Learner Modelling and Adaptation in Math-Bridge Sergey Sosnovsky Saarland University
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Learner Modelling and Adaptation in Math-Bridge Sergey Sosnovsky!
Saarland University
Learning Content Presentation: Dashboard
Learning Content Presentation: Main View
Personalised Course Generation
1 2
3
4
Adaptive Link Annotation
Micro-course generation
Intelligent Adaptive e-Learning System:Main Components
Instructional Content
Interaction
0..1..1..0..1..1..
DomainModel !!!
Learner Model
PedagogicalModel
Adaptation
Me t a d a t a
Learning Events of Math-Bridge
0..1..1..0..1..1..
Rich continuos stream of learning data ❖ Any interaction of the student with Math-Bridge causes
an event in the system logs;!
❖ More than 30 types of events (e.g., system login/logout, course started/finished, exercise started/finished, etc.);!
❖ More than 50 attributes (e.g., for the exerciseStep event: time, user, session, courseId, successRate, metadataText, userInputDelay, userInputText,…);
Content and knowledge modelling in Math-Bridge
Instructional Content
DomainModel !!!
Me t a d a t a
Knowledge Items
Abstract Concepts
Concepts with content
Content
Metadata❖ Descriptive!
❖ author!❖ date…!
❖ Pedagogical!❖ difficulty!❖ competency!❖ educational level…!
❖ Semantic!❖ is prerequisite for!❖ is exercise for!❖ is introduction for…
Ontology❖ 536 symbols!
❖ will, probably, need to be extended
Martin Homik 5th Sakai Conference 2006, Vancouver !14
Knowledge Representation
D
S
EX
P
T
S S
S
isA
D
D T
XE
Definition
E
Symbol
Example
Theorem
ProofExercise
X
forfor
forforfor
D D
for counter
P
for
S S
for depends on
depends on
Abstract Layer
Content Layer
Satellite Layer
OMDoc❖ All content and its metadata, are
represented in OMDoc!
❖ OMDoc is an XML dialect developed for math documents !
❖ Formulas are written in OpenMath!
❖ OpenMath is an extensible standard for representing the semantics of mathematical objects
<definition id="c6s1p4_Th2_def_monoid" for="c6s1p4_monoid„ <metadata> <depends-on> <ref theory="cp1_Th3" name="structure" /> </depends-on> <Title xml:lang="en">Definition of a monoid</Title> </metadata> <CMP xml:lang="en" format="omtext"> A monoid is a <ref xref="cp1_Th3_def_structure"> structure </ref> <OMOBJ> <OMS cd="elementary" name="ordered-triple"/> <OMV name="M"/> <OMS cd="cp4_Th2" name="times"/> <OMS cd="cp4_Th2" name="unit"/> </OMOBJ> in which <OMOBJ> <OMS cd="elementary" name="ordered-pair"/> <OMV name="M"/> <OMS cd="cp4_Th2" name="times"/> </OMOBJ> is a semi-group with <ref xref="c6s1p3_Th2_def_unit">e</ref> <OMOBJ xmlns="http://www.openmath.org/OpenMath"> <OMS cd="cp4_Th2" name="unit"/> </OMOBJ>. </CMP> <FMP><OMOBJ> ... </OMOBJ></FMP> </definition>
Definition of a Monoid
Learner Modelling in Math-Bridge
Background
❖ Dynamic Overlay Model with forgetting!
❖ Specific challenges !
❖ Dynamic Domain Model!
❖ Dynamic Content Base and Metadata annotations!
❖ SLM (Eric, Arndt, Salim)
Evidences
❖ (s,e,c,p,l,a)!
❖ Student!
❖ Exercise!
❖ Concept!
❖ Competency!
❖ Achievement
Updates❖ Direct evidence - individual events for 1 concept, 1
process!
❖ Indirect evidence - propagation!
❖ Intra-Concept: across competencies!
❖ Inter-Concept: prerequisite, for
Amplitude of the update❖ IRT:
psychometric theory for testing!
❖ Used successfully since 20+ years
IRT Usage
❖ Pool of calibrated items with known ICC!
❖ Logistic function (difficulty, discrimination, guess)!
❖ Idea: Measure latent trait 𝞱!
❖ Administer sequence of test items!
❖ 𝞱 uncovered by responses to items
IRT vs. MthBridge—IRTPropoer IRT MathBridge—IRT
ICC Empirical Theoretical
Input Item Response Sequence
Sparse Evidences
Answers Dichotomous Continuous
Difficulty Single factor Difficulty/Competency
IndependenceItems are
independent of each other
Exercises are often related
LearningNo learning between
or during assessment
Learning is essential for Math-Bridge
Belief Masses
❖ Round achievement to {1,0}!
❖ if r=1: m(H(b)) = P(correct | 𝞱 =b)!
❖ if r=0: m(H(b)) = 1-P(correct | 𝞱 =b)!
!
❖ restrict updated hypotheses to Information Radius interval: [irtdiff ±δ]
𝞱
p(co
rrec
t)
Mastery inference
Learning Event (Raw evidence)
𝞱
p(co
rrec
t)
Dempster-Shafer Best belief about mastery
Competency Models
❖ Bloom (subset: K / C / A)!
❖ PISA (☈ operationalization)!
❖ Math-Bridge !
❖ TU-D cognitive operators!
❖ Commonality: Multi-dimensional overlays
Exercise
Concept
is For
Competency
Mastery Aggregate❖ Single “mastery” value!
❖ Necessary for Course Generation!
❖ Implemented as (weighted) average of competencies
Adaptation in Math-Bridge
PedagogicalModel Adaptation
Scenario LearnNewIntroduce
Develop
Practice
Connect
Reflect
Scenario LearnNew
Introduce
Develop
Practice
Connect
Reflect
Motivate
Context
Illustrate
Prerequisites
Scenario LearnNew
Introduce
Develop
Practice
Connect
Reflect
Motivate
Context
Illustrate
Prerequisites
(:method (motivate! ?c) ((learnerProperty hasEducationalLevel ?el) (learnerProperty hasAnxiety ?c ?an) (?an <= 2) (GetElement ((class Exercise) (class Introduction) (relation isFor ?c) (property hasLearningContext ?el) (property hasDifficulty very_easy)))) ((insert! ?element)))
IF
THEN
Scenario LearnNew
Introduce
Develop
Practice
Connect
Reflect
Motivate
Context
Illustrate
Prerequisites
(:method (motivate! ?c) ((learnerProperty hasEducationalLevel ?el) !! (GetElement ((class Example) (class Introduction) (relation isFor ?c) (property hasLearningContext ?el) (property hasDifficulty very_easy)))) ! ((insert! ?element)))
IF
THEN
(:method (motivate! ?c) ((learnerProperty hasEducationalLevel ?el) (learnerProperty hasAnxiety ?c ?an) (?an <= 2) (GetElement ((class Exercise) (class Introduction) (relation isFor ?c) (property hasLearningContext ?el) (property hasDifficulty very_easy)))) ((insert! ?element)))
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