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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DESCRIPTION

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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Page 1: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 2: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 3: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 4: Interactive Concept Mapping in ActiveMath (iCMap)

Not a Concept Map

Page 5: Interactive Concept Mapping in ActiveMath (iCMap)

A Concept Map

Page 6: Interactive Concept Mapping in ActiveMath (iCMap)

iCMap (CoolModes plugin)

Page 7: Interactive Concept Mapping in ActiveMath (iCMap)

iCMap (CoolModes plugin)

Page 8: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 9: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 10: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 11: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 12: Interactive Concept Mapping in ActiveMath (iCMap)

iCMap Feedback

Page 13: Interactive Concept Mapping in ActiveMath (iCMap)

iCMap Feedback

Page 14: Interactive Concept Mapping in ActiveMath (iCMap)

Local Feedback

Page 15: Interactive Concept Mapping in ActiveMath (iCMap)

Verification

1. Against knowledge base2. Against authored exercise3. Deduction

Page 16: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 17: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 18: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 19: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 20: Interactive Concept Mapping in ActiveMath (iCMap)

ActiveMath Architecture

mBasemBase

WebServer

WebServer

SessionManager

SessionManager

PresentationGenerator

(XSLT)

PresentationGenerator

(XSLT)

User Model

HistoryHistoryProfileProfile

XML-RPC

Java

http

JNLP (http)

Page 21: Interactive Concept Mapping in ActiveMath (iCMap)

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

Page 22: Interactive Concept Mapping in ActiveMath (iCMap)

Thank you!