Ergodicity and the Merits of the Single Case

Catastrophe Theory Applied to Neuropsychological Data: Nonlinear Effects of Depression on Financial Capacity in Amnestic Mild Cognitive Impairment and Dementia

“…Complexity theory offers a theoretical framework and a rich array of methodological tools to support research designs and data analysis. Even though the present investigation used a large sample and cross-sectional data to infer nonlinearity, the effective methodological approach to study CASs is time series analysis [ 63 , 64 ]. This framework has been fruitfully applied in many process approaches [ 65 , 66 , 67 , 68 ], where bifurcation phenomena are theoretically anticipated and are worth examining.…”

Growing Points for a Synthesis Between the Sciences of Learning, School Reform, and Inequity: Insights From Complex Dynamical Systems Theory

“…Analyzing the relationships between systemic components requires a holistic perspective on the phenomenon of interest. This orientation marks an important difference between CDST and linear cause and effect models, such as those investigated through randomized control trial studies, which surmount the local dependencies of the system under study to enable generalization across settings (Koopmans, 2014(Koopmans, , 2016b(Koopmans, , 2020a.…”

“…There is, of course, no shortage of ideas about how the system ought to be transformed. However, one of the dilemmas that the educational system faces is that schools and districts do incorporate innovations in their practices on an ongoing basis, to the credit of policymakers and others working outside of the system (Elmore, 2016;Hess, 1999;Koopmans, 2016b), while those who are implementing those initiatives are faced with the challenge of making the innovations work, often within a timeline that does not allow for them to be fully incorporated into the culture and daily practice of the school system. Thus, with premature evidence being unsupportive, these initiatives tend to be discarded to be replaced by yet newer ones, which, in due course, meet the same fate.…”

Fractality and Power Law Distributions: Shifting Perspectives in Educational Research

“…And while there is an extensive literature on sampling rigor across subjects (e.g., Cohen, 1988), no similar sampling rigor is found across the time spectrum where a small number of measurement occasions is generally deemed sufficient and no further interest is taken in how the behavior of the system evolves over time. Thus, any propensity toward change that the system may possess falls outside of the scope of the research (Koopmans, 2016). While the longitudinal perspective has long been part of the pantheon of educational research methods (e.g., Singer & Willett, 2003) and the applicability of time series analysis to education has been discussed in some detail (Glass, 1972), the use of time series approaches to address the influence of the passage of time on the behavior of systems is infrequent at best in education.…”