Skip to main content
SpringerLink
Log in

Scope of Graphical Indices in Educational Diagnostics

  • Chapter
  • First Online:
Computer-Based Diagnostics and Systematic Analysis of Knowledge

Abstract

Knowledge representation is a key concept in psychological and educational diagnostics. Graph theory is a promising approach and its fundamentals have been applied in various fields of research and practice, e.g., decision making, project management, network problems. A graph is constructed from a set of vertices whose relationships are represented by edges. We describe various graphical indices, e.g., average degree of vertices, connectedness, cycles of graphs, and link them with educational diagnostics. We then present and discuss experimental results. We conclude by outlining the immense field of applications for graphical indices in educational diagnostics and discussing future applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Acton, W. H., Johnson, P. J., & Goldsmith, T. E. (1994). Structural knowledge assessment: Comparison of referent structures. Journal of Educational Psychology, 86(2), 303–311.

    Article  Google Scholar 

  • Al-Diban, S., & Ifenthaler, D. (in press). Comparison of two analysis approaches for measuring externalized mental models: Implications for diagnostics and applications. Journal of Educational Technology & Society.

    Google Scholar 

  • Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Anzai, Y., & Yokoyama, T. (1984). Internal models in physics problem solving. Cognition and Instruction, 1(4), 397–450.

    Article  Google Scholar 

  • Bai, L., Qin, W., Tian, J., Dai, J., & Yang, W. (2009). Detection of dynamic brain networks modulated by acupuncture using a graph theory model. Progress in Natural Science, 19(7), 827–835.

    Article  Google Scholar 

  • Balaban, A. T. (1985). Graph theory and theoretical chemistry. Journal of Molecular Structure: THEOCHEM, 120, 117–142.

    Article  Google Scholar 

  • Bonato, M. (1990). Wissenstrukturierung mittels Struktur-Lege-Techniken. Eine grapentheoretische Analyse von Wissensnetzen. Frankfurt am Main: Lang.

    Google Scholar 

  • Bronevich, A. G., & Meyer, W. (2008). Load balancing algorithms based on gradient methods and their analysis through algebraic graph theory. Journal of Parallel and Distributed Computing, 68(2), 209–220.

    Article  Google Scholar 

  • Cañas, A. J., Hill, R., Carff, R., 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 (pp. 125–133). Pamplona: Universidad Pública de Navarra.

    Google Scholar 

  • Chartrand, G. (1977). Introductory graph theory. New York: Dover.

    Google Scholar 

  • Chowdhury, A. S., Bhandarkar, S. M., Robinson, R. W., & Yu, J. C. (2009). Virtual craniofacial reconstruction using computer vision, graph theory and geometric constraints. Pattern Recognition Letters, 30(10), 931–938.

    Article  Google Scholar 

  • Clariana, R. B., & Wallace, P. E. (2007). A computer-based approach for deriving and measuring individual and team knowledge structure from essay questions. Journal of Educational Computing Research, 37(3), 211–227.

    Article  Google Scholar 

  • Coffey, J. W., Carnot, M. J., Feltovich, P. J., Feltovich, J., Hoffman, R. R., Cañas, A. J., et al. (2003). A summary of literature pertaining to the use of concept mapping techniques and technologies for education and performance support. Pensacola, FL: Chief of Naval Education and Training.

    Google Scholar 

  • Collins, L. M., & Sayer, A. G. (Eds.). (2001). New methods for the analysis of change. Washington, DC: American Psychological Associtation.

    Google Scholar 

  • Darvish, M., Yasaei, M., & Saeedi, A. (2009). Application of the graph theory and matrix methods to contractor ranking. International Journal of Project Management, 27(6), 610–619.

    Article  Google Scholar 

  • Derbentseva, N., Safayeni, F., & Cañas, A. J. (2004). Experiments on the effects of map structure and concept quantification during concept map construction. 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 (pp. 125–132). Pamplona: Universidad Pública de Navarra.

    Google Scholar 

  • Diestel, R. (2000). Graph theory. New York: Springer.

    Google Scholar 

  • Ding, L., & Guan, Z. H. (2008). Modeling wireless sensor networks using random graph theory. Physica A: Statistical Mechanics and its Applications, 387(12), 3008–3016.

