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# Interactive Concept Mapping in ActiveMath (iCMap)

## by Martin Homik, IT Consultant / Software Developer at 1&1 Internet AG on Jan 20, 2008

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Describes a tool for conept mapping in mathematics that offers feedback, evaluation, and suggestions. It is part of the ActiveMath learning environment.

Describes a tool for conept mapping in mathematics that offers feedback, evaluation, and suggestions. It is part of the ActiveMath learning environment.

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• Maximale Dauer: 30 Minuten inklusive Diskussion. Pädagogen verwenden eher Mindmaps: Assoziatives Netzwerk Thematische Nähe Concept Maps: Unterstützen Analyse und Reflektion Hierarchisch geordnetes Netzwerk von Begriffen Inhaltliche und logische Beziehungen

## Interactive Concept Mapping in ActiveMath (iCMap)Presentation Transcript

• 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 I C Map
• Motivation
• Concept 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
• Not a Concept Map Fraction calculation Subtraction Addition Multiplication Parts of units Integer Extension Mixed number Division Reduction
• Nominator * Nominator,
• Denominator * Denominator
• Reduction
• Create mixed number if possible
• Multiply first fraction with the second fraction’s reciprocal
• Common denominator
• No common denominator
• Find common denominator
• 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
• Not a Concept Map
• A Concept Map
• iCMap (CoolModes plugin)
• iCMap (CoolModes plugin)
• Knowledge Representation
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3
• Knowledge Representation
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for for for for for for for for for
• Knowledge Representation
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for for Domain prerequisite Domain prerequisite Domain prerequisite
• Knowledge Representation
• Abstract concept level:
• Symbols
• Content Concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for against isA
• iCMap Feedback
• iCMap Feedback
• Local Feedback
• Verification
• Against knowledge base
• Against authored exercise
• Deduction
• Deductive Relation: Transitivity
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 isA isA isA
• Deductive Relation: Transitivity
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 Domain prerequisite Domain prerequisite Domain prerequisite
• Deductive Relation: Equivalence
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 S 3 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 isA isA for for equivalence equivalence
• Fault Tolerance
• Abstract concept level:
• Symbols
• Content concept level:
• Definitions
• Theorems
• Satellite level:
• Examples
• Exercises
S 1 S 2 D 1 D 2 D 3 T 1 T 2 T 3 Exc 1 Exc 2 Exc 3 Exa 1 Exa 2 Exa 3 for isA isA for for for
• ActiveMath Architecture mBase Web Server Session Manager Presentation Generator (XSLT) XML-RPC Java http User Model History Profile JNLP (http)
• 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
• Thank you!