Objectives

Propose preliminary answers to 2 questions:

Can methods from CM enrich research in SD about how people understand dynamically complex situations?

Can SD enrich or complement CM in educational research where it deals with the understanding of complex processes in the economy or in the firm?

CM→SD

SD→CM

Analyze similarities and differences between Concept Mapping (CM) and System Dynamics (SD)

Concept Mapping (CM)Purpose Support learning and representing knowledge

Process Start with a focus question.Then articulate concepts and link them

Components

Context

Propositions (concepts related by a named relationship)

Banks Moneylend

Concepts Banks Money

Theory of learning based on assimilation and notion of knowledge as semantic network

Relations lend

Concept Mapping (CM)Theoretical Context• Assimilation Theory of Learning (Ausubel, e.g. 1961)

– hierarchical map structure– knowledge gain as subsumtion, superordinate learning, progressive differentiation,

integrative reconciliation

• Associationist Memory (Deese, e.g. 1959)– no limitation to hierarchies -> instead all kinds of map structures are possible

• Semantic networks (e.g. Collins & Quillian, 1967; Norman & Rumelhart, 1978)– basic assumption: network structure of maps corresponds with the notion of knowledge

as semantic network

• Dual coding (Paivio, 1986)/Cognitive Theory of Multimedia Learning (Mayer, e.g. 2001)– Verbal and pictorial information can be processed simultaneously in different chanels.

Concept maps as logical pictures contain both verbal and pictorial information and thus enable effective information processing

• ... (Nesbit & Adesope, 2006)

Concept Mapping (CM)Evaluation of knowledge using concept maps

Representing, evaluating, and statistically assessing all concept maps of a test sample

Descriptive

Methodology

Contents Enabling targeted qualification of students in the respective domain by improved diagnostics of (prior) knowledge

Modalmap

Map

Map

Map

Normative Identifying differences and congruencies between all individual maps and a

Referencemap

Map

Map

Map

CM: knowledge evaluationC O M P O N E N T S K E Y D A T A/I N D I C A T O R Ssingle components/total map• quantitative• one or more points in time

No. of concepts/relations/propositionsGraph theory- Extent ->no. of propositions- Jaggedness (no. of partial maps)- centrality – diameter (longest continued chain in the map)- …

single components/total map• qualitative• one or more points in time

No. of correct or wrong concepts/propositions (0/1 – coding); judgment of one or more expertsverbal description of maps (idiografic analysis)…

single components/total map• qualitative and quantitative• one or more points in time

Modal map -> representation of a test sample by a map which contains the most commonly used propositionsPrototype map -> map with the lowest distance to all other maps of a test sample (calculation based on distance matrix)Distance between individual maps and a reference map…

ComparisonSD CM

Dynamical problems

General situations and phenomena

Focus on problem

solving and learning

Formal modelsSimulation

Semi-formal models

Matrix representation

Widespread in Education

Incipient in Education

Comparison based on variables, links

and loops

Comparison based on concepts,

relations, and/or propositions

Causal Loop Diagram → Concept Map

SD: Causal Loop Diagram CMVariable ConceptPositive causal link without delay Relation of type „+“

Positive causal link with delay Relation of type „+ D“Negative causal link without delay Relation of type „-“

Negative causal link with delay Relation of type „- D“

Stock & Flow Diagram → Concept Map

SD: Stock & Flow Diagram CMStock variable Concept of type “stock”Flow variable Concept of type “flow”Intermediate variable (auxiliary, converter)

Concept of type “intermediate”

Information flow Relation „influences“

Hybrid Diagram → Concept Map

SD: Hybrid Diagram CMStock variable Concept of type “stock”Flow variable Concept of type “flow”Intermediate variable (auxiliary, converter)

Concept of type “intermediate”

Positive causal link without delay Relation of type „+“Positive causal link with delay Relation of type „+ D“Negative causal link without delay Relation of type „-“Negative causal link with delay Relation of type „- D“

Example: Easter Island 1birth rate

death rateavailable trees

per person

consumption perperson

desired number ortrees per person

sufficiency oftrees

-

-

+

Population

births

deaths

+

Trees

consumption

+

+

+

+

+

+

-

R1

B1

B2

B3

birth rate

death rate available treesper person

consumption perperson

desirednumber ortrees perperson

sufficiency of trees

-

- +

Population

births

deaths

+

Trees

consumption

+

+

+

+

+

+

-

R1

B1

B2

B3

Example: Easter Island 1 – cont.intermediate variables flow rates

stocks

PropositionsFirst concept (cause) Linking phrase Second concept (effect)

population + deathssufficiency of trees - death ratetrees + available trees per persondeaths - populationdeath rate + deathsconsumption per person + consumptionbirth rate + birthsbirths - available trees per personpopulation + consumptionbirths + populationdesired number of trees per person

- sufficiency of trees

available trees per person + sufficiency of treesconsumption - treespopulation + births

Example: Easter Island 1 – cont.

Example: Easter Island 1 – cont.Procedure of Data AnalysisAchieve comparability

1. Unit of Analysis: concepts and relations aggregation of according to semantic similarity → comparable networks

2. Unit of Analysis: propositionstandardization → comparable networks

Concept X Concept: for each relation accumulated over all test persons → calculate modal maps.