    Article  Google Scholar 

  • Durso, F. T., & Coggins, K. A. (1990). Graphs in social and psychological sciences: Empirical contributions to Pathfinder. In R. W. Schvaneveldt (Ed.), Pathfinder associative networks: Studies in knowledge organization (pp. 31–51). Norwood, NJ: Ablex Publishing Corportion.

    Google Scholar 

  • Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: Verbal reports as data. Cambridge, MA: MIT Press.

    Google Scholar 

  • Fiedler, M. (2007). Reminiscences related to graph theory. Computer Science Review, 1(1), 65–66.

    Article  Google Scholar 

  • Foster, B. L. (1978). Formal network studies and the anthropological perspective. Social Networks, 1(3), 241–255.

    Article  Google Scholar 

  • Gentner, D., & Stevens, A. L. (1983). Mental models. Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Goldsmith, T. E., Johnson, P. J., & Acton, W. H. (1991). Assessing structural knowledge. Journal of Educational Psychology, 83(1), 88–96.

    Article  Google Scholar 

  • Harary, F. (1974). Graphentheorie. München: Oldenbourg.

    Google Scholar 

  • Hietaniemi, J. (2008). Graph-0.84. Retrieved May 6, 2008, from http://search.cpan.org/~jhi/Graph-0.84/lib/Graph.pod

  • Hox, J. (2002). Multilevel analysis. Techniques and applications. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Hsia, T. C., Shie, A. J., & Chen, L. C. (2008). Course planning of extension education to meet market demand by using data mining techniques – an example of Chinkuo technology university in Taiwan. Expert Systems with Applications, 34(1), 596–602.

    Article  Google Scholar 

  • Huang, H. C., Lo, S. M., Zhi, G. S., & Yuen, R. K. K. (2008). Graph theory-based approach for automatic recognition of CAD data. Engineering Applications of Artificial Intelligence, 21(7), 1073–1079.

    Article  Google Scholar 

  • Ifenthaler, D. (2008a). Practical solutions for the diagnosis of progressing mental models. In D. Ifenthaler, P. Pirnay-Dummer, & J. M. Spector (Eds.), Understanding models for learning and instruction. Essays in honor of Norbert M. Seel (pp. 43–61). New York: Springer.

    Chapter  Google Scholar 

  • Ifenthaler, D. (2008b). 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 

  • Ifenthaler, D. (in press-a). Learning and instruction in the digital age. Introduction. In J. M. Spector, D. Ifenthaler, P. Isaías, Kinshuk & D. G. Sampson (Eds.), Learning and instruction in the digital age: Making a difference through cognitive approaches, technology-facilitated collaboration and assessment, and personalized communications. New York: Springer.

    Google Scholar 

  • Ifenthaler, D. (in press-b). Model-based feedback for improving expertise and expert performance. Technology, Instruction, Cognition and Learning.

    Google Scholar 

  • Ifenthaler, D., & Hetterich, B. (under review). Identifying between-domain distinguishing features of cognitive structures: Instructional implications.

    Google Scholar 

  • Ifenthaler, D., Isaias, P., Spector, J. M., Kinshuk, & Sampson, D. G. (2009). Editors’ introduction to the special issue on cognition & learning technology. Educational Technology Research and Development. doi: 10.1007/s11423-009-9127-8

    Google Scholar 

  • Ifenthaler, D., Masduki, I., & Seel, N. M. (2009). The mystery of cognitive structure and how we can detect it. Tracking the development of cognitive structures over time. Instructional Science. doi: 10.1007/s11251-009-9097-6

    Google Scholar 

  • Ifenthaler, D., & Seel, N. M. (2005). The measurement of change: Learning-dependent progression of mental models. Technology, Instruction, Cognition and Learning, 2(4), 317–336.

    Google Scholar 

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

    Google Scholar 

  • Johnson, T. E., Ifenthaler, D., Pirnay-Dummer, P., & Spector, J. M. (2009). Using concept maps to assess individuals and team in collaborative learning environments. In P. L. Torres & R. C. V. Marriott (Eds.), Handbook of research on collaborative learning using concept mapping (pp. 358–381). Hershey, PA: Information Science Publishing.

