Graph-Theoretical Representation of the Structure of Developmental Models

Vangeert, P

doi:10.1159/000275801

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…For instance, in a system of production rules that describes how the child solves the balance scale task (e.g., Siegler, 1983), a specific decision rule is either part of the rule system or not. In a transformational generative model of syntactic development, the child's grammar either contains a rule to change the subject–verb position in questions or not, but it does not contain rules such as “Change the subject–verb position arbitrarily in 27% of the cases.” Put differently, the distinctions between developmentally different states of a cognitive structure occur in the form of discrete steps (see van Geert, 1987a, 1988c, for a more general account). However, the performance concerned does not change in the form of a sudden discrete leap corresponding to a state shift, but rather follows a gradual, sometimes irregular, increase (discussed later).…”

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confidence: 99%

A dynamic systems model of cognitive and language growth.

Vangeert¹

1991

Psychological Review

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382

274

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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.

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confidence: 99%

A dynamic systems model of cognitive and language growth.

Vangeert¹

1991

Psychological Review

Self Cite

382

274

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“…In a series of articles that I published some 20 years ago (Van Geert, 1987a, 1987b, 1987c, 1988, I argued that this is exactly what 'classical' theories of development do: they give you a recipe to cut up the developmental pie (basically by telling you how the pie is baked, but the metaphor is clearly carrying us away . .…”

Section: Cutting Up the Developmental Piementioning

confidence: 97%

Time, Models and Narratives: Towards Understanding the Dynamics of Life

Geert

2006

Culture & Psychology

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Whereas Rudolph's (2006a) article provides a discussion of mathematical models of time, Yamado and Kato (2006a) present a particular image of time-circular time-as a key feature of an entirely different model of temporality, namely people life-span narratives. In the present article, I attempt to apply some aspects of Rudolph's models to actual developmental research, namely math learning by children in special education, social development, attachment and the timing of puberty. The dynamics of these processes require not only an understanding of how they unfold in time-and which model of time to choose in order to adequately describe them-but also an understanding of the participants' narratives, in an attempt to understand their actions as intentional, with concerns or goals that determine their sequencing and timing. I conclude by saying that, metaphorical or not, the models and narratives presented in the key articles by Rudolph and Yamada and Kato have contributed to at least my own understanding of developmental dynamics by providing particular challenges for reformulating existing issues.

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“…According to the rules for gen erating retrospectively defined models of de velopment [van Geert, 1986b[van Geert, , 1987a, we should first infer the description of the ini tial state, by taking the opposite values of the variables describing the final state. Thus, the initial state will have the following character istics: the mental act takes place first, exter nally, second, with material (or materialized) objects, and third, in a complete, unabbre viated form.…”

Section: A Reconstruction O F the Stage Mode! Based On The 'Abbreviatmentioning

confidence: 99%

The Structure of Gal’perin’s Model of the Formation of Mental Acts

Vangeert¹

1987

Human Development

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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.

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Graph-Theoretical Representation of the Structure of Developmental Models

Cited by 9 publications

References 15 publications

A dynamic systems model of cognitive and language growth.

A dynamic systems model of cognitive and language growth.

Time, Models and Narratives: Towards Understanding the Dynamics of Life

The Structure of Gal’perin’s Model of the Formation of Mental Acts

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