Nonlinear dynamical interaction patterns in collaborative groups: Discourse analysis with orbital decomposition

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.