1. Source: Erica MelisLeActiveMath 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. Source: Erica Melis The Partners and Disciplines Helen Pain

3. Source: Erica Melis 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. Source: Erica Melis Some Research Questions How to design feedback and 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 motivation and emotions –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 tools and how to employ them Interoperability of tools Moderate constructivist view

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

6. Source: Erica Melis ActiveMath in Action

7. Source: Erica Melis Adapts to Learning Goals LeAM: competencies

8. Source: Erica Melis … and Scenarios: English

9. Source: Erica Melis and Scenarios: Chinese

10. Source: Erica Melis and Scenarios: Russian

11. Source: Erica Melis Scenario: Detailed

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

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

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

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

16. Source: Erica Melis Tutorial Dialogue

17. Source: Erica Melis Interactive Concept Map Tool

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

19. Source: Erica Melis Conclusion 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

20. Source: Erica Melis 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. Source: Erica Melis Feedback 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 LeAM: more tutorial strategies, tutorial dialogues

22. Source: Erica Melis Knowledge Representation in ActiveMath –OMDoc XML-language: structures semantics (OpenMath, MathML) –ontology for Mathematics –ActiveMath extensions by didactical metadata several relations several verbosities (book, slide, summary) – educational ontology

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

24. Source: Erica Melis Instructional items in OMDoc A monoid is a s tructure [M times unit] in which [M times] is a semi-group with unit e A monoid is a s tructure [M times unit] in which [M times] is a semi-group with unit e A monoid is a s tructure [M times unit] in which [M times] is a semi-group with unit e... Definition of a monoid A monoid is a s tructure [M times unit] in which [M times] is a semi-group with unit e... Definition of a monoid A monoid is a s tructure in which is a semi-group with unit....

25. Source: Erica Melis Architecture of ActiveMath browser Course generator Pedagogical rules MBase Session Manager WebServer history User model profile evaluator http request CAS Math systems XSLT htmlxml

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