A Learning Environment for Mathematics Martin Homik, Erica Melis -- ActiveMath Group – ABIS 2004, Berlin German Research C...
Outline <ul><li>Features </li></ul><ul><li>Examples </li></ul><ul><li>Key components: </li></ul><ul><ul><li>Knowledge repr...
<ul><li>Adaptive course generation </li></ul><ul><li>Adaptive presentation </li></ul><ul><li>Semantic knowledge representa...
Different users – one topic <ul><li>Anton </li></ul><ul><li>Mathematics </li></ul><ul><li>Bachelor student </li></ul><ul><...
„ Eva‘s Books“
„ A Book“ Good mastery Medium mastery Weak mastery
„ A Book“
Scenario: Overview
Scenario: Exam
Scenario: No sufficient knowledge
Scenario: No sufficient knowledge
Adaptivity: Field Mathematics Biology Physics
Knowledge Representation <ul><li>Extended OMDoc   </li></ul><ul><li>Extension of OpenMath </li></ul><ul><li>Markup format ...
Knowledge Representation <ul><li>Content items </li></ul><ul><li>unique ID </li></ul>Concepts Additional Definitions Asser...
User Model <ul><li>History </li></ul><ul><li>Profile </li></ul><ul><li>Content IDs </li></ul><ul><li>Start/End timestamp  ...
User Model: Justification <ul><li>Concept: </li></ul><ul><li>Concept ID </li></ul><ul><li>Mastery: </li></ul><ul><ul><li>K...
User Model: Update <ul><li>Trigger (Action): </li></ul><ul><li>Page changed </li></ul><ul><li>Exercise finished </li></ul>...
Software Eyetracker (DFKEye) <ul><li>Trace attention on regions </li></ul><ul><li>More fine-grained mastery evaluation </l...
Course Generation User Model mBase 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 ...
Architecture mBase Pedagogical Rules Web Server Session Manager Math Systems Course Generator Presentation Generator (XSLT...
LeActiveMath <ul><li>Tutorial dialogues </li></ul><ul><li>Data base of interactive exercises </li></ul><ul><li>Learning-ef...
Conclusion  www.activemath.org <ul><li>Stable!!! </li></ul><ul><li>Currently available content: </li></ul><ul><ul><li>Anal...
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Abis04

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Presentation of ActiveMath system at the ABIS 2004 event in Berlin.

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  • Let me briefly introduce myself. My name …, working at …, Today I present ActiveMath, a learning environment for Mathematics
  • Abis04

