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LeActiveMath

LeActiveMath. Language-enhanced, user-adaptive, interactive eLearning for Mathematics. Erica Melis Competence Center for Technology-Enhanced Learning German Research Center for Artificial Intelligence (DFKI) and University of Saarland. Helen Pain. The Partners and Disciplines.

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LeActiveMath

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  1. LeActiveMath Language-enhanced, user-adaptive, interactive eLearning for Mathematics Erica Melis Competence Center for Technology-Enhanced Learning German Research Center for Artificial Intelligence (DFKI) and University of Saarland

  2. Helen Pain The Partners and Disciplines

  3. Technology-Oriented but Aware of …Contexts • Adaptivity and personalisation, pedagogical scenarios • Tutorial dialogues and other language facilities • Motivational and emotional diagnosis and reaction (autonomy & approval) • Open student modeling • Learning-effective tools • Reusable tools • Semantic Web application • semantic representation and reuse • Web services/distributed architecture • Open repository of interactive exercises • … • Classroom evaluation, work with schools

  4. Some Research Questions Moderate constructivist view • How to design feedbackand tutorial dialogues for • discovery of mistakes • deep reasoning • self-explanation, reflection • How to evaluate student input (equivalence? …) • Other support of meta-cognition • How to diagnose and react to motivationandemotions • approval, autonomy, anxiety • How open should learner model be • How to learn from errors • What is useful adaptivity and how to generate adaptively • How to reuse material • How to operationalize competencies • Which useful toolsand how to employ them • Interoperability of tools

  5. ActiveMath 2004 http://www.activemath.org • - personalized/adapted content • variety of types of exercises • - feedback and prototypicallearning suggestions • OMDoc (XML)-representation • Internationalized system • …

  6. ActiveMath in Action

  7. Adapts to Learning Goals LeAM: competencies

  8. … and Scenarios: English

  9. and Scenarios: Chinese

  10. and Scenarios: Russian

  11. Scenario: Detailed

  12. Scenario: Overview LeAM: More pedagogically validated scenarios replanning, editable

  13. LeAM: more adaptivity and flavours Mathematics Biology Engineering Adaptivity: Field

  14. Learner Model LeAM: extended learner model… what should be open?

  15. Feedback Various tutorial strategies • Orienting feedback (modulo equivalence) • Effort by student • … • Knowledge of correct result

  16. Tutorial Dialogue

  17. Interactive Concept Map Tool

  18. Exercises with CAS Maple LeAM: services based on OpenMath

  19. Collaboration of pedagogy, cognition, computer science, users Improve learning and motivation by technology Intelligent tutoring Adaptive hypermedia User modeling Computational linguistics Web technology Language technology Automated reasoning Machine learning Computer algebra systems Conclusion

  20. Personalization, Motivation , Dialogues • Jan. 2004 – Dec. 2006 • - best rating in first FP6 call DFKI Eurice GmbH University Edinburgh University Northumbria TU Eindhoven Universidad Malaga Universität Augsburg Ernst Klett Verlag Universität des Saarlandes 

  21. Feedback LeAM: more tutorial strategies, tutorial dialogues • Local and global feedback • State correctness/incorrectnes THEN give away correct solution • Check for final solution and return correctness • Feedback on every step vs. on evaluation request

  22. Knowledge Representation in ActiveMath • OMDocXML-language: • structures • semantics (OpenMath, MathML) • ontology for Mathematics • ActiveMath extensions by • didactical metadata • several relations • several verbosities (book, slide, summary) • educational ontology

  23. Relations xxx-for, depends-on prerequisite similar-to counterexample Exercises and examples difficulty field abstractness type learning activity learning context Dublin Core Metadata… Two Ontologies

  24. Instructional items in OMDoc <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 asemi-group with<ref xref="c6s1p3_Th2_def_unit">unit</ref> <OMOBJ xmlns="http://www.openmath.org/OpenMath"> <OMS cd="cp4_Th2" name="unit"/> </OMOBJ>. </CMP> <FMP><OMOBJ> ... </OMOBJ></FMP> </definition> <definition id="c6s1p4_Th2_def_monoid" for="c6s1p4_monoid"> A monoid is astructure [M times unit] in which [M times] is asemi-group with unit e </definition> <definition id="c6s1p4_Th2_def_monoid" for="c6s1p4_monoid"> <CMP xml:lang="en" format="omtext"> A monoid is astructure [M times unit] in which [M times] is asemi-group with unit e </CMP> <FMP><OMOBJ> ... </OMOBJ></FMP> </definition> <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 astructure [M times unit] in which [M times] is asemi-group with unit e </CMP> <FMP><OMOBJ> ... </OMOBJ></FMP> </definition> A monoid is astructure [M times unit] in which [M times] is asemi-group with unit e

  25. xml html XSLT Session Manager WebServer browser request http Coursegenerator Pedagogical rules CAS Math systems MBase User model history profile evaluator Architecture of ActiveMath

  26. Pedagogical Rules IF field(user) = ?F THEN addEx(?C, field)=?F IF learnGoal=appl AND uk(?C low) THEN addEx(?C,diff)=(1,1,2,3) THEN addEx(?C, diff)=(3) IF learnGoal=appl AND NOT uk(?C low) pattern=(concept,exm,ex) IF scenario(overview) THEN pattern=(motiv,intro, concept,exm,exc) IF scenario(detail) THEN

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