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

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 Abis04 Presentation Transcript

  • A Learning Environment for Mathematics Martin Homik, Erica Melis -- ActiveMath Group – ABIS 2004, Berlin German Research Center for Artificial Intelligence DFKI GmbH, Saarbrücken
  • Outline
    • Features
    • Examples
    • Key components:
      • Knowledge representation
      • User model
      • Course generator
    • Conclusion
    • Adaptive course generation
    • Adaptive presentation
    • Semantic knowledge representation
    • User model
    • Pedagogical knowledge
    • Interactive exercises
    • Suggestion mechanism
    ActiveMath‘s Features
  • Different users – one topic
    • Anton
    • Mathematics
    • Bachelor student
    • Group theory
    • Exam exercises
    • Train interactively
    • At home
    • Eva
    • Computer science
    • PhD student
    • Group theory
    • Profound knowledge
    • Overview
    • At university
  • „ 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
    • Extended OMDoc
    • Extension of OpenMath
    • Markup format for mathematical documents
    • Content items (concept, additional)
    • Metadata
      • Difficulty
      • Abstractness
      • Field
      • Learning context
  • Knowledge Representation
    • Content items
    • unique ID
    Concepts Additional Definitions Assertions Proof Axioms Examples Exercises Motivation Elaboration
    • Relations:
    • Mathematical dependency
    • Pedagogical prerequisite
    • Relations:
    • Pedagogical dependency
  • User Model
    • History
    • Profile
    • Content IDs
    • Start/End timestamp
    • Rate of success (exercise)
    • Type:
      • read
      • example
      • exercise
      • self assessment
    • Preferences:
      • Language
      • Field
      • Gender
      • Scenario
      • Goals
    • Mastery (per concept):
      • Knowledge
      • Comprehension
      • Application
    • Justification
    A 1 A 2 A 3 A 4 A 5
  • User Model: Justification
    • Concept:
    • Concept ID
    • Mastery:
      • Knowledge (0.3)
      • Comprehension (0.1)
      • Application (0.1)
    • Justification
      • History Step 4
      • History Step 2
    • Concept:
    • Concept ID
    • Mastery:
      • Knowledge (0.5)
      • Comprehension (0.3)
      • Application (0.1)
    • Justification
      • History Step 5
      • History Step 4
    History Profile (mastery) A 1 A 2 A 3 A 4 A 5
  • User Model: Update
    • Trigger (Action):
    • Page changed
    • Exercise finished
    • Evaluator (page):
    • fetch list of page items
    • compute values:
      • knowledge
      • comprehension
    • User Model:
    • update
    • Evaluator (exercise):
    • compute application value:
      • difficulty
      • sucess rate
  • Software Eyetracker (DFKEye)
    • Trace attention on regions
    • More fine-grained mastery evaluation
  • Course Generation User Model mBase Pedagogical Rules Course Generator
  • Course Generation (1) Goal concept
    • 1. Retrieve content from knowledge base
      • Start with goal concept
      • Collect recursively concepts the goal depends on
      • … plus additional information (e.g. examples)
  • Course Generation (2) Goal concept
    • 2. Filter concepts
      • According to pedagogical rules
      • According to the user model
    • Defrule PatternExamPrep
      • Allow (definition, exercise)
      • Order (definition, exercise)
    • Defrule ReqAppEx
      • Allow (definition, exercise)
      • Test (user-kb(definition)<0.3)
      • Add ex-for(definition 0.3)
      • ex-for(definition 0.5)
  • Course Generation (3) Goal concept
    • 3. Linearize graph
      • according to mathematical dependency
      • according to pedagogical dependency
  • Architecture mBase Pedagogical Rules Web Server Session Manager Math Systems Course Generator Presentation Generator (XSLT) XML-RPC Java http http User Model History Profile
  • LeActiveMath
    • Tutorial dialogues
    • Data base of interactive exercises
    • Learning-effective tools
    • Extend knowledge representation
    • Improve open user model
    • Classroom tests
  • Conclusion www.activemath.org
    • Stable!!!
    • Currently available content:
      • Analysis
      • Algebra
      • Optimization
      • Operation research
      • Statistics
    • Internationalization
    • Employed at school and at university