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Abstract

When it comes to the judgment of expertise, we often rely on assumptions which propose that expert knowledge is structured differently than novice knowledge. However, regardless of how much descriptive plausibility there might be in single cases, hypotheses like this cannot be investigated across domains unless there is a way to subtract the content from the structure which allows testing for structure only. A new algorithm introduced in this chapter is designed to solve this problem. The algorithm works for small and medium graphs, is capable of completely mapping the structure of an undirected graph, and also allows one to compare full structure sets between pairs of graphs. In my discussion of this algorithm, I derive additional computing-efficient graph feature-based heuristics from the original algorithm and compare the two in order to show how large graphs can be analyzed in a similar way. I then present standard applications of the algorithm from empirical studies on different kinds of expertise. Finally, I provide examples and a guideline in which the application and the interpretation of the structure comparison measure are discussed with a focus on research practice.

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References

  • Al-Diban, S. (2002). Diagnose mentaler modelle [Assessment of mental models]. Hamburg: Kovac.

    Google Scholar 

  • Bar-Ilan, J. (2001). Data collection on the Web for informetric purposes: A review and analysis. Scientometrics, 50(1), 7–32.

    Article  Google Scholar 

  • Cañas, A. J., Hill, G., Carff, N., Suri N., Lott, J., Eskridge, T., et al. (2004). CmapTools: A knowledge modeling and sharing environment. In A. J. Cañas, J. D. Novak, & F. M. González (Eds.), Concept maps: Theory, methodology, technology, proceedings of the first international conference on concept mapping. Pamplona, Spain: Universidad Pública de Navarra.

    Google Scholar 

  • Cilibrasi, R. L., & Vitanyi, P. M. B. (2007). The Google similarity distance. IEEE Transaction on Knowledge and Data Engineering, 19(3), 370–383.

    Article  Google Scholar 

  • Eckert, A. (1998). Kognition und Wissensdiagnose. Die Entwicklung und empirische Ãœberprüfung des computergestützten wissensdiagnostischen Instrumentariums Netzwerk-Elaborations-Technik (NET). Lengerich: Pabst.

    Google Scholar 

  • Ellson, J., Gansner, E. R., Koutsofios, E., North, S. C., & Woodhull, G. (2003). GraphViz and dynagraph. static and dynamic graph drawing tools. Florham Park, NJ: AT&T Labs – Research.

    Google Scholar 

  • Falkenhainer, B., Forbus, K. D., & Gentner, D. (1989). The structure-mapping engine: Algorithm and examples. Artificial Intelligence, 41, 1–63.

    Article  Google Scholar 

  • Forbus, K. D., Gentner, D., & Law, K. (1995). MAC/FAC: A model of similarity-based retrieval. Cognitive Science, 19, 141–205.

    Article  Google Scholar 

  • Forbus, K. D., Gentner, D., Markman, A. B., & Ferguson, R. W. (1998). Analogy just looks like high level perception: Why a domain-general approach to analogical mapping is right. Journal of experimental and Theoretical Artificial Intelligence, 10(2), 231–257.

    Article  Google Scholar 

  • Gentner, D., & Bowdle, B. (2008). Metaphor as structure-mapping. In R. Gibbs (Ed.), The Cambridge handbook of metaphor and thought (pp. 109–128). New York: Cambridge University Press.

    Google Scholar 

  • Gentner, D., & Markman, A. B. (2006). Defining structural similarity. Journal of Cognitive Science, 6, 1–20.

    Google Scholar 

  • Gilovich, T., & Griffin, D. (2002). Introduction – Heuristics and Biases: Then and now. In T. Gilovich, D. W. Griffin, & D. Kahneman (Eds.), Heuristics and biases: The psychology of intuitive judgement (pp. 1–18). Cambridge, UK; New York: Cambridge University Press.

    Google Scholar 

  • Glaser, R. (1992). Expert knowledge and process of thinking. In D. F. Halpern (Ed.), Enhancing thinking skills in the sciences and mathematics. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Glaser, E. M., Abelson, H. H., & Garrison, K. N. (1983). Putting knowledge to use: Facilitating the diffusion of knowledge and the implementation of planned change (1st ed.). San Francisco, CA: Jossey-Bass.

    Google Scholar 

  • Gruber, H. (1994). Expertise Modelle und empirische Untersuchungen [Expertise. Models and empirical studies]. Opladen: Westdt. Verl.

    Google Scholar 

  • Helbig, H. (2006e). Knowledge representation and the semantics of natural language. Berlin, New York: Springer.

    Google Scholar 

  • Ifenthaler, D. (2006). Diagnose lernabhängiger Veränderung mentaler Modelle Entwicklung der SMD-Technologie als methodologisches Verfahren zur relationalen, strukturellen und semantischen Analyse individueller Modellkonstruktionen. Freiburg: FreiDok.

