Assistants

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m-ICTE2005 Caceres (Spain) June 7th-10th 2005
Mathematics in Virtual Knowledge Spaces User
adaption by Intelligent Assistants University of
Technology Berlin
Dr. Sabina Jeschke Dr. Thomas Richter
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Prospects for Intelligent Assistant Technologies
in eLearning environments for Mathematics
Problem Broad audience

• (Pure) mathematical research
• Applied sciences require mathematics as key
  technology
• high level of adaptivity required

Exploitable by concepts developed in AI
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Classification of eLearning/Knowlegde Systems in
Mathematics
Content Area
Intelligent Training Area
Semantic Retrieval Area
Virtual Laboratories Area
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• Content Area

• Composition of courses from granular knowledge
  atoms
• Composition with the CourseCreator tool
• Interactive multimedia elements
• Nonlinear navigation within courses
• Visualization of mathematical concepts and objects

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Mumie Content Area Anchor point for
Intelligent Assistants
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• Semantic Retrieval Area
• Separate talk on Friday, 1245-1300

• Knowledge networks
• User defined construction
• Includes an encyclopaedia

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• Intelligent Training Area

• Exercises, combined into exercise paths
• Interactive, constructive
• Embedded in an exercise network
• Intelligent input control mechanisms
• Integration of CAS Numerical Software

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Network of Exercises
encodes mathematical dependencies of exercises
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Mumie Intelligent Training Area Anchor point
for Intelligent Assistants
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• VirtLab Area
• Separate talk on Wednesday, 1230-1245

• Freely Combinable experiments
• Explorative learning and research
• Experiments integrating CAS Numerical Software
  Tools
• Intelligent input control mechanisms
• Separation of lab kernel and user interface
  (open heterogeneous approach)
• Several GUIs of variing complexety offering user
  adaptivity
• Support of cooperative (incl. remote) learning
  scenarios

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What are Virtual Laboratories?
Simple Java GUI for hands-on training and
demonstration
Composition of the Laboratory Equipment into
Experiments
Definition of Virtual Labs Virtual Labs are
software environments that use the metaphor of
real labs they allow to design, setup and carry
out experiments by means of the
computer. Experiments are typically run on
computer implemented abstract algorithms rather
than real objects these algorithms model either
real devices and items, or theoretical concepts
and objects.
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User Adaption in the Virtual Lab
Wizards ease the setup of the image filter
Example Course on Matrix Convolution
Tutor programs provide exercises, validate inputs
and give hints
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Storyboarding in Exercise Networks
Image moves left Recall definition of convolution
Move image to the right...
Exercise 1
Exercise 2
Exercise 3
Move image upwards
Exercise 4
Build smoothing filter
Exercise 5
not isotropic
Exercise 6
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User Adaption in Virtual Labs
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Summary

• eLearning environments for mathematical education
  include a high potential for the integration of
  different types of intelligent assistent
  technologies
• concepts are not generally restricted to
  mathematics (and other theoretical fields),
  mathematics may act a as toy model/prototype for
  other, less formalized disciplines

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The End!
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Architecture Virtual Laboratory
Virtual Lab (simulation computation)
external Virtual Labs
Interfaces
intelligent assistent
connec- tors
connec- tors
alternative user interfaces
external numerical software CAS
Integration of external tools
front-end
front-end
front-end
cooperative usage
browser/ interface
browser/ interface
browser/ interface
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gt main research focus

• Concepts for intelligent training environments
• Design of explorative learning environments
• eBologna concepts (distributed learning and
  teaching)
• Models for user adaptivity (intelligent
  assistents)

Pedagogical Aspects

• Semantic encoding analysis of mathematical
  language
• Specific matter ontologies
• Automatic validation of assignment solutions
• Design of semantic retrieval systems
• Integration technologies for open eLearning
  environments
• Design of distributed cooperative systems

Technical Aspects
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Mumie Content - CourseCreator
Course with content
Course without content
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Mumie navigation network
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Mumie Fields of Learning

• Courses from granular elements of knowledge
• Composition with the CourseCreator tool
• Interactive multimedia elements
• Nonlinear navigation

• Exercises, combined into exercise paths
• Interactive, constructive
• Embedded in an exercise network
• Intelligent input control mechanisms

• Knowledge networks
• User defined construction
• Includes an encyclopaedia

• Combinable experiments
• Explorative learning and research
• Experiments integrating CAS Num. Tools
• Intelligent input control mechanisms

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Mumie Semantic Retrieval Area Characteristics

• (Semi-automatic) natural language analysis of
  mathematical content
• Representation of field specific connections
• Visualization of semantic networks (ongoing
  work)
• User driven information retrieval system
  (ongoing work)

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Mumie (Retrieval) Knowledge Nets I
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Mumie (Retrieval) Knowledge Nets II
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Mumie Semantic Retrieval Area Anchor point for
Intelligent Assistents

• Extraction
• semantic analysis of mathematical texts (encoded
  in natural language)
• result network of mathematical relations

• Retrieval
• presents connections between mathematical
  objects and concepts
• answers to individual user requests
• result representation of mathematical relations
• as semantics (sub)networks (e.g.)
• answers adapted to individual user profil

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Mumie Intelligent Training Area Characteristics

• Hierarchically networked exercises of decreasing
  complexity
• Intelligent feedback mechanisms (ongoing work)
• Intelligent validation mechanisms (ongoing work)
• Integration of CAS Numerical Software (ongoing
  work)

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Mumie VirtLab Area Characteristics

• Free (incl. graphical) composition of laboratory
  components
• Separation of lab kernel and user interface
  (open heterogeneous approach)
• Integration of computer algebra systems
• Several GUIs of variing complexety offering user
  adaptivity
• Support of cooperative (incl. remote) learning
  scenarios
• Intelligent input validation mechanisms

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Virtual Lab Oorange GUI
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Generations of eLTR technologies
WebCT Co.
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• Overview
• Background
• Introduction
• Content Area
• Semantic Retrieval Area
• Intelligent Training Area
• Virtual Laboratories
• Conclusion

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• Background

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• Introduction

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• Conclusion

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Mumie Content Area Characteristics

• Granular context-free re-usable knowledge
  atoms
• Composed by the Course-Creator tool
• Organized in a specific matter ontology
• Visualization of field-specific connections
• Non-linear navigation networks
• Usage of precise mathematical language
• Semantically enriched language (ongoing work)
• Visualization of mathematical objects concepts

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Background

• Berlin University of Technology
• Multimedia Center for eLearning, eTeaching and
  eResearch MuLF
• Integrated in Department of Mathematics and
  Natural Science
• Additional to MuLF-Team Several third party
  funded projects (Mumie, Moses, Nemesis, Genesis,
  BeLearning, Members, DFG-VirtLabs, ...)

• Special teaching focus an mathematical education
• for mathematicians and physicists
• for engineers and computer scientists