Objectives Analyze similarities and differences between Concept Mapping

Objectives Analyze similarities and differences between Concept Mapping (CM) and System Dynamics (SD) Propose preliminary answers to 2 questions: CM→SD Can methods from CM enrich research in SD about how people understand dynamically complex situations? SD→CM 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?

Concept Mapping (CM) Purpose Support learning and representing knowledge Components Concepts Banks Money lend Relations Propositions (concepts related by a named relationship) Banks lend Money Process Start with a focus question. Then articulate concepts and link them Context Theory of learning based on assimilation and notion of knowledge as semantic network

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 Methodology Descriptive Map Map Normative Map Map Contents Representing, evaluating, and statistically assessing all concept maps of a test sample Modal map Identifying differences and congruencies between all individual maps and a Reference map Enabling targeted qualification of students in the respective domain by improved diagnostics of (prior) knowledge

CM: knowledge evaluation COMPONENTS K 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 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 verbal description of maps (idiografic analysis) … 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 …

SD Dynamical problems Formal models Simulation Incipient in Education Comparison based on variables, links and loops Comparison Focus on problem solving and learning Matrix representation CM General situations and phenomena Semi-formal models Widespread in Education Comparison based on concepts, relations, and/or propositions

Causal Loop Diagram → Concept Map SD: Causal Loop Diagram Variable Positive causal link without delay CM Concept Relation of type „+“ Positive causal link with delay Negative causal link without delay Relation of type „+ D“ Relation of type „-“ Negative causal link with delay Relation of type „- D“

Stock & Flow Diagram → Concept Map SD: Stock & Flow Diagram Stock variable Flow variable Intermediate variable (auxiliary, converter) Information flow CM Concept of type “stock” Concept of type “flow” Concept of type “intermediate” Relation „influences“

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

Example: Easter Island 1

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

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

Example: Easter Island 1 – cont. 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 Defining adjacency matrices Concept X Concept: for each relation accumulated over all test persons → calculate modal maps. Person X Person: for each proposition → calculate distances between persons

Example: Easter Island 1 – cont. Adjacency matrix

Person X Proposition matrix

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

Many implicit details articulated!

Example: Easter Island 2 Retranslated

Comparison Simple links have become chains!

Conclusions (1) Concept Map have more Relationship types is a kind of SD diagrams is a have more Operational details SD diagramming brings operational clarity to diagrams & Þ SD enriches. Stock problem structuring Causal Loop Hybrid in traditional CM Flow contexts for dynamic situations Diagram Þ 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). ÞUse CM analysis for SD work ÞInclude chains of links into MMDS analysis

Research questions CM→SD 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? SD→CM 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?

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

Example: Easter Island 1 – cont. Loops Loop R 1 B 1 Pol. + - Delay Variables 0 births, Population 0 Population, consumption, Trees, available trees person, sufficiency of trees, death rate, deaths B 2 - 0 Population, available trees person, sufficiency of trees, death rate, deaths B 3 - 0 Population, deaths