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_t+1 = f (y_t), 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.     

An empirical validation of a dynamic systems model of interaction: do children of different sociometric statuses differ in their dyadic play?

Studying short-term dynamic processes and change mechanisms in interaction yields important knowledge that contributes to understanding long-term social development of children. In order to get a grip on this short-term dynamics of interaction processes, the authors made a dynamic systems model of dyadic interaction of children during one play session. The control parameters of the model relate to children's goal-directedness, concerns, emotional appraisals, social power, and social competence. Three groups of dyads of different sociometric statuses are represented by specific control parameter values. The model's order parameters consist of children's emotional expressions and other- versus self-directed actions. This article describes the empirical validation of the model and the methods needed for such validation. It focuses on the model's predictions of averages and distributions of the major variables, of the occurrence of attractors and power law distributions, and on the model's sensitivity. Overall, the model fits the empirical data well. In the discussion, we reflect on the developmental and methodological implications for explaining social interaction on the short-term as well as on the long-term time scale. In addition, implications for intervention and assessment are presented, in particular relating to the problem of rejection.     

The dynamics of scaffolding

In this article we have reinterpreted a relatively standard definition of scaffolding in the context of dynamic systems theory. Our main point is that scaffolding cannot be understood outside the context of a dynamic approach of learning and (formal or informal) teaching. We provide a dynamic systems model of learning and teaching in which the notion of scaffolding plays a central role. The model is illustrated with a study of the math learning of five children in a school for special education. The model predicts various non-linear properties of learning and teaching phenomena, which need to be tested in further empirical research. In order to explain scaffolding and learning processes observed in real contexts, the basic dynamic model must be embedded in a broader model, that of embodied and socially situated dynamics of concern-governed action.