Cumulative Auto-Recurrence Quantification Analysis for Educational Data

Learning is a complex process - one that empirical studies capture using educational data collection methodologies but typically reduce to averages and static snapshots of behaviors rather than capturing the dynamic, nonlinear patterns that have the potential to reflect meaningful learning processes. The focus of this chapter is to introduce and provide a tutorial of cumulative auto-recurrence quantification analysis (aRQA), a nonlinear time series analytical methodology designed to reveal the emergence of complexity within time series data as it unfolds over time. Essentially, cumulative aRQA allows us to visualize and quantify how system behaviors change over time. This method builds off of the base technique of recurrence quantification analysis (Webber et al., 2009; Webber & Zbilut, 2004) used in complex systems theory (Thurner et al., 2018) and non-linear dynamical systems theory (Favela, 2023a; Guastello et al., 2008), to quantify the emergence of complexity metrics rather than providing post-hoc metrics of a full dataset that is traditionally output. Unlike traditional linear models, which assume independence and stability over time, cumulative aRQA evaluates how patterns of learner behavior, cognition, emotion, etc. evolve and recur during interactions with educational technologies. This approach enables researchers to examine the temporal structure and self-organization of learning processes as they unfold. By applying cumulative aRQA to educational data (including both continuous and categorical data such as log files, verbalizations, eye tracking, and physiological signals), researchers can identify when learning processes demonstrate complexity, adaptivity, stochasticity, and determinism. In doing so, cumulative aRQA advances the methodological toolkit available to educational technology researchers seeking to understand learning as a complex, dynamic system.