Interactive Concept Mapping in ActiveMath (iCMap)
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nteractive oncept ping in (iCMap)
Martin Homik, Erica Melis, Philipp Kärger
-- ActiveMath Group –
Delfi 2005, Rostock
German Research Center for Artificial Intelligence (DFKI GmbH)
University of Saarland
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MotivationConcept Maps:• Understanding of structures and dependencies• Support analysis and reflection skills• Mathematics has well defined concepts• School teachers use intuitive mind maps• No tools for concept mapping in math
iCMap:• Integrated into ActiveMath learning environment• Mathematical knowledge base and ontology• Interactivity• Feedback• Author support
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Not a Concept Map
Fraction calculation
Subtraction
Addition
Multiplication
Parts of units
Integer
Extension
Mixed number
DivisionReduction
• Nominator * Nominator, • Denominator * Denominator• Reduction• Create mixed number if possible
• Multiply first fraction with the second fraction’s reciprocal
• Common denominator• Add nominators
• No common denominator• Find common denominator• Add nominators
• Reduction• Create mixed number if possible
• Common denominator• Subtract nominators
• No common denominator• Find common denominator• Subtract nominators
• Reduction• Create mixed number if possible
• by a give number• as far as possible over the fraction line
• Transform fractions into mixed number• Transform mixed number into fractions
• with given number
• Basic times table• Prime numbers• Square numbers• Prime factor decomposition• Multiple• Factor• Factor diagrams• Highest common factor• Least common multiple
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Not a Concept Map
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A Concept Map
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iCMap (CoolModes plugin)
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iCMap (CoolModes plugin)
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Knowledge Representation
Abstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
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Knowledge Representation
Abstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
for for for
for for
for for
for for
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Knowledge Representation
Abstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
for
for
Domain prerequisite
Domain prerequisite
Domain prerequisite
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Knowledge Representation
Abstract concept level:• Symbols
Content Concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
for against
isA
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iCMap Feedback
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iCMap Feedback
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Local Feedback
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Verification
1. Against knowledge base2. Against authored exercise3. Deduction
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Deductive Relation: TransitivityAbstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
isAisA
isA
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Deductive Relation: TransitivityAbstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
Domain prerequisite
Domain prerequisite Domain prerequisite
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Deductive Relation: EquivalenceAbstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2 S3
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
isA
isA
for for
equivalence
equivalence
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Fault Tolerance
Abstract concept level:• Symbols
Content concept level:• Definitions• Theorems
Satellite level:• Examples• Exercises
S1 S2
D1 D2
D3
T1 T2
T3
Exc1 Exc2
Exc3
Exa1 Exa2
Exa3
for
isA
isA
forfor for
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ActiveMath Architecture
mBasemBase
WebServer
WebServer
SessionManager
SessionManager
PresentationGenerator
(XSLT)
PresentationGenerator
(XSLT)
User Model
HistoryHistoryProfileProfile
XML-RPC
Java
http
JNLP (http)
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Conclusion
• Concept maps: support (meta-)cognitive skills• Mathematics is a huge concept map itself• iCMap:
– Integrated into ActiveMath learning environment– Mathematical ontology and knowledge base– Interactivity, Feedback, Hints– Supports self-responsible and explorative learning
• Evaluation: – Till end of 2005 at school and university
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Thank you!