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http://css.uni-graz.at Competence-based knowledge structures for personalised learning Jürgen Heller, Christina Steiner, Cord Hockemeyer, & Dietrich Albert Cognitive Science Section, Department of Psychology, University of Graz, Austria ProLearn-iClass Thematic Workshop 3-4 March 2005, Leuven
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http://css.uni-graz.at 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
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http://css.uni-graz.at 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?
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http://css.uni-graz.at 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 correct answer to other problems captured by surmise relation Knowledge Space Theory d a c b e
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http://css.uni-graz.at 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} Knowledge Space Theory d a c b e
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http://css.uni-graz.at knowledge structure Knowledge Space Theory
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http://css.uni-graz.at 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 Knowledge Space Theory
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http://css.uni-graz.at 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 Competence-based Knowledge Structures
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http://css.uni-graz.at 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 Competence-based Knowledge Structures
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http://css.uni-graz.at 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
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http://css.uni-graz.at Deriving Skills from Domain Ontologies a)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‘
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http://css.uni-graz.at Deriving Skills from Domain Ontologies a)skills as sub-structures of a concept map a structure on the skills is induced, for example, by set- inclusion if skill x is subset of skill y then skill x is subordinated to skill y
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http://css.uni-graz.at Deriving Skills from Domain Ontologies b)component-attribute approach concept map represents results from curriculum and content analysis basic concepts to be taught e.g. ‘Theorem of Pythagoras’ learning objectives related to these concepts include required activities of the learner may be captured by action verbs e.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’
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http://css.uni-graz.at Deriving Skills from Domain Ontologies b)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´ c3c3 c4c4 c1c1 c2c2 a1a1 a2a2
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http://css.uni-graz.at Deriving Skills from Domain Ontologies b)component-attribute approach building the direct product of these two component orderings results in a surmise relation on the skills e.g. skill c 2 a 2 is a prerequisite to the skills c 2 a 1, c 1 a 2, and c 1 a 1
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http://css.uni-graz.at 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
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http://css.uni-graz.at Assigning Skills to Assessment Problems example Q = {a, b, c, d} and S = {s, t, u} skill function: s(a)={{s, u}} s(b)={{u}} s(c)={{s}, {t}} s(d)={{t}} p(Ø)=Ø p({s})={c}{c} p({t})={c, d} p({u})={b}{b} p({s, t})={c, d} p({s, u})={a, b, c} p({t, u})={b, c, d} p(S)=Q corresponding problem function: knowledge structure
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http://css.uni-graz.at step 1 adaptive assessment of knowledge state problem c solved problem d solved problem e not solved Problem-based Skill Assessment
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http://css.uni-graz.at 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 s(a)={{s, u}} s(b)={{u}} s(c)={{s}, {t}} s(d)={{t}}
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http://css.uni-graz.at 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
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http://css.uni-graz.at 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
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http://css.uni-graz.at 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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http://css.uni-graz.at THANK YOU FOR YOUR ATTENTION!!!
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