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Nonlinear Dynamical Interaction Patterns in Collaborative Groups: Discourse Analysis with Orbital Decomposition

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Complex Dynamical Systems in Education

Abstract

Social learning theories, contrary to traditional teacher-centered approaches, emphasize social interaction in educational settings, which is the hypothesized driving force in promoting learning. Methodologically, studies of the interaction processes in question often include recording qualities from students’ discourses (e.g., utterances) or other variables measured at the nominal level and examining the distributional features of them, which are potentially associated with learning outcomes. This chapter discusses and illustrates the use of nonlinear framework (NDS) by implementing the orbital decomposition analysis (ODA) when investigating the interaction processes in learning-in-groups approach. Data analysis from unstructured setting, where students freely interact with each other, demonstrates the nonlinear dynamical nature of the underlying processes and reveals how some initial conditions, the unfolding patterns of social interaction, along with individual characteristics might affect the outcomes. OD is a time series analysis of categorical data, which estimates the optimal length of recurrent patterns and calculates nonlinear measures of the time series, such as Shannon entropy, topological entropy, fractal dimension, and Lyapunov exponents. The NDS analysis suggests that the process under investigation could be a complex pattern possessing thresholds and bifurcations, behavior unseen by traditional methods and the black-box approach. Finally, in this chapter an epistemological discussion is provided, which addresses the connection of the social interaction patterns at a microlevel and the fulfillment of the fundamental aims of educational settings anticipated at the macro-level.

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References

  • Appleton, K. (1997). Analysis and description of students’ learning during science classes using a constructivistic-based model. Journal of Research in Science Teaching, 34, 303–318.

    Article  Google Scholar 

  • Arrow, H., McGrath, J. E., & Berdahl, J. L. (2000). Small groups as complex systems. Formation, coordination, development, and adaptation. Thousand Oaks, CA: Sage.

    Google Scholar 

  • Attneave, R. (1959). Applications of information theory to psychology: A summary of basic concepts, methods, and results. New York: Holt, Rinehart, & Winston.

    Google Scholar 

  • Bak, P. (1996). How nature works: The science of self-organized criticality. New York: Springer-Verlag.

    Book  Google Scholar 

  • Bales, R. R. (1999). Social interaction systems: Theory and measurement. New Brunswick, NJ: Transaction Publishing.

    Google Scholar 

  • Bandura, A. (1977). Self-efficiency: Towards a unified theory of behavioral change. Psychological Review, 84, 191–215.

    Article  Google Scholar 

  • Barnes, D., & Todd, R. (1995). Communication and learning revisited, making meaning through talk. Portsmouth, NH: Boynton/Cook.

    Google Scholar 

  • Bowen, C. W. (2000). A quantitative literature review of cooperative learning effects on high school and college chemistry achievements. Journal of Chemical Education, 77, 118–121.

    Google Scholar 

  • Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., et al. (2000). Graph structure in the Web. Computer Networks, 33, 309–320.

    Article  Google Scholar 

  • Denzin, N., & Lincoln, Y. (2005). Qualitative research. New Delhi: Sage.

    Google Scholar 

  • Guastello, S. J. (1998). Self-organization in leadership emergence. Nonlinear Dynamics in Psychology and Life Sciences, 2, 303–316.

    Article  Google Scholar 

  • Guastello, S. J. (2000). Symbolic dynamic patterns of written exchanges: Hierarchical structures in an electronic problem-solving group. Nonlinear Dynamics, Psychology, and Life Sciences, 4, 169–189.

    Article  Google Scholar 

  • Guastello, S. J. (2005). Statistical distributions and self-organizing phenomena: What conclusions should be drawn? Nonlinear Dynamics, Psychology, and Life Sciences, 9, 463–478.

    Google Scholar 

  • Guastello, S. J. (2009). Group dynamics: Adaptation, coordination, and leadership emergence. In S. J. Guastello, M. Koopmans, & D. Pincus (Eds.), Chaos and complexity in psychology: Theory of nonlinear dynamics (pp. 402–433). New York: Cambridge University Press.

    Google Scholar 

  • Guastello, S. J. (2011). Orbital decomposition: Identification of dynamical patterns in categorical data. In S. Guastello & R. Gregson (Eds.), Nonlinear dynamics systems analysis for the behavioral sciences using real data (pp. 499–516). New York: CRC Press.