Defining adjacency matrices

Person X Person: for each proposition → calculate distances between persons

Adjacency matrixAdjacency matrix

Popu

latio

n

birt

hs

birt

h ra

te

deat

hs

deat

h ra

te

avai

labl

e tr

ees p

er p

erso

n

suffi

cien

cy o

f tre

es

desir

ed n

umbe

r of t

rees

per

per

son

cons

umpti

on p

er p

erso

n

cons

umpti

on

Tree

s

Population 1 1 -1 1births 1birth rate 1deaths -1death rate 1available trees per person 1sufficiency of trees -1desired number of trees per person -1consumption per person 1consumption -1Trees 1

Example: Easter Island 1 – cont.

Adjacency matrixExample: Easter Island 1 – cont.

Adjacency matrix

Popu

latio

n

birt

hs

birt

h ra

te

deat

hs

deat

h ra

te

avai

labl

e tr

ees p

er p

erso

n

suffi

cien

cy o

f tre

es

desir

ed n

umbe

r of t

rees

per

per

son

cons

umpti

on p

er p

erso

n

cons

umpti

on

Tree

s

Population 8 11 0 13births 13birth rate 12deaths 7death rate 17available trees per person 15sufficiency of trees 0desired number of trees per person 12consumption per person 11consumption 12Trees 10

Person X Proposition matrix

Persons Propositions8 Population + births

11 Population + deaths0 Population - available trees per person

13 Population + consumption13 births + Population12 birth rate + births7 deaths - Population

17 death rate + deaths15 available trees per person + sufficiency of trees0 sufficiency of trees - death rate

12 desired number of trees per person - sufficiency of trees11 consumption per person + consumption12 consumption - Trees10 Trees + available trees per person

Example: Easter Island 2

Which variables are stocks?

Which variables are flows?

Which variables are auxiliaries?

Easter IslandPopulation

Statues

Agriculturalcapabilities

builds

Coconutpalmsdeforestation

+

+

soil fertility /health

diminished

+

-

ecosystemfunctionality

+

reduction

--

B1B2

Slavetrade

Diseasesincrease in+

+

+

Many implicit details articulated!

RetranslatedExample: Easter Island 2

Comparison

Propositions of the original CM# First concept (cause) Link Second concept (influenced)1 deforestation of coconut palm - soil fertility / health2 Diminished Agricultural capabilities - Easter Island Population3 Disease - Easter Island Population4 Easter Island Population + Statues5 ecosystem collapse - Easter Island Population6 Slave trade - Easter Island Population7 soil fertility / health + ecosystem collapse8 soil fertility / health + Diminished Agricultural capabilities9 Statues + deforestation of coconut palm

10 Slave trade + Disease

Propositions of the reconstructed CM# First concept (cause) Link Second concept1 build + Statues2 Coconut palms + soil fertility / health3 deforestation - Coconut palms4 ecosystem functionality - reduction5 soil fertility / health + diminished6 diminished - Agricultural capabilities7 Agricultural capabilities - reduction8 soil fertility / health + ecosystem functionality9 Easter Island Population + build10 reduction + Easter Island Population11 Slave trade + increase12 Diseases + reduction13 Slave trade + reduction14 Statues + deforestation15 increase + Diseases

Original CM Reconstructed CM1 3, 22 7, 103 12, 104 9, 15 4, 106 13, 107 5, 68 89 14, 310 11, 15

Simple links have become chains!

Conclusions (1)

SD diagrams

Concept Map

is a kind of

Causal Loop Diagram

Stock & Flow

Diagram

HybridDiagram

is a

Operational detailshave more

Relationship typeshave more

SD diagramming brings operational clarity to diagramsÞ SD enriches problem structuring in traditional CM

contexts for dynamic situationsÞ reach the Educational community

Conclusions (2)

SD diagrams can be translated into Concept Maps.

Concept mapping has analysis methods based on proposition (chains of causal links).

Þ Use CM analysis for SD work

Þ Include chains of links into MMDS analysis

Research questionsCan the methods for analysing concept maps qualitatively and quantitatively applied to the analysis of MMDS? In particular, is the modal-, prototype, and reference-net approach useful for • calculating modal and prototype MMDS• defining a reference MMDS based upon expert

opinions? • assessing the quality of individual MMDS?

Does the development of system dynamics diagrams and models improve the quality of concept maps with respect more operationally relevant details, recognizing that some things are stocks while others are flows and clustering of concepts related by feedback loops?

CM→SD

SD→CM

Thank you!

Questions?

Backup

General

Specific

Enterprise

For-profitEnterprise

can beProgressive

differentiation

Subsumption

SocialEnterprise

is a

Superordinate learning

Organization

is a

Armed Forces

Integrative reconciliation

Cognitive key processes

Loops

Loop Pol. Delay VariablesR1 + 0 births, Population

B1 - 0

Population, consumption, Trees, available trees per person, sufficiency of trees, death rate, deaths

B2 - 0Population, available trees per person, sufficiency of trees, death rate, deaths

B3 - 0 Population, deaths

Example: Easter Island 1 – cont.