Helping Students to Learn Mathematics Beyond LMS   Martin Homik Sakai Conference 2006, Vancouver Saarland University, Saar...
Overview <ul><li>What is ActiveMath? </li></ul><ul><ul><li>Motivation, tools and content </li></ul></ul><ul><li>Technologi...
What/Who is ActiveMath? <ul><li>User-adaptive, personalization </li></ul><ul><li>Web-based, open architecture </li></ul><u...
Artificial Intelligence in ActiveMath <ul><li>User modeling  </li></ul><ul><li>Content planning </li></ul><ul><li>Adaptive...
Pedagogical Goals <ul><li>Personalization </li></ul><ul><ul><li>Contents, exercises </li></ul></ul><ul><ul><li>Presentatio...
Pedagogical Approaches <ul><li>OECD PISA framework: competencies </li></ul><ul><ul><li>problem solving,  </li></ul></ul><u...
Hands-On ActiveMath: Main Page by author/teacher created by learner
Book Page
Chinese Student
German Student
Spanish Student
“Internationalized” Pictures <ul><li>English </li></ul><ul><li>German </li></ul><ul><li>Spanish </li></ul>
“ Internationalized”  Applets <ul><li>English </li></ul><ul><li>German </li></ul><ul><li>Spanish </li></ul>
Exercise with different feedback 3. Correct answer 2. Correct, but not simplified. 1. False, but error identified
Exercise with Input Editor
Exercise with Input Editor
Exercise with hints Problem  statement
Exercise with hints Hint! Problem  statement
Exercise Student asks for another hint
Exercise Chooses wrong answer Repeat problem statement
Exercise Student asks for another hint
Exercise Answer is correct Continue with sub problem
Exercise Rest is correct
Interactive Concept Mapping Workspace Drag-and-drop Drag-and-drop Palette
Search derivation
Search
Search (continued)
Search (continued)
Function Plotter
Course Generation 1. Select area of interest
Course Generation 2. Give your book a title 3. Describe your book 4. Select book type
Course Generation 5. Select book topics
Course Generation Approve
Course Generation: Final Book
More Tools
Content Projects de 50 students,  200 pages  HTW Saarland Statistics  100 pages  70 students 50 pages  100 exercises 20 st...
Overview <ul><li>What is ActiveMath? </li></ul><ul><ul><li>Motivation, tools and content </li></ul></ul><ul><li>Technologi...
Technological Principles <ul><li>Reuse of contents through standards (OpenMath, OMDoc, partly LOM) </li></ul><ul><li>Reuse...
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 ...
Metadata X Learning context school, university, .. Difficulty easy, medium, difficult Abstractness abstract, neutral, conc...
Example OMDoc <definition id=&quot;def_diff&quot; for=&quot;deriv_symbols/diff&quot;> <metadata> <Title xml:lang=&quot;en&...
Example OMDoc Metadata <metadata> … <extradata> <relation type=&quot;domain_prerequisite&quot;> <ref xref=&quot;diffquot_s...
Content Presentation Knowledge Base Knowledge Base Fetching Pre-processing Transformation Assembly Personalisation Compila...
Math: XHTML+MathML, PDF
Course Generation User Model Knowledge Base Pedagogical Rules Course Generator
Course Generation (1) Goal concept <ul><li>1.   Retrieve content from knowledge base </li></ul><ul><ul><li>Start with goal...
Course Generation (2) Goal concept <ul><li>2. Filter concepts </li></ul><ul><ul><li>According to pedagogical rules </li></...
Course Generation (3) Goal concept <ul><li>3. Linearize graph  </li></ul><ul><ul><li>according to mathematical dependency ...
iCMap Verification <ul><li>Match directly against knowledge base and predefines exercise </li></ul><ul><li>Some reasoning:...
MVC Architecture
Overview <ul><li>What is ActiveMath? </li></ul><ul><ul><li>Motivation, tools and content </li></ul></ul><ul><li>Technologi...
ActiveMath and Sakai: Why?
ActiveMath and Sakai: Why ?
ActiveMath integration into Sakai: how ? <ul><li>Many common technologies </li></ul><ul><ul><li>web-application, logging, ...
<ul><li>ActiveMath is a complex learning environment </li></ul><ul><ul><li>Integrates a variety of tools </li></ul></ul><u...
Thank you! Questions?
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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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  • Present ActiveMath … comes with mathematical content … and a set of tools and services But it lacks sophisticated LMS functionality
  • 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?
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