state´ prerequisite for `apply´

15. Deriving Skills from Domain Ontologies • component-attribute approach • building the direct product of these two component orderings results in a surmise relation on the skills • e.g. skill c2a2 is a prerequisite to the skills c2a1, c1a2, and c1a1

16. Assigning Skills to Assessment Problems • relationship between assessment problems and skills is formalised by two mappings • skill function s • associates to each problem a collection of subsets of skills, each of which consists of those skills sufficient for solving the problem • problem function p • associates to each subset of skills the set of problems that can be solved in it • both concepts are equivalent, i.e. given one function the other is uniquely determined • the assignment of skills puts constraints on the possible knowledge states and thus defines a knowledge structure

17. Assigning Skills to Assessment Problems • example • Q = {a, b, c, d} and S = {s, t, u} skill function: corresponding problem function: knowledge structure

18. Problem-based Skill Assessment • step 1 • adaptive assessment of knowledge state • problem c • solved • problem d • solved • problem e • not solved

19. Problem-based Skill Assessment • step 2 • mapping of the knowledge state identified for a learner into the corresponding competence state • using the skill function • example • knowledge state {b} • knowledge state {c} • non-unique assignments have to be resolved

20. Assigning Skills to Learning Objects • once the competence state of a learner has been determined a personalised learning path may be selected • based on assigning skills to learning objects • relationship between learning objects and skills is mediated by two mappings • mapping r associates to each LO a subset of skills (required skills), characterising the prerequisites for dealing with it • mapping t associates to each LO a subset of skills (taught skills), referring to the content actually taught by the LO

21. Assigning Skills to Learning Objects • the mappings r and t • induce a learning structure on the set of LOs • impose constraints on the competence states that can occur • resulting competence structure characterises the learning progress • allow deciding upon next LO, given a certain competence state • referring to learning path of the competence structure • a suitable learning object is selected, featuring • required skills that the learner has already available • taught skills that correspond to next step in learning path

22. Conclusions • extended Knowledge Space Theory • takes into account skills and competencies as psychological constructs underlying the observable behaviour • allows for integrating ontological information • provides a basis for efficient adaptive assessment of skills and competencies • incorporates learning objects into a set-theoretical framework • forms a basis for personalised learning

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