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Helping Students to Learn Matehmatics Beyond LMS

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Martin Homik
Martin Homik

Descrinbes how to integrate ActiveMath in learning management systems.

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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
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
What/Who is ActiveMath? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Artificial Intelligence in ActiveMath ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Pedagogical Goals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Pedagogical Approaches ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Hands-On ActiveMath: Main Page by author/teacher created by learner
Book Page
Chinese Student
German Student
Spanish Student
“Internationalized” Pictures ,[object Object],[object Object],[object Object]
“ Internationalized” Applets ,[object Object],[object Object],[object Object]
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 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
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Technological Principles ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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
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
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>
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>
Content Presentation Knowledge Base Knowledge Base Fetching Pre-processing Transformation Assembly Personalisation Compilation Presentation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],View Templates
Math: XHTML+MathML, PDF
Course Generation User Model Knowledge Base Pedagogical Rules Course Generator
Course Generation (1) Goal concept ,[object Object],[object Object],[object Object],[object Object]
Course Generation (2) Goal concept ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Course Generation (3) Goal concept ,[object Object],[object Object],[object Object]
iCMap Verification ,[object Object],[object Object],[object Object],[object Object],Knowledge Base <exercise ..> … </exercise>
MVC Architecture
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
ActiveMath and Sakai: Why?
ActiveMath and Sakai: Why ?
ActiveMath integration into Sakai: how ? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Conclusion
Thank you! Questions?

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Helping Students to Learn Matehmatics Beyond LMS

  • 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
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  • 7. Hands-On ActiveMath: Main Page by author/teacher created by learner
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  • 14. Exercise with different feedback 3. Correct answer 2. Correct, but not simplified. 1. False, but error identified
  • 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
  • 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
  • 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.
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  • 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>
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  • 45. Course Generation User Model Knowledge Base Pedagogical Rules Course Generator
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Hinweis der Redaktion

  1. Present ActiveMath … comes with mathematical content … and a set of tools and services But it lacks sophisticated LMS functionality