Elsevier

Developmental Review

Volume 25, Issues 3–4, September–December 2005, Pages 408-442
Developmental Review

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

https://doi.org/10.1016/j.dr.2005.10.003Get rights and content

Abstract

The basic properties of a dynamic systems approach of development are illustrated by contrasting two simple equations. One, yt+1 = f (yt), is characteristic of dynamic systems models. The other, yi = f (xi), 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.

Section snippets

Dynamic systems gets you into problems…

Being a developmental psychologist and applying dynamic systems theory is almost like begging for trouble. A quick look through handbooks on dynamic systems theory (for instance Jackson, 1991, Katok and Hasselblatt, 2005) reveals an amassment of abstract terms and mathematical equations most of which are simply not accessible for the mathematically untrained reader, which the developmental psychologist is likely to be. It gets worse if instead of the handbooks the real mathematicians working in

The study of development: Two basic equations

The two basic equations that will be discussed in this section reflect an almost paradigmatical difference in the approach to development. In this light, it is worthwhile to give some thought to the original meaning of the word “development.” Etymologically, the English word development stems from the Old French desvoloper, which means “to unwrap.” The German and Dutch words Entwicklung and ontwikkeling are literal translations of that term. The word is also related to the Latin evolutio (to

The basic equation of dynamic systems

The CRC Concise Encyclopedia of Mathematics (Weisstein, 1999) provides a particularly helpful—and remarkably frugal—definition of a dynamic system. It defines it as “… a means of describing how one state develops into another state over the course of time” (Weisstein, 1999, p. 501) . Thus, if yt is a specification of a “state” of a variable y at time t, a dynamic model takes the formyt+1=f(yt),which should be read as “the value of y at time t + 1 is a function “f” of the value of y at time t.”

Results from the agent model

The second, i.e., agent model consists of a considerably more extensive set of coupled dynamic equations than the first model. The equations are referring to model components such as preference, emotional evaluation, coupling with emotional expression, effect of the other child’s action, effect of emotional expression and so forth. The relations between the components are represented graphically in Fig. 4. The arrows refer to simple quantitative relationships. White arrows refer to

Conclusion and discussion

A major goal of this article was to show that what we have—somewhat unscientifically—called the Groningen brand of dynamic systems might contribute to the understanding of developmental processes. The main idea of our approach was cast in the form of an elementary dynamic equation, which was compared with the elementary equation that underlies the majority of developmental research (which we called the standard approach). The latter equation represents an association between an independent

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