This document summarizes the ActiveMath learning environment, its goals and features. It discusses how ActiveMath uses artificial intelligence techniques like user modeling, adaptive interfaces and feedback to personalize learning. It also describes how ActiveMath represents knowledge semantically and generates courses by retrieving reusable content. Finally, it discusses how integrating ActiveMath with the Sakai learning management system provides user management and a way to make ActiveMath's tools and open content available within Sakai.

1. Helping Students to Learn Mathematics Beyond LMS Martin Homik Sakai Conference 2006, Vancouver Saarland University, Saarbrücken German Research Center for Artificial Intelligence, DFKI GmbH www. .org

7. Hands-On ActiveMath: Main Page by author/teacher created by learner

8. Book Page

9. Chinese Student

10. German Student

11. Spanish Student

14. Exercise with different feedback 3. Correct answer 2. Correct, but not simplified. 1. False, but error identified

15. Exercise with Input Editor

16. Exercise with Input Editor

17. Exercise with hints Problem statement

18. Exercise with hints Hint! Problem statement

19. Exercise Student asks for another hint

20. Exercise Chooses wrong answer Repeat problem statement

21. Exercise Student asks for another hint

22. Exercise Answer is correct Continue with sub problem

23. Exercise Rest is correct

24. Interactive Concept Mapping Workspace Drag-and-drop Drag-and-drop Palette

25. Search derivation

26. Search

27. Search (continued)

28. Search (continued)

29. Function Plotter

30. Course Generation 1. Select area of interest

31. Course Generation 2. Give your book a title 3. Describe your book 4. Select book type

32. Course Generation 5. Select book topics

33. Course Generation Approve

34. Course Generation: Final Book

35. More Tools

36. Content Projects de 50 students, 200 pages HTW Saarland Statistics 100 pages 70 students 50 pages 100 exercises 20 students 300 pages 30 pages 50 pages (exc) 250 students 100 pages ) 3x50 students 150 students… 450 pages LeActiveMath Calculus Universität Augsburg University of Glasgow de, en, es Optimization, Operations Research Mary State University ru, en 1st year Calculus U. Westminster, London en Algebra Interactive! TU/Eindhoven, DFKI en Analysis Individuell Uni Koblenz Uni Saarland de Matheführerschein FH Dortmund 3 schools de Fractions Gesamtschule Bellevue de

39. Knowledge Representation D S E X P T S S S isA D D T X E Definition E Symbol Example Theorem Proof Exercise X for for for for for D D for counter P for S S for depends on depends on Abstract Layer Content Layer Satellite Layer

40. Metadata X Learning context school, university, .. Difficulty easy, medium, difficult Abstractness abstract, neutral, concrete Typical learning time Field mathematics, biology, physics, .. Representation speech, images, numbers, … Competency think, argue, model, solve, .. Competency level knowledge, multistep, complex

41. Example OMDoc <definition id=&quot;def_diff&quot; for=&quot;deriv_symbols/diff&quot;> <metadata> <Title xml:lang=&quot;en&quot;>Definition of the derivative, resp., differential quotient</Title> <Title xml:lang=&quot;de&quot;>Definition der Ableitung bzw. des Differentialquotienten</Title> <extradata>…</extradata> </metadata> <CMP xml:lang=&quot;en&quot;> A <textref xref=&quot;functions_symbols/function&quot;>function</textref> $f$ is called <highlight type=&quot;important&quot;>differentiable at $x_0$</highlight> … </CMP> <CMP xml:lang=&quot;de&quot;> Eine <textref xref=&quot;functions_symbols/function&quot;>Funktion</textref> $f$ heißt <highlight type=&quot;important&quot;>differenzierbar an der Stelle $x_0$</highlight> … </CMP> <CMP xml:lang=&quot;x-all&quot;> $ap(diff(f),x_0)=lim(x_0,both_sides,lambda(x,(ap(f,x)-ap(f,x_0))/(x-x_0)))$. </CMP> </definition>

42. Example OMDoc Metadata <metadata> … <extradata> <relation type=&quot;domain_prerequisite&quot;> <ref xref=&quot;diffquot_symbols/diff_quot&quot;/> <ref xref=&quot;maplimits_symbols/maplimit&quot;/> </relation> <learningcontext value=&quot;secondary_education&quot;/> <learningcontext value=&quot;higher_education&quot;/> <learningcontext value=&quot;university_first_year&quot;/> <field value=&quot;all&quot;/> <typicallearningtime value=&quot;00:01:00&quot;/> <representation value=&quot;verbal&quot;/> <representation value=&quot;symbolic&quot;/> <abstractness value=&quot;abstract&quot;/> </extradata> </metadata>

44. Math: XHTML+MathML, PDF

45. Course Generation User Model Knowledge Base Pedagogical Rules Course Generator

50. MVC Architecture

52. ActiveMath and Sakai: Why?

53. ActiveMath and Sakai: Why ?

56. Thank you! Questions?