    Google Scholar 

  • Guastello, S. J., & Bond, R. W., Jr. (2007). The emergence of leadership in coordination-intensive groups. Nonlinear Dynamics, Psychology, and Life Sciences, 11, 91–117.

    Google Scholar 

  • Guastello, S. J., Hyde, T., & Odak, M. (1998). Symbolic dynamic patterns of verbal exchange in a creative problem solving group. Nonlinear Dynamics, Psychology, and Life Sciences, 2, 35–58.

    Article  Google Scholar 

  • Guastello, S. J., Koopmans, M., & Pincus, D. (Eds.). (2009). Chaos and complexity in psychology: Theory of nonlinear dynamics. New York: Cambridge University Press.

    Google Scholar 

  • Hall, R. H., Rocklin, T. R., Dansereau, D. R., Skaggs, L. P., O’Donnell, A. M., Lambiotte, J. G., et al. (1988). The role of individual differences in the cooperative learning of technical material. Journal of Educational Psychology, 80, 172–178.

    Article  Google Scholar 

  • Hodges, A. (2012). Alan Turing: The Enigma. London: Princeton University Press.

    Book  Google Scholar 

  • Horn, E. M., Collier, W. C., Oxford, J. A., Bond, C. R., Jr., & Dansereau, D. R. (1998). Individual differences in dyadic cooperative learning. Journal of Educational Psychology, 90, 153–161.

    Article  Google Scholar 

  • Johnson, D. W., & Johnson, R. (1991). Joining together: Group theory and group skills (4th ed.). Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Johnson, D. W., Johnson, R., & Maruyama, C. (1983). Interdependence and interpersonal attraction among heterogeneous and homogeneous individuals: A theoretical formulation and a meta-analysis of the research. Review of Educational Research, 53, 5–54.

    Article  Google Scholar 

  • Johnson, D. W., Johnson, R., Ortiz, A., & Stanne, M. (1991). Impact of positive goal and resource interdependence on achievement, interaction, and attitudes. Journal of General Psychology, 118, 341–347.

    Article  Google Scholar 

  • Johnson, D. W., Johnson, R., Stanne, M., & Garibaldi, A. (1990). Impact of group processing on achievement in cooperative groups. Journal of Social Psychology, 130, 507–516.

    Article  Google Scholar 

  • Kauffman, S. A. (1995). At home in the universe. New York: Oxford University Press.

    Google Scholar 

  • Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge, MA: MIT Press.

    Google Scholar 

  • Kelso, J. A. S., & Engstrøm, D. A. (2006). The complementary nature. Cambridge, MA: MIT Press.

    Google Scholar 

  • Kempa, R. R., & Ayob, A. (1991). Learning interactions in group work in science. International Journal of Science Education, 13, 341–354.

    Article  Google Scholar 

  • Kempa, R. R., & Ayob, A. (1995). Learning from group work in science. International Journal of Science Education, 17, 743–754.

    Article  Google Scholar 

  • Koopmans, M. (2014a). Nonlinear change and the black box problem in educational research. Nonlinear Dynamics, Psychology and Life Sciences, 18, 5–22.

    Google Scholar 

  • Koopmans, M. (2014b). Change, self-organization, and the search for causality in educational research and practice. Complicity: An International Journal of Complexity in Education, 11, 20–39.

    Google Scholar 

  • Kumpulainen, K., & Mutanen, M. (1999). The situated dynamics of peer group interaction: An introduction to an analytic framework. Learning and Instruction, 9, 449–474.

    Article  Google Scholar 

  • Lathrop, D. P., & Kostelich, E. J. (1989). Characterization of an experimental strange attractor by periodic orbits. Physics Review, 40, 4028–4031.

    Article  Google Scholar 

  • Lawson, A. E. (1978). Development and validation of the classroom test of formal reasoning. Journal of Research in Science Teaching, 15, 11–24.