    1. 1. A Learning Environment for Mathematics Martin Homik, Erica Melis -- ActiveMath Group – ABIS 2004, Berlin German Research Center for Artificial Intelligence DFKI GmbH, Saarbrücken
    2. 2. Outline <ul><li>Features </li></ul><ul><li>Examples </li></ul><ul><li>Key components: </li></ul><ul><ul><li>Knowledge representation </li></ul></ul><ul><ul><li>User model </li></ul></ul><ul><ul><li>Course generator </li></ul></ul><ul><li>Conclusion </li></ul>
    3. 3. <ul><li>Adaptive course generation </li></ul><ul><li>Adaptive presentation </li></ul><ul><li>Semantic knowledge representation </li></ul><ul><li>User model </li></ul><ul><li>Pedagogical knowledge </li></ul><ul><li>Interactive exercises </li></ul><ul><li>Suggestion mechanism </li></ul><ul><li>… </li></ul>ActiveMath‘s Features
    4. 4. Different users – one topic <ul><li>Anton </li></ul><ul><li>Mathematics </li></ul><ul><li>Bachelor student </li></ul><ul><li>Group theory </li></ul><ul><li>Exam exercises </li></ul><ul><li>Train interactively </li></ul><ul><li>At home </li></ul><ul><li>Eva </li></ul><ul><li>Computer science </li></ul><ul><li>PhD student </li></ul><ul><li>Group theory </li></ul><ul><li>Profound knowledge </li></ul><ul><li>Overview </li></ul><ul><li>At university </li></ul>
    5. 5. „ Eva‘s Books“
    6. 6. „ A Book“ Good mastery Medium mastery Weak mastery
    7. 7. „ A Book“
    8. 8. Scenario: Overview
    9. 9. Scenario: Exam
    10. 10. Scenario: No sufficient knowledge
    11. 11. Scenario: No sufficient knowledge
    12. 12. Adaptivity: Field Mathematics Biology Physics
    13. 13. Knowledge Representation <ul><li>Extended OMDoc </li></ul><ul><li>Extension of OpenMath </li></ul><ul><li>Markup format for mathematical documents </li></ul><ul><li>Content items (concept, additional) </li></ul><ul><li>Metadata </li></ul><ul><ul><li>Difficulty </li></ul></ul><ul><ul><li>Abstractness </li></ul></ul><ul><ul><li>Field </li></ul></ul><ul><ul><li>Learning context </li></ul></ul><ul><ul><li>… </li></ul></ul>
    14. 14. Knowledge Representation <ul><li>Content items </li></ul><ul><li>unique ID </li></ul>Concepts Additional Definitions Assertions Proof Axioms Examples Exercises Motivation Elaboration <ul><li>Relations: </li></ul><ul><li>Mathematical dependency </li></ul><ul><li>Pedagogical prerequisite </li></ul><ul><li>Relations: </li></ul><ul><li>Pedagogical dependency </li></ul>
    15. 15. User Model <ul><li>History </li></ul><ul><li>Profile </li></ul><ul><li>Content IDs </li></ul><ul><li>Start/End timestamp </li></ul><ul><li>Rate of success (exercise) </li></ul><ul><li>Type: </li></ul><ul><ul><li>read </li></ul></ul><ul><ul><li>example </li></ul></ul><ul><ul><li>exercise </li></ul></ul><ul><ul><li>self assessment </li></ul></ul><ul><li>Preferences: </li></ul><ul><ul><li>Language </li></ul></ul><ul><ul><li>Field </li></ul></ul><ul><ul><li>Gender </li></ul></ul><ul><ul><li>Scenario </li></ul></ul><ul><ul><li>Goals </li></ul></ul><ul><li>Mastery (per concept): </li></ul><ul><ul><li>Knowledge </li></ul></ul><ul><ul><li>Comprehension </li></ul></ul><ul><ul><li>Application </li></ul></ul><ul><li>Justification </li></ul>A 1 A 2 A 3 A 4 A 5
    16. 16. User Model: Justification <ul><li>Concept: </li></ul><ul><li>Concept ID </li></ul><ul><li>Mastery: </li></ul><ul><ul><li>Knowledge (0.3) </li></ul></ul><ul><ul><li>Comprehension (0.1) </li></ul></ul><ul><ul><li>Application (0.1) </li></ul></ul><ul><li>Justification </li></ul><ul><ul><li>History Step 4 </li></ul></ul><ul><ul><li>History Step 2 </li></ul></ul><ul><li>Concept: </li></ul><ul><li>Concept ID </li></ul><ul><li>Mastery: </li></ul><ul><ul><li>Knowledge (0.5) </li></ul></ul><ul><ul><li>Comprehension (0.3) </li></ul></ul><ul><ul><li>Application (0.1) </li></ul></ul><ul><li>Justification </li></ul><ul><ul><li>History Step 5 </li></ul></ul><ul><ul><li>History Step 4 </li></ul></ul>History Profile (mastery) A 1 A 2 A 3 A 4 A 5
    17. 17. User Model: Update <ul><li>Trigger (Action): </li></ul><ul><li>Page changed </li></ul><ul><li>Exercise finished </li></ul><ul><li>Evaluator (page): </li></ul><ul><li>fetch list of page items </li></ul><ul><li>compute values: </li></ul><ul><ul><li>knowledge </li></ul></ul><ul><ul><li>comprehension </li></ul></ul><ul><li>User Model: </li></ul><ul><li>update </li></ul><ul><li>Evaluator (exercise): </li></ul><ul><li>compute application value: </li></ul><ul><ul><li>difficulty </li></ul></ul><ul><ul><li>sucess rate </li></ul></ul>
    18. 18. Software Eyetracker (DFKEye) <ul><li>Trace attention on regions </li></ul><ul><li>More fine-grained mastery evaluation </li></ul>
    19. 19. Course Generation User Model mBase Pedagogical Rules Course Generator
    20. 20. 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>
    21. 21. 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>
    22. 22. 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>
    23. 23. Architecture mBase Pedagogical Rules Web Server Session Manager Math Systems Course Generator Presentation Generator (XSLT) XML-RPC Java http http User Model History Profile
    24. 24. LeActiveMath <ul><li>Tutorial dialogues </li></ul><ul><li>Data base of interactive exercises </li></ul><ul><li>Learning-effective tools </li></ul><ul><li>Extend knowledge representation </li></ul><ul><li>Improve open user model </li></ul><ul><li>Classroom tests </li></ul>
    25. 25. Conclusion www.activemath.org <ul><li>Stable!!! </li></ul><ul><li>Currently available content: </li></ul><ul><ul><li>Analysis </li></ul></ul><ul><ul><li>Algebra </li></ul></ul><ul><ul><li>Optimization </li></ul></ul><ul><ul><li>Operation research </li></ul></ul><ul><ul><li>Statistics </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Internationalization </li></ul><ul><li>Employed at school and at university </li></ul>
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