Abstract
Despite an upswing of interest in learning dynamics, and theoretical models that endorse particular sequences of learning behaviors, learning scientists lack the analytical tools necessary for investigating attention-related manifestations of learning processes as they unfold over time. One candidate technique is orbital decomposition (OD). OD is an example of symbolic dynamics, a class of analyses that quantify patterns in strings of nominal data. Originating in chaos theory, OD provides an index of the systematicity of recurring sequences in a time series. Products include entropy values which reveal the degree to which sequences are random or comprised of recurring patterns. As an illustration of its potential utility, this chapter includes a study in which OD is used in conjunction with symbol sequence figures and statistical tests to investigate how variations in visual attention sequences manifest within episodes ofself-regulated learning (SRL). Incorporating OD into the analysis of individuals’ learning episodes reveals significant, nonlinear relationships between entropy and the proportions of time spent viewing particular learning materials, and significant variations that are contingent on global task strategies such as note-taking. After considering findings in terms of the questions they raise about the dynamics involved in SRL processes, this chapter concludes with a summary of steps that can be followed to support the conceptualization of learning related phemonena as exemplars of complex dynamic systems.
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Appendix: Calculation of Number of Recurring String Patterns (N C )
Appendix: Calculation of Number of Recurring String Patterns (N C )
N C is estimated by first creating a separate transition matrix M C for each C sequence length with the allowable strings on each axis. Each cell then contains 1 if the row string is immediately followed by the column string or 0 if it does not:
AD | DA | EA | AE | ||
M C= | AD | 1 | 0 | 0 | 1 |
DA | 0 | 1 | 0 | 0 | |
EA | 0 | 1 | 1 | 0 | |
AE | 1 | 0 | 0 | 0 |
The diagonal of the matrix (bolded in the example above) indicates if a string is immediately followed by itself (1) or not (0). Rather than using the determinant of this matrix, which could be very large and computationally intensive, the trace of M C (trM C) can be easily computed by summing the 1s from the diagonal (Lathrop & Kostelich, 1989). Hence, trM C represents the number of strings that are immediately repeated (e.g., for C = 2, trM C = 3) and is used to compute H T.
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Garner, J.K., Russell, D.M. (2016). The Symbolic Dynamics of Visual Attention During Learning: Exploring the Application of 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_16
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