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

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

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

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

S1 S2 S3

D1 D2

D3

T1 T2

T3

Exc1 Exc2

Exc3

Exa1 Exa2

Exa3

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

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

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

iCMap Feedback

iCMap Feedback

Local Feedback

Verification

1. Against knowledge base2. Against authored exercise3. Deduction

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

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

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

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

ActiveMath Architecture

mBasemBase

WebServer

WebServer

SessionManager

SessionManager

PresentationGenerator

(XSLT)

PresentationGenerator

(XSLT)

User Model

HistoryHistoryProfileProfile

XML-RPC

Java

http

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!