    Google Scholar 

  • Ifenthaler, D. (2008). Relational, structural, and semantic analysis of graphical representations and concept maps. Educational Technology Research and Development. doi: 10.1007/s11423-008-9087-4

    Google Scholar 

  • Jackendoff, R. (2007). Linguistics in cognitive science: The state of the art. The linguistic review, 24(4), 347–401.

    Article  Google Scholar 

  • Janetzko, D. (2008). Objectivity, reliability, and validity of search engine count estimates. International Journal of Internet Science, 3(1), 3–77.

    Google Scholar 

  • Jonassen, D. H., Beissner, K., & Yacci, M. (1993). Structural knowledge: Techniques for representing, conveying, and acquiring structural knowledge. Hillsdale, NJ: L. Erlbaum.

    Google Scholar 

  • Johnson-Laird, P. N. (1983). Mental models. Toward a cognitive science of language, inference and language. Cambridge: Cambridge University Press.

    Google Scholar 

  • Johnson-Laird, P. N., & Byrne, R. M. J. (1991). Deduction. Hove: Lawrence Erlbaum.

    Google Scholar 

  • Kant, I. (1787). Critik der reinen Vernunft [The critique of pure reason]. Riga: J. F. Hartknoch.

    Google Scholar 

  • Kruskal, J. B. (1957). On the shortest spanning subtree of a graph and the travelling salesman problem. Proceeding of the American Mathematical Society, 7, 48–50.

    Google Scholar 

  • Kubose, T. T., Holyoak, K. J., & Hummel, J. E. (2002). The role of textual coherence in incremental analogical mapping. Journal of memory and language, 47(3), 407–435.

    Google Scholar 

  • Langacker, R. W. (2008). Cognitive grammar: A basic introduction. Oxford, New York: Oxford University Press.

    Google Scholar 

  • Link, G. (1979). Montague-Grammatik. München: Wilhelm Fink.

    Google Scholar 

  • Montague, R. (1974). Formal philosophy: Selected papers of Richard Montague. New Haven, CT: Yale University Press.

    Google Scholar 

  • Nückles, M. (2004). Mind maps und concept maps: Visualisieren, Organisieren, Kommunizieren. München: Deutscher Taschenbuch-Verlag.

    Google Scholar 

  • Pirnay-Dummer, P. N. (2006). Expertise und Modellbildung – MITOCAR. Freiburg: FreiDok

    Google Scholar 

  • Pirnay-Dummer, P. N. (2008). Rendezvouz with a quantum of learning. Effect metaphors, extended design experiments and omnivariate learning instances. In D. Ifenthaler, P. Pirnay-Dummer, & J. M. Spector (Eds.), Understanding models for learning and instruction. Essays in honor of Norbert M. Seel (pp. 105–143). New York: Springer.

    Chapter  Google Scholar 

  • Pirnay-Dummer, P. N., Ifenthaler, D., & Spector, J. M. (2009). Highly integrated model assessment technology and tools. Educational Technology Research and Development. doi:10.1007/s11423-009-9119-8

    Google Scholar 

  • Preece, P. F. W. (1976). Mapping cognitive structure: A comparison of methods. Journal of Educational Psychology, 68, 1–8.

    Article  Google Scholar 

  • Schvaneveldt, R. W., Durso, F. T., Goldsmith, T. E., Breen, T. J., Cooke, N. M., Tucker, R. G., et al. (1985). Measuring the structure of expertise. International Journal of Man-Maschine Studies, 23, 699–728.

    Article  Google Scholar 

  • Seel, N. M. (2003). Model centered learning and instruction. Technology, Instruction, Cognition and Learning, 1(1), 59–85.

    Google Scholar 

  • Seel, N. M., Al-Diban, S., & Blumschein, P. (2002). Mental models and instructional planning. In J. M. Spector (Ed.), Integrated and holistic perspectiveson learning, instruction and technology: Understanding complexity. Dordrecht: Kluwer.

    Google Scholar 

  • Snow, R. E. (1990). New approaches to cognitive and conative assessment in education. International Journal of Educational Research, 14(5), 455–473.

    Google Scholar 

  • Taylor, J. R. (2007). Cognitive linguistics and autonomous linguistics. In D. Geeraerts & H. Cuyckens (Eds.), Cognitive linguistics (pp. 566–588). New York: Oxford University Press.

    Google Scholar 

  • Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.

    Google Scholar 

  • van Someren, M. W., Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method. A practical guide to modelling cognitve processes. London: Academic Press.

    Google Scholar 

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Correspondence to Pablo Pirnay-Dummer .

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Pirnay-Dummer, P. (2010). Complete Structure Comparison. In: Ifenthaler, D., Pirnay-Dummer, P., Seel, N. (eds) Computer-Based Diagnostics and Systematic Analysis of Knowledge. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5662-0_13

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