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Learner Modelling and Adaptation in Math-Bridge
- 1. Learner Modelling and Adaptation in Math-Bridge Sergey Sosnovsky! Saarland University
- 2. Learning Content Presentation: Dashboard
- 3. Learning Content Presentation: Main View
- 4. Personalised Course Generation 1 2 3 4
- 7. Intelligent Adaptive e-Learning System: Main Components Instructional Content Interaction 0..1..1 ..0..1.. 1.. Domain Model ! ! ! Learner Model Pedagogical Model Adaptation Me t a d a t a
- 9. 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,…);
- 10. Content and knowledge modelling in Math-Bridge Instructional Content Domain Model ! ! ! Me t a d a t a
- 11. Knowledge Items Abstract Concepts Concepts with content Content
- 12. Metadata ❖ Descriptive! ❖ author! ❖ date…! ❖ Pedagogical! ❖ difficulty! ❖ competency! ❖ educational level…! ❖ Semantic! ❖ is prerequisite for! ❖ is exercise for! ❖ is introduction for…
- 13. Ontology ❖ 536 symbols! ❖ will, probably, need to be extended
- 14. 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
- 15. 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
- 17. Background ❖ Dynamic Overlay Model with forgetting! ❖ Specific challenges ! ❖ Dynamic Domain Model! ❖ Dynamic Content Base and Metadata annotations! ❖ SLM (Eric, Arndt, Salim)
- 18. Evidences ❖ (s,e,c,p,l,a)! ❖ Student! ❖ Exercise! ❖ Concept! ❖ Competency! ❖ Achievement
- 19. Updates ❖ Direct evidence - individual events for 1 concept, 1 process! ❖ Indirect evidence - propagation! ❖ Intra-Concept: across competencies! ❖ Inter-Concept: prerequisite, for
- 20. Amplitude of the update ❖ IRT: psychometric theory for testing! ❖ Used successfully since 20+ years
- 21. 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
- 22. IRT vs. MthBridge—IRT Propoer IRT MathBridge—IRT ICC Empirical Theoretical Input Item Response Sequence Sparse Evidences Answers Dichotomous Continuous Difficulty Single factor Difficulty/ Competency Independence Items are independent of each other Exercises are often related Learning No learning between or during assessment Learning is essential for Math-Bridge
- 23. 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(correct)
- 24. Mastery inference Learning Event (Raw evidence) 𝞱 p(correct) Dempster-Shafer Best belief about mastery
- 25. Competency Models ❖ Bloom (subset: K / C / A)! ❖ PISA (☈ operationalization)! ❖ Math-Bridge ! ❖ TU-D cognitive operators! ❖ Commonality: Multi-dimensional overlays Exercise Concept is For Competency
- 26. Mastery Aggregate ❖ Single “mastery” value! ❖ Necessary for Course Generation! ❖ Implemented as (weighted) average of competencies
- 30. 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
- 31. 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)))