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…

Notes advantages of using dynamic models to understand cognitive functioning: (1) they are specifically intended to represent changes that systems undergo as they evolve; (2) they can capture change in a continuous fashion; (3) they can account for development of behavior that appears orderly at times and disorderly at others, and (4) chaotic…

Notes that there has been far less mathematical modeling of children's memory than of adults' memory. Explores the flaw in fuzzy-trace model, and maintains that situations in which partial verbatim information is used along with partial gist information fall outside the boundary of this type of model. Suggests refining the concepts of and…

Notes that spontaneous false memories are a routine part of everyday memory and more common than implanted false memory. Commends the fuzzy-trace theory for the separation and explanation of these two sources of inaccuracy. Demonstrates the theory's handling of three phenomena concerning the creation and maintenance of false memories. (LBT)

Notes that fuzzy-trace theory provides a link between indices of memory performance and the theoretical processes that underlie that performance. Author argues false memories can arise because of processes that normally affect forgetting. Maintains that, to the extent that memories lose their distinctive properties, such memories may become…

Suggests that fuzzy-trace theory may replace dominant metaphors of cognitive development. Discusses theoretical climate of the 1980s when the theory was first formulated. Describes how, by integrating new ideas about how cognitive development was viewed into a coherent framework, the theory slowly gained acceptance as critical aspects of it were…

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…

Comments that fuzzy-trace theory is broadly comprehensive and contains compelling experimental manipulations; debates assumptions of the theory. Describes aspects of the historical and theoretical context of the theory and its usefulness in organizing false memory phenomena. Suggests some limitations concerning the representation of child…

Describes the origins of fuzzy-trace theory, including Piagetian, interference, information-processing, and judgment and decision-making influences. Discusses similarities and differences between fuzzy-trace theory and other approaches to memory falsification. Considers the theory's predictions regarding age differences in memory falsification and…

This paper discusses a model of information storage and retrieval, the k-d tree (Bentley, 1975), a binary, hierarchical tree with multiple associate terms, which has been explored in computer research, and it is suggested that this model could be useful for describing human cognition. Included are two models of human long-term memory--networks and…

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

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'…