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Learner Modelling and Adaptation in Math-Bridge Sergey Sosnovsky!
Saarland University
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Learning Content Presentation: Dashboard
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Learning Content Presentation: Main View
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Personalised Course Generation
1 2
3
4
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Adaptive Link Annotation
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Micro-course generation
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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
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Learning Events of Math-Bridge
0..1..1..0..1..1..
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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,…);
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Content and knowledge modelling in Math-Bridge
Instructional Content
DomainModel !!!
Me t a d a t a
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Knowledge Items
Abstract Concepts
Concepts with content
Content
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Metadata❖ Descriptive!
❖ author!❖ date…!
❖ Pedagogical!❖ difficulty!❖ competency!❖ educational level…!
❖ Semantic!❖ is prerequisite for!❖ is exercise for!❖ is introduction for…
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Ontology❖ 536 symbols!
❖ will, probably, need to be extended
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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
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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
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Learner Modelling in Math-Bridge
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Background
❖ Dynamic Overlay Model with forgetting!
❖ Specific challenges !
❖ Dynamic Domain Model!
❖ Dynamic Content Base and Metadata annotations!
❖ SLM (Eric, Arndt, Salim)
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Evidences
❖ (s,e,c,p,l,a)!
❖ Student!
❖ Exercise!
❖ Concept!
❖ Competency!
❖ Achievement
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Updates❖ Direct evidence - individual events for 1 concept, 1
process!
❖ Indirect evidence - propagation!
❖ Intra-Concept: across competencies!
❖ Inter-Concept: prerequisite, for
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Amplitude of the update❖ IRT:
psychometric theory for testing!
❖ Used successfully since 20+ years
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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
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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
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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)
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Mastery inference
Learning Event (Raw evidence)
𝞱
p(co
rrec
t)
Dempster-Shafer Best belief about mastery
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Competency Models
❖ Bloom (subset: K / C / A)!
❖ PISA (☈ operationalization)!
❖ Math-Bridge !
❖ TU-D cognitive operators!
❖ Commonality: Multi-dimensional overlays
Exercise
Concept
is For
Competency
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Mastery Aggregate❖ Single “mastery” value!
❖ Necessary for Course Generation!
❖ Implemented as (weighted) average of competencies
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Adaptation in Math-Bridge
PedagogicalModel Adaptation
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Scenario LearnNewIntroduce
Develop
Practice
Connect
Reflect
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Scenario LearnNew
Introduce
Develop
Practice
Connect
Reflect
Motivate
Context
Illustrate
Prerequisites
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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
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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)))