Explaining after by before:Basic aspects of a dynamic systems approach to the study of development

The basic properties of a dynamic systems approach of development are illustrated by contrasting two simple equations. One, y(i+1) =f(y(i))7 is characteristic of dynamic systems models. The other, y(i)=f(x(i)), refers to what, for the sake of simplicity, is referred to as the standard developmental approach. We give illustrations from cognitive, language and social development to show the characteristic differences of these two types of models and show their complementarity. The article further compares the "Bloomington" with the "Groningen" approach to dynamic systems theorizing in developmental psychology. It continues with a discussion of two important questions. One involves the issue of measurement and the nature of developmental variables from the viewpoint of dynamic systems. The second concerns the question of short- and long-term time scales in developmental models, which is discussed on the basis of an example, namely dyadic interaction of young children in the context of different social statuses. (c) 2005 Elsevier Inc. All rights reserved.