Discrete dynamical systems have been used to theoretically model the complex dynamics of classrooms. While time-series analyses of these models has yielded some insights, state space analyses can yield additional insights; this paper will explore state space analyses and their application to classroom situations. One benefit of state space analysis is that it allows simultaneous exploration of multiple time-series, and so can more easily provide information about divergence and convergence of paths. Additionally, state space analysis, more easily than time-series analysis, can provide information about the existence of multiple paths leading toward a desired state. Further, state space analysis can identify different regimes of behaviors, finding boundaries near which there may be divergent behaviors, and also using those regimes to define a (sometimes) relatively small number of archetypical behaviors. This is particularly useful in tracking behaviors at a microgenetic level, since multiple initial conditions may get to the same (or very close) final states, but in dramatically different ways, and these different routes may have implications for future classroom experiences. Because of these advantages, state space analysis can be used to inform attempts at differentiated instruction in a classroom, assist modelers in identifying appropriate parameter scales, and provide guidance for empirical studies of classroom learning. These ideas will be illustrated through state space analysis of an existing model of teacher-student interactions, identifying four regimes of behaviors, and leading to several implications for classroom practice and research.
Ricca, Bernard P. and Green, Kris H., "State Space Analysis and its Connection to the Classroom" (2016). Mathematics Faculty Publications. Paper 15.
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