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

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

Knowledge Space Theory  knowledge domain: set of assessment problems a. ½ x 5/6 = ? b. 378 x 605 = ? c 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?

 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

 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

 knowledge structure 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 Knowledge Space Theory

 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

 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

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

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‘

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

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’

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

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

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

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

 step 1  adaptive assessment of knowledge state  problem c  solved  problem d  solved  problem e  not solved Problem-based Skill Assessment

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}}

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

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

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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