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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


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 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?


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


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}


d

a

c

b

e


{a, b, c, d, e}

{a, b, c, e}

{b, c, e}

{b, c}

{b} {a}

{a, b}

{a, b, c}

{a, b, c, d}

knowledge structure



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


{a, b, c, d, e}

{a, b, c, e}

{b, c, e}

{b, c}

{b} {a}

{a, b}

{a, b, c}

{a, b, c, d}


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



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



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



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‘



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 subordinatedto skill y



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’




concepts with their hierachical structure

e.g. `Theorem of Pythagoras´ prerequisite for Àltitude Theoremćorresponding to curriculum

order on the action verbs

e.g.: `state´ prerequisite for àpply´

c3

c4

c1

c2

a1

a2




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

c2a2

c1a1

c3a2

c1a2

c2a1

c3a1

c4a2

c4a1



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



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}

p({t}) = {c, d}

p({u}) = {b}

p({s, t}) = {c, d}

p({s, u}) = {a, b, c}

p({t, u}) = {b, c, d}

p(S) = Q

corresponding problem function:

knowledgestructure


{a, b, c, d, e}

{a, b, c, e}

{b, c, e}

{b, c}

{b} {a}

{a, b}

{a, b, c}

{a, b, c, d}

step 1

adaptive assessment of knowledge state

problem c

solved

problem d

solved

problem e

not solved




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


THANK YOU FOR YOUR ATTENTION!!!

http://css.uni-graz.at competence-based knowledge structures for personalised learning jürgen...

Documents

structure skills

potential knowledge

domain ontologies skills

c b e slide

set q of assessment

certain problems

subsets of problems

underlying skills