Le Active Math Language-enhanced user-adaptive interactive e Learning

Le. Active. Math Language-enhanced, user-adaptive, interactive e. Learning for Mathematics Erica Melis Competence Center for Technology-Enhanced Learning German Research Center for Artificial Intelligence (DFKI) and University of Saarland Source: Erica Melis

The Partners and Disciplines Helen Pain 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 Source: Erica Melis

Some Research Questions Moderate constructivist view • • • 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 Source: Erica Melis

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

Active. Math in Action Source: Erica Melis

Adapts to Learning Goals Source: Erica Melis Le. AM: competencies

… and Scenarios: English Source: Erica Melis

and Scenarios: Chinese Source: Erica Melis

and Scenarios: Russian Source: Erica Melis

Scenario: Detailed Source: Erica Melis

Scenario: Overview Le. AM: More pedagogically validated scenarios replanning, editable Source: Erica Melis

Adaptivity: Field Le. AM: more adaptivity and flavours Mathematics Biology Engineering Source: Erica Melis

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

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

Tutorial Dialogue Source: Erica Melis

Interactive Concept Map Tool Source: Erica Melis

Exercises with CAS Maple Source: Erica Melis Le. AM: services based on Open. Math

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 Source: Erica Melis

Personalization, Motivation , Dialogues - Jan. 2004 – Dec. 2006 - best rating in first FP 6 call Source: Erica Melis DFKI Eurice Gmb. H University Edinburgh University Northumbria TU Eindhoven Universidad Malaga Universität Augsburg Ernst Klett Verlag Universität des Saarlandes

Feedback Le. AM: 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 Source: Erica Melis

Knowledge Representation in Active. Math – OMDoc XML-language: • structures • semantics (Open. Math, Math. ML) – ontology for Mathematics – Active. Math extensions by • didactical metadata • several relations • several verbosities (book, slide, summary) – educational ontology 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 Source: Erica Melis • Dublin Core

Instructional items in OMDoc A monoid is a structure a monoid structure [M A monoid [M times unit] is a structure in monoid is a A which structure [M in which in which [M times] in a semi-group is which [M times] is a semi-group is a semi-group withsemi-group is a unit e a semi-group is with unit with unit e e . . . . . . . Source: Erica Melis

xml html Web. Server Session Manager Architecture of Active. Math XSLT request Course generator MBase Pedagogical rules User model profile Source: Erica Melis Math CAS systems evaluator history http browser

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