2. 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 )

3. Concept Mapping (CM) PurposeSupport 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 ) BanksMoney lend Concepts BanksMoney Theory of learning based on assimilation and notion of knowledge as semantic network Relations lend

4. 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)

5. 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 Modal map Map Normative Identifying differences and congruencies between all individual maps and a Reference map Map

6. CM: knowledge evaluation C O M P O N E N T SK E Y D A T A/I N D I C A T O R S single components/ total map quantitative one or more points in time No. of concepts/relations/propositions Graph 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 experts verbal 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 propositions Prototype 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 …

7. Comparison SD CM Dynamical problems General situations and phenomena Focus on problem solving and learning Formal models Simulation 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

8. Causal Loop Diagram → Concept Map SD: Causal Loop DiagramCM VariableConcept Positive causal link without delayRelation of type „+“ Positive causal link with delayRelation of type „+ D“ Negative causal link without delayRelation of type „-“ Negative causal link with delayRelation of type „- D“

9. Stock & Flow Diagram → Concept Map SD: Stock & Flow DiagramCM Stock variableConcept of type “stock” Flow variableConcept of type “flow” Intermediate variable (auxiliary, converter) Concept of type “intermediate” Information flowRelation „influences“

10. Hybrid Diagram → Concept Map SD: Hybrid DiagramCM Stock variableConcept of type “stock” Flow variableConcept of type “flow” Intermediate variable (auxiliary, converter) Concept of type “intermediate” Positive causal link without delayRelation of type „+“ Positive causal link with delayRelation of type „+ D“ Negative causal link without delayRelation of type „-“ Negative causal link with delayRelation of type „- D“

11. Example: Easter Island 1

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

13. Propositions First concept (cause)Linking phraseSecond concept (effect) population+deaths sufficiency of trees-death rate trees+available trees per person deaths-population death rate+deaths consumption per person+consumption birth rate+births -available trees per person population+consumption births+population desired number of trees per person -sufficiency of trees available trees per person+sufficiency of trees consumption-trees population+births Example: Easter Island 1 – cont.

14. Procedure of Data Analysis Achieve comparability 1.Unit of Analysis: concepts and relations aggregation of according to semantic similarity → comparable networks 2.Unit of Analysis: proposition standardization → 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

15. Adjacency matrix Example: Easter Island 1 – cont.

16. Adjacency matrix Example: Easter Island 1 – cont.

17. Person X Proposition matrix

18. Example: Easter Island 2 Which variables are stocks? Which variables are flows? Which variables are auxiliaries?

19. Many implicit details articulated!

20. Retranslated Example: Easter Island 2

21. Comparison Simple links have become chains!

22. Conclusions (1) SD diagrams Concept Map is a kind of Causal Loop Diagram Stock & Flow Diagram Hybrid Diagram is a Operational details have more Relationship types have more SD diagramming brings operational clarity to diagrams  SD enriches problem structuring in traditional CM contexts for dynamic situations  reach the Educational community

23. Conclusions (2) SD diagrams can be translated into Concept Maps. Concept mapping has analysis methods based on proposition (chains of causal links).  Use CM analysis for SD work  Include chains of links into MMDS analysis

24. Research questions Can 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

25. Thank you! Questions?

26. Backup

27. General Specific Enterprise For-profit Enterprise can be Progressive differentiation Subsumption Social Enterprise is a Superordinate learning Organization is a Armed Forces Integrative reconciliation Cognitive key processes

28. Loops LoopPol.DelayVariables R1+0births, Population B1-0 Population, consumption, Trees, available trees per person, sufficiency of trees, death rate, deaths B2-0 Population, available trees per person, sufficiency of trees, death rate, deaths B3-0Population, deaths Example: Easter Island 1 – cont.