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Helping Students to Learn Matehmatics Beyond LMS


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Descrinbes how to integrate ActiveMath in learning management systems.

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Helping Students to Learn Matehmatics Beyond LMS

  1. 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
  2. 2. Overview <ul><li>What is ActiveMath? </li></ul><ul><ul><li>Motivation, tools and content </li></ul></ul><ul><li>Technological basis </li></ul><ul><ul><li>Knowledge representation and architecture </li></ul></ul><ul><li>Integration into Sakai </li></ul><ul><ul><li>Why and how? </li></ul></ul><ul><li>Conclusion </li></ul>
  3. 3. What/Who is ActiveMath? <ul><li>User-adaptive, personalization </li></ul><ul><li>Web-based, open architecture </li></ul><ul><li>Interactive exercises </li></ul><ul><li>Feedback and suggestions </li></ul><ul><li>Semantic knowledge representation </li></ul><ul><li>Integrated learning tools and repositories </li></ul>
  4. 4. Artificial Intelligence in ActiveMath <ul><li>User modeling </li></ul><ul><li>Content planning </li></ul><ul><li>Adaptive user interfaces </li></ul><ul><li>Problem solving systems, deduction systems </li></ul><ul><li>Knowledge representation </li></ul><ul><li>Error diagnosis </li></ul><ul><li>Agent-based feedback </li></ul><ul><li>Natural language processing </li></ul>
  5. 5. Pedagogical Goals <ul><li>Personalization </li></ul><ul><ul><li>Contents, exercises </li></ul></ul><ul><ul><li>Presentation, language </li></ul></ul><ul><ul><li>Feedback, support </li></ul></ul><ul><li>Interaction and self-regulation </li></ul><ul><ul><li>For content </li></ul></ul><ul><ul><li>In interactive exercises </li></ul></ul><ul><ul><li>Learning tools </li></ul></ul><ul><ul><li>Reflection </li></ul></ul><ul><li>Diagnosis and feedback </li></ul><ul><ul><li>Motivational support </li></ul></ul>
  6. 6. Pedagogical Approaches <ul><li>OECD PISA framework: competencies </li></ul><ul><ul><li>problem solving, </li></ul></ul><ul><ul><li>the use of mathematical language </li></ul></ul><ul><ul><li>mathematical modeling </li></ul></ul><ul><li>Problem-based learning </li></ul><ul><li>Formalization of pedagogical strategies </li></ul><ul><li>Meta-cognitive abilities </li></ul><ul><li>Thoughtful processing of information, tutorial dialogue </li></ul>
  7. 7. Hands-On ActiveMath: Main Page by author/teacher created by learner
  8. 8. Book Page
  9. 9. Chinese Student
  10. 10. German Student
  11. 11. Spanish Student
  12. 12. “Internationalized” Pictures <ul><li>English </li></ul><ul><li>German </li></ul><ul><li>Spanish </li></ul>
  13. 13. “ Internationalized” Applets <ul><li>English </li></ul><ul><li>German </li></ul><ul><li>Spanish </li></ul>
  14. 14. Exercise with different feedback 3. Correct answer 2. Correct, but not simplified. 1. False, but error identified
  15. 15. Exercise with Input Editor
  16. 16. Exercise with Input Editor
  17. 17. Exercise with hints Problem statement
  18. 18. Exercise with hints Hint! Problem statement
  19. 19. Exercise Student asks for another hint
  20. 20. Exercise Chooses wrong answer Repeat problem statement
  21. 21. Exercise Student asks for another hint
  22. 22. Exercise Answer is correct Continue with sub problem
  23. 23. Exercise Rest is correct
  24. 24. Interactive Concept Mapping Workspace Drag-and-drop Drag-and-drop Palette
  25. 25. Search derivation
  26. 26. Search
  27. 27. Search (continued)
  28. 28. Search (continued)
  29. 29. Function Plotter
  30. 30. Course Generation 1. Select area of interest
  31. 31. Course Generation 2. Give your book a title 3. Describe your book 4. Select book type
  32. 32. Course Generation 5. Select book topics
  33. 33. Course Generation Approve
  34. 34. Course Generation: Final Book
  35. 35. More Tools
  36. 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
  37. 37. Overview <ul><li>What is ActiveMath? </li></ul><ul><ul><li>Motivation, tools and content </li></ul></ul><ul><li>Technological basis </li></ul><ul><ul><li>Knowledge representation and architecture </li></ul></ul><ul><li>Integration into Sakai </li></ul><ul><ul><li>Why and how? </li></ul></ul><ul><li>Conclusion </li></ul>
