The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

One of the main tenets of the mental model theory is that when individuals reason, they think about possibilities. According to this theory, reasoning on what is possible from the truth of a sentence would be psychologically basic, whereas reasoning the other way round, on the truth or falsity of a sentence from a given state of affairs, would…

The increasing opening of French freemasonry to lower social classes raises the question of how individuals from different social backgrounds can be assimilated into the practice of context-independent ways of speaking and writing. I address these issues by, first, describing a selection by existing members based on the dispositions already…

Three studies examined the development of category-based induction using an induction then recognition (ITR) procedure in which participