Objectives Propose preliminary answers to 2 questions: Can methods from CM enrich research in SD...
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Transcript of Objectives Propose preliminary answers to 2 questions: Can methods from CM enrich research in SD...
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.