Argues that Vygotsky's "zone of proximal development" (ZPD) can be redefined as a nonlinear dynamic model. Presents a mathematical reformulation that generates a variety of developmental patterns and has the capacity to show under which conditions unwanted or unsuccessful developmental paths may occur. Illustrates how this reformulation…

A conceptual framework of cognitive growth is sketched and a mathematical model of cognitive growth is presented with the conclusion that the most plausible model is a model of logistic growth with delayed feedback. The model is transformed into a dynamic systems model based on the logistic-growth equation. (SLD)

Argues that what matters is not the difference between learning and development, but the dynamic relationships that form the key to understanding. Examined two models of these relationships: (1) a semantic approach, distinguishing five dimensions along which learning and development can be compared; and (2) a mathematical nonlinear growth model…