    Google Scholar 

  • Jonassen, D. H. (2009). Externally modeling mental models. In L. Moller, J. B. Huett, & D. Harvey (Eds.), Learning and instructional technologies for the 21st century. Visions of the future (pp. 49–74). New York: Springer.

    Google Scholar 

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

    Google Scholar 

  • Jonassen, D. H., & Cho, Y. H. (2008). Externalizing mental models with mindtools. In D. Ifenthaler, P. Pirnay-Dummer, & J. M. Spector (Eds.), Understanding models for learning and instruction. Essays in honor of Norbert M. Seel (pp. 145–160). New York: Springer.

    Chapter  Google Scholar 

  • Kirwan, B., & Ainsworth, L. K. (1992). A Guide to task analysis. London: Taylor & Francis Group.

    Google Scholar 

  • Koubek, R. J., Clarkston, T. P., & Calvez, V. (1994). The training of knowledge structures for manufacturing tasks: An empirical study. Ergonomics, 37(4), 765–780.

    Article  Google Scholar 

  • Lee, Y., & Nelson, D. (2004). Instructional use of visual representations of knowledge. Paper presented at the Society for Information Technology and Teacher Education International Conference 2004, Atlanta, GA, USA.

    Google Scholar 

  • Mandl, H., Gruber, H., & Renkl, A. (1995). Mental models of complex systems: When veridicality decreases functionality. In C. Zucchermaglio, S. Bagnara, & S. U. Stucky (Eds.), Organizational learning and technological change (pp. 102–111). Berlin: Springer.

    Google Scholar 

  • Mayer, R. E. (1989). Models for understanding. Review of Educational Research, 59(1), 43–64.

    Google Scholar 

  • Minsky, M. (1981). A framework for representing knowledge in mind design. In R. J. Brachmann & H. J. Levesque (Eds.), Readings in knowledge representation (pp. 245–262). Los Altos, CA: Morgan Kaufmann.

    Google Scholar 

  • Moskowitz, D. S., & Hershberger, S. L. (Eds.). (2002). Modelling intraindividual variability with repeated measures data. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Nenninger, P. (1980). Anwendungsmöglichkeiten der Graphentheorie in der Erziehungswissen-schaft. Zeitschrift für Empirische Pädagogik, 4, 85–106.

    Google Scholar 

  • Norman, D. A., & Rumelhart, D. E. (Eds.). (1978). Strukturen des Wissens. Wege der Kognitionsforschung. Stuttgart: Klett.

    Google Scholar 

  • Novak, J. D. (1998). Learning, creating, and using knowledge: Concept maps as facilitative tools in schools and corporations. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Ohtsuki, H., Pacheco, J. M., & Nowak, M. A. (2007). Evolutionary graph theory: Breaking the symmetry between interaction and replacement. Journal of Theoretical Biology, 246(4), 681–694.

    Article  Google Scholar 

  • Piaget, J. (1950). La construction du réel chez l’enfant. Neuchatel: Delachaux et Niestlé S.A.

    Google Scholar 

  • Piaget, J. (1976). Die Äquilibration der kognitiven Strukturen. Stuttgart: Klett.

    Google Scholar 

  • Picard, C. F. (1980). Graphs and questionnaires. Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  • Pirnay-Dummer, P., Ifenthaler, D., & Johnson, T. E. (2008). Reading with the guide of automated graphical representations. How model based text visualizations facilitate learning in reading comprehension tasks. Paper presented at the AREA 2008, New York.

    Google Scholar 

  • Pirnay-Dummer, P., 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 

  • Prigent, M., Fontenelle, G., Rochet, M. J., & Trenkel, V. M. (2008). Using cognitive maps to investigate fishers’ ecosystem objectives and knowledge Ocean and Coastal Management, 51(6), 450–462.

    Article  Google Scholar 

  • Rao, R. V., & Padmanabhan, K. K. (2007). Rapid prototyping process selection using graph theory and matrix approach. Journal of Materials Processing Technology, 194(1), 81–88.

    Article  Google Scholar 

  • Ryle, G. (1949). The concept of mind. London: Hutchinson.

    Google Scholar 

  • Scaife, M., & Rogers, Y. (1996). External cognition: How do graphical representations work? International Journal of Human – Computer Studies, 45(2), 185–213.