    Article  Google Scholar 

  • Lazarowitz, R., & Hertz-Lazarowitz, R. (1998). Cooperative learning in science curriculum. In B. J. Rraser & K. G. Tobin (Eds.), International handbook of science education (pp. 449–469). Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

  • Lazarowitz, R., Hertz-Lazarowitz, R., & Baird, J. (1994). Learning science in cooperative settings: Academic achievement and affective outcomes. Journal of Research in Science Teaching, 31, 1121–1131.

    Article  Google Scholar 

  • Lemke, J. L. (1998). Multiplying meaning: Visual and verbal semiotics in scientific text. In J. R. Martin & R. Veel (Eds.), Reading science (pp. 87–113). London: Routledge.

    Google Scholar 

  • Lemke, J. L. (1999). Multimedia literacy demands of the scientific curriculum. Linguistics and Education, 10, 1–25.

    Google Scholar 

  • Lynch, M., & Woolgar, S. (Eds.). (1990). Representation in scientific practice. Cambridge, MA: MIT Press.

    Google Scholar 

  • Mercer, N. (1996). The quality of talk in children’s collaborative activity in the classroom. Learning and Instruction, 6, 359–377.

    Article  Google Scholar 

  • Newhouse, R., Ruell, D., & Takens, F. (1978). Occurrence of strange attractors: An axiom near quasi-periodic flows on TM, M ≥ 3. Communication in Mathematical Physics, 64, 35–41.

    Article  Google Scholar 

  • Nicolis, S. J. (1991). Chaos and information processing. Singapore: World Scientific.

    Book  Google Scholar 

  • Nicolis, G., & Nicolis, C. (2007). Foundations of complex systems. Singapore: World Scientific.

    Book  Google Scholar 

  • Nicolis, G., & Prigogine, I. (1989). Exploring complexity. New York: Freeman.

    Google Scholar 

  • Noddings, N. (1989). Theoretical and practical concerns about small groups in mathematics. Elementary School Journal, 89, 607–623.

    Article  Google Scholar 

  • Nowak, A., Szamrej, J., & LatanĂ©, B. (1990). From private attitude to public opinion: A dynamic theory of social impact. Psychological Review, 97, 362–376.

    Article  Google Scholar 

  • O’Donnell, A. M., Dansereau, D. R., & Rocklin, T. R. (1991). Individual differences in cooperative learning of concrete procedures. Learning and Individual Differences, 3, 149–162.

    Article  Google Scholar 

  • Peressini, A. F., & Guastello, S. J. (2010). Orbital decomposition: A short user’s guide to ORBDE v2.4. Retrieved May 2014, from http://www.societyforchaostheory.org/resources/#4g

    Google Scholar 

  • Piaget, J. (1973). To understand is to invent: The future of education. New York: Free Press.

    Google Scholar 

  • Pincus, D. (2001). A framework and methodology for the study of non-linear, self-organizing family dynamics. Nonlinear Dynamics, Psychology, and Life Sciences, 5(2), 139–174.

    Article  Google Scholar 

  • Pincus, D., Fox, K. M., Perez, K. A., Turner, J. S., & McGee, A. R. (2008). Nonlinear dynamics of individual and interpersonal conflict in an experimental group. Small Group Research, 39(2), 150–178.

    Article  Google Scholar 

  • Pincus, D., & Guastello, S. J. (2005). Nonlinear dynamics and interpersonal correlates of verbal turn-taking patterns in group therapy. Small Group Research, 36, 635–677.

    Article  Google Scholar 

  • Prigogine, I., & Stengers, I. (1984). Order out of chaos: Man’s new dialog with nature. New York: Bantam.

    Google Scholar 

  • Schroeder, M. (1991). Fractals, chaos, power laws. New York: Freeman.

    Google Scholar 

  • Shachar, H., & Fischer, S. (2004). Cooperative learning and the achievement of motivation and perceptions of students in 11th grade chemistry classes. Learning and Instruction, 14, 69–87.

    Article  Google Scholar 

  • Shannon, C. E. (1948). The mathematical theory of communication. Bell System Technical Journal, 27, 379–423.

    Article  Google Scholar 

  • Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. Urbana, IL: University of Illinois Press.

    Google Scholar 

  • Stamovlasis, D. (2006). The nonlinear dynamical hypothesis in science education problem solving: A catastrophe theory approach. Nonlinear Dynamics, Psychology and Life Sciences, 10(1), 37–70.

