The article considers the mathematical models of the growth and accumulation of scientific and applied knowledge since it is seen as the main potential and key competence of modern companies. The problem is examined on two levels--the growth and evolution of objective knowledge and knowledge evolution of a particular individual. Both processes are…

Niche construction is the modification of components of the environment through an organism's activities. Humans modify their environments mainly through ontogenetic and cultural processes, and it is this reliance on learning, plasticity and culture that lends human niche construction a special potency. In this paper we aim to facilitate…

This paper provides a survey of models for the analysis of individual growth data emphasizing the problems posed by serial or time dependence in the application of polynomial regression models. The concepts of serial correlation and autoregressive models are illustrated. It is demonstrated that standard inference procedures may be quite misleading…

Extends dynamic model of cognitive growth proposed by van Geert in three directions: (1) added a term to consider exposure to material to be learned; (2) developed method to apply model to cross-sectional studies; and (3) developed procedure to scale cognitive abilities tests with items of varying difficulty. Tests model with 2- to 15-year-olds'…

A family of finite mixture distribution models is presented that allows specification of basically different developmental processes in distinct latent subpopulations. These models are introduced within the framework of mixed latent Markov chains with multiple indicators per occasion, and they are illustrated with empirical data on therapeutic…

Comments on van Geert's mathematical model of Vygotsky's zone of proximal development, in this issue. Supports van Geert's use of a nonlinear model, noting that linear statistical models overlook variability in psychological phenomena. Discusses the time asymmetry in van Geert's model, which does not account for a subject's "developmental…

Growth curve models are a useful tool for developmentalists because they can estimate an attribute's developmental function by providing a mathematical description of growth on an attribute over time. However, selection of a growth curve model appropriate for estimating individual developmental functions is problematic. The ideal model is the one…

Methodological implications of a person-oriented, holistic-interactionistic perspective in research on individual development are outlined, desirable properties of a mathematical model of a phenomenon are discussed, and selected methods for carrying out person-oriented research are briefly overviewed. These methods are: (1) the classificatory…

Argues that Vygotsky's "zone of proximal development" (ZPD) can be redefined as a nonlinear dynamic model. Presents a mathematical reformulation that generates a variety of developmental patterns and has the capacity to show under which conditions unwanted or unsuccessful developmental paths may occur. Illustrates how this reformulation…

Hawkin's procedure for testing a sequence of observations for a shift in location could have applicability for assessing change within a single subject. Monte Carlo results suggest that Hawkins' procedure is robust with respect to moderate violations of its underlying assumptions of homogeneity of variance and normality. (Author/GDC)

The logical structure of the Campbell and Fiske multitrait-multimethod approach is applied to the problem of studying growth and its determinants. The resulting model is a special case of Joreskog's general model for the analysis of covariance structures. The relationships of traditional psychometric formulations to this model are detailed.…

The hierarchical structure of the formal operational period of Piaget's theory of cognitive development was explored through the application of ordering theoretical methods to a set of data that systematically utilized the various formal operational schemes. Results suggested a common structure underlying task performance. (Author/BH)

Quantitative growth curve models for estimating individual developmental functions from various types of longitudinal data are discussed in the context of investigator assumptions and research design characteristics. Linear and nonlinear models that estimate growth curves are illustrated, and contrasted when they are fit to speech development…

Many educational questions of research interest focus on individual differences in attitudes and behaviors related to academic achievement, changes in such attitudes and behaviors over time, and the types of academic environments that facilitate or prevent development of achievement attitudes and behaviors at school. This paper, the first in a…

The measurement of change in quasi-experimental educational research was discussed. Problems related to measuring change exist to varying degrees in all research designs; these issues are less troublesome in experimental studies because the investigator can manipulate the interest variables and observe their effects on other variables. Measuring…