In the first part of the article, a conceptual framework is sketched to define cognitive growth, including language growth, as a process of growth under limited resources. Important conceptsare the process, level, and rate of growth; minimal structural growth level; carrying capacity and unutilized capacity for growth; and feedback delay. Second, a mathematical model of cognitive growth under limited resources is presented, with the conclusion that the most plausible model is a mode] of logistic growth with delayed feedback. Third, the model is transformed into a dynamic systems model based on the logistic growth equation. This model describes cognitive growth as a system of supportive and competitive interactions between growers. Models of normal logistic growth, U-shaped growth, bootstrap growth, and competitive growth are also presented. An overview is presented of forms of adaptation of resources (e.g., parental and tutorial assistance and support) to the growth characteristics of a cognitive or linguistic competence. Finally, the question of how the model can account for stages of growth is discussed.

An analysis of the underlying structure of Gal’perin’s model of the formation of mental acts is presented, based on a generative method developed by van Geert in 1987. First, an overview of Gal’perin’s five-stage model is given. Then, two analyses of the underlying state and sequence rules are presented, one according to a prospective, another according to a retrospective strategy. It is concluded that a retrospective strategy yields the best result. It is argued that the five-stage model should be viewed as a particular transformation of an underlying model of four main stages, each including four substages. Finally, an analysis of the transition rules is given. It includes a model of transitions and process components and a model of a transition topology. The topology is a structure of overlapping domains. The particular form of the overlap accounts for the stepwise and controlled character of the formation of a mental act.

A graph-theoretical representation of the structure of developmental models is described. The graph representation relates several aspects of models, namely, the structure of elementary changes of developmental features (in the structural graph), the conditional relationships between the features defining a developmental process (in the combinatorial graph), the ‘deep structure’ of a developmental model (in the model graph), and the surface form of the model (in the transition and path graphs). The graph representation is illustrated with examples drawn from cognitive development (Piaget’s and Gal’perin’s models, conservation research), language development, and identity development (Erikson’s and Marcia’s models).

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