    Article  Google Scholar 

  • Scheele, B., & Groeben, N. (1984). Die Heidelberger Struktur-Lege-Technik (SLT). Eine Dialog-Konsens-Methode zur Erhebung subjektiver Theorien mittlerer Reichweite. Weinheim: Beltz.

    Google Scholar 

  • Schvaneveldt, R. W. (1990). Pathfinder associative networks: Studies in knowledge organization. Norwood: NJ: Ablex Publishing Corporation.

    Google Scholar 

  • Seel, N. M. (1991). Weltwissen und mentale Modelle. Göttingen: Hogrefe.

    Google Scholar 

  • Seel, N. M. (1995). Mental models, knowledge transfer, and teaching strategies. Journal of Structural Learning and Intelligent Systems, 12(3), 197–213.

    Google Scholar 

  • Seel, N. M. (1999a). Educational diagnosis of mental models: Assessment problems and technology-based solutions. Journal of Structural Learning and Intelligent Systems, 14(2), 153–185.

    Google Scholar 

  • Seel, N. M. (1999b). Educational semiotics: School learning reconsidered. Journal of Structural Learning and Intelligent Systems, 14(1), 11–28.

    Google Scholar 

  • Seel, N. M., & Dinter, F. R. (1995). Instruction and mental model progression: Learner-dependent effects of teaching strategies on knowledge acquisition and analogical transfer. Educational Research and Evaluation, 1(1), 4–35.

    Article  Google Scholar 

  • Seel, N. M., Ifenthaler, D., & Pirnay-Dummer, P. (2009). Mental models and problem solving: Technological solutions for measurement and assessment of the development of expertise. In P. Blumschein W. Hung, D. H. Jonassen & J. Strobel (Eds.), Model-based approaches to learning: Using systems models and simulations to improve understanding and problem solving in complex domains (pp. 17–40). Rotterdam: Sense Publishers.

    Google Scholar 

  • Shavelson, R. J. (1972). Some aspects of the correspondence between content structure and cognitive structure in Physics education. Journal of Educational Psychology, 63(3), 225–234.

    Article  Google Scholar 

  • Snow, R. E. (1989). Toward assessment of cognitive and conative structures in learning. Educational Researcher, 18(9), 8–14.

    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 

  • The Perl Foundation. (2008). Perl 6. Retrieved February 11, 2008, from http://www.perlfoundation.org/

  • Tittmann, P. (2003). Graphentheorie. Eine anwendungsorientierte Einführung. München: Carl Hanser Verlag.

    Google Scholar 

  • Todd, C. S., Toth, T. M., & Busa-Fekete, R. (2009). GraphClus, a MATLAB program for cluster analysis using graph theory. Computers & Geosciences, 35(6), 1205–1213.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wagner, W., & Wagner, S. U. (1985). Presenting questions, processing responses, and providing feedback in CAI. Journal of Instructional Development, 8(4), 2–8.

    Article  Google Scholar 

  • White, R. T. (1985). Interview protocols and dimensions of cognitive structure. In L. H. T. West & A. L. Pines (Eds.), Cognitive structure and conceptual change. Orlando, FL: Academic Press.

    Google Scholar 

  • Willett, J. B. (1988). Questions and answers in the measurement of change. Review of Research in Education, 15, 345–422.

    Google Scholar 

  • Xenos, M., & Papadopoulos, T. (2007). Computer aided evaluation of higher education tutors’ performance. Studies in Educational Evaluation, 33(2), 175–196.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Albert-Ludwigs-University, Freiburg, Germany

    Dirk Ifenthaler

Authors
  1. Dirk Ifenthaler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dirk Ifenthaler .

Editor information

Editors and Affiliations

  1. Abt. Lernforschung, Universität Freiburg, Rempartstr. 11, Freiburg, 79085, Germany

    Dirk Ifenthaler

  2. Abt. Lernforschung, Universität Freiburg, Rempartstr. 11, Freiburg, 79085, Germany

    Pablo Pirnay-Dummer

  3. Inst. Erziehungswissenschaft, Univ. Freiburg, Freiburg, 79085, Germany

    Norbert M. Seel

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Ifenthaler, D. (2010). Scope of Graphical Indices in Educational Diagnostics. 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_12

Download citation

Publish with us

Policies and ethics

Search

Navigation