    Google Scholar 

  • Stamovlasis, D. (2010). Methodological and epistemological issues on linear regression applied to psychometric variables in problem solving: Rethinking variance. Chemistry Education, Research and Practice, 11, 59–68.

    Article  Google Scholar 

  • Stamovlasis, D. (2011). Nonlinear dynamics and Neo-Piagetian theories in problem solving: Perspectives on a new epistemology and theory development. Nonlinear Dynamics, Psychology and Life Sciences, 15, 145–173.

    Google Scholar 

  • Stamovlasis, D., Dimos, A., & Tsaparlis, G. (2006). A study of group-interaction processes in learning lower-secondary physics. Journal of Research in Science Teaching, 43(6), 556–576.

    Article  Google Scholar 

  • Taggar, S. (2001). Group composition, synergy, and group performance. Journal of Creative Behavior, 35, 261–285.

    Article  Google Scholar 

  • Teasley, S. (1995). The role of talk in children’s peer collaborations. Developmental Psychology, 31, 207–220.

    Article  Google Scholar 

  • Vallacher, R. R., & Nowak, A. (2006). Coherence in human experience and psychological science. In P. Van Lange (Ed.), Bridging social psychology: The benefits of transdisciplinary approaches (pp. 77–82). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Vallacher, R. R., & Nowak, A. (2007). Dynamical social psychology: On complexity and coordination in interpersonal relations. In M. Uhl-Bien & R. Marion (Eds.), Complexity and leadership, Volume 1: Conceptual foundations (pp. 49–81). Charlotte, NC: Information Age Publishers.

    Google Scholar 

  • Vallacher, R. R., & Nowak, A. (2009). The dynamics of human experience: Fundamentals of dynamical social psychology. In S. Guastello, M. Koopmans, & D. Pincus (Eds.), Chaos and complexity in psychology: Theory of nonlinear dynamical systems (pp. 370–401). Boston, MA: Cambridge University Press.

    Google Scholar 

  • Vallacher, R. R., Van Geert, P., & Nowak, A. (2015). The intrinsic dynamics of psychological process. Current Directions in Psychological Science, 24(1), 58–64.

    Article  Google Scholar 

  • Vygotsky, L. (1978). Mind in society. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Waldrop, M. M. (1992). Complexity: The emerging science at the edge of chaos. New York: Simon & Schuster.

    Google Scholar 

  • Webb, N. M. (1989). Peer interaction and learning in small groups. International Journal of Educational Research, 13, 21–39.

    Article  Google Scholar 

  • Webb, N. M. (1991). Task related verbal interaction and mathematics learning in small groups. Journal of Research in Mathematics Education, 22, 366–389.

    Article  Google Scholar 

  • Webb, N. M., Troper, J. D., & Fall, R. (1995). Constructive activity and learning in collaborative small groups. Journal of Educational Psychology, 87(3), 406–423.

    Article  Google Scholar 

  • West, B. J., & Deering, B. (1995). The lure of modern science: Fractal thinking. Studies of nonlinear phenomena in life sciences (Vol. 3). New Jersey: World Scientific.

    Google Scholar 

  • Wheelan, S. A. (2005). The handbook of group research and practice. London: Sage.

    Google Scholar 

  • Zady, M., Portes, O., & Ochs, D. (2002). Examining classroom interactions related to differences in students’ science achievements. Science Education, 87, 40–63.

    Article  Google Scholar 

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Authors and Affiliations

  1. Aristotle University of Thessaloniki, Department of Philosophy and Education, 54124, Thessaloniki, Greece

    Dimitrios Stamovlasis

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  1. Dimitrios Stamovlasis
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Correspondence to Dimitrios Stamovlasis .

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Editors and Affiliations

  1. School of Education, Mercy College, Dobbs Ferry, New York, USA

    Matthijs Koopmans

  2. Department of Philosophy and Education, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Dimitrios Stamovlasis

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Stamovlasis, D. (2016). Nonlinear Dynamical Interaction Patterns in Collaborative Groups: Discourse Analysis with Orbital Decomposition. In: Koopmans, M., Stamovlasis, D. (eds) Complex Dynamical Systems in Education. Springer, Cham. https://doi.org/10.1007/978-3-319-27577-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-27577-2_13

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