  38. 38. Technological Principles <ul><li>Reuse of contents through standards (OpenMath, OMDoc, partly LOM) </li></ul><ul><li>Reuse and interoperability of tools and components </li></ul><ul><li>Semantics for formulae </li></ul><ul><li>Various output formats and appearances </li></ul><ul><li>Open web-architecture, modular design, configurability </li></ul><ul><li>Standard XML-communication </li></ul><ul><li>Platform-independence </li></ul><ul><li>Open source </li></ul>
  39. 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. 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. 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. 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>
  43. 43. Content Presentation Knowledge Base Knowledge Base Fetching Pre-processing Transformation Assembly Personalisation Compilation Presentation <ul><li>Retrieve single learning items from knowledge base </li></ul><ul><li>Inserts server-specific information into the XML content </li></ul><ul><li>Transformation into the output format by XSLT </li></ul><ul><li>Assemble the fragments to form the requested page </li></ul><ul><li>Add personalized data to the document </li></ul><ul><li>Compile in case of LaTeX </li></ul><ul><li>Present </li></ul>View Templates
  44. 44. Math: XHTML+MathML, PDF
  45. 45. Course Generation User Model Knowledge Base Pedagogical Rules Course Generator
  46. 46. Course Generation (1) Goal concept <ul><li>1. Retrieve content from knowledge base </li></ul><ul><ul><li>Start with goal concept </li></ul></ul><ul><ul><li>Collect recursively concepts the goal depends on </li></ul></ul><ul><ul><li>… plus additional information (e.g. examples) </li></ul></ul>
  47. 47. Course Generation (2) Goal concept <ul><li>2. Filter concepts </li></ul><ul><ul><li>According to pedagogical rules </li></ul></ul><ul><ul><li>According to the user model </li></ul></ul><ul><li>Defrule PatternExamPrep </li></ul><ul><ul><li>Allow (definition, exercise) </li></ul></ul><ul><ul><li>Order (definition, exercise) </li></ul></ul><ul><li>Defrule ReqAppEx </li></ul><ul><ul><li>Allow (definition, exercise) </li></ul></ul><ul><ul><li>Test (user-kb(definition)<0.3) </li></ul></ul><ul><ul><li>Add ex-for(definition 0.3) </li></ul></ul><ul><ul><li>ex-for(definition 0.5) </li></ul></ul>
  48. 48. Course Generation (3) Goal concept <ul><li>3. Linearize graph </li></ul><ul><ul><li>according to mathematical dependency </li></ul></ul><ul><ul><li>according to pedagogical dependency </li></ul></ul>
  49. 49. iCMap Verification <ul><li>Match directly against knowledge base and predefines exercise </li></ul><ul><li>Some reasoning: transitivity, equivalence </li></ul><ul><li>Fault-tolerance </li></ul><ul><li>Suggestions </li></ul>Knowledge Base <exercise ..> … </exercise>
  50. 50. MVC Architecture
  51. 51. Overview <ul><li>What is ActiveMath? </li></ul><ul><ul><li>Motivation, tools and content </li></ul></ul><ul><li>Technological basis </li></ul><ul><ul><li>Knowledge representation and architecture </li></ul></ul><ul><li>Integration into Sakai </li></ul><ul><ul><li>Why and how? </li></ul></ul><ul><li>Conclusion </li></ul>
  52. 52. ActiveMath and Sakai: Why?
  53. 53. ActiveMath and Sakai: Why ?
  54. 54. ActiveMath integration into Sakai: how ? <ul><li>Many common technologies </li></ul><ul><ul><li>web-application, logging, velocity, hibernate, .... </li></ul></ul><ul><li>Make ActiveMath a web-application tool </li></ul><ul><ul><li>drop-in-Sakai installation </li></ul></ul><ul><ul><li>single sign-on </li></ul></ul><ul><ul><li>push all user-manipulations to Sakai </li></ul></ul><ul><ul><ul><li>good for privacy </li></ul></ul></ul><ul><ul><ul><li>good for administration </li></ul></ul></ul><ul><ul><li>provide tools for links to ActiveMath facilities </li></ul></ul><ul><ul><ul><li>list my books, link to this book, .... </li></ul></ul></ul><ul><li>Thus far: </li></ul><ul><ul><li>single-sign-on working </li></ul></ul>
  55. 55. <ul><li>ActiveMath is a complex learning environment </li></ul><ul><ul><li>Integrates a variety of tools </li></ul></ul><ul><ul><li>Offers diverse open content </li></ul></ul><ul><li>Sakai provides missing user-centered management </li></ul><ul><li>Sakai + ActiveMath = Powerful Symbiosis </li></ul>Conclusion
  56. 56. Thank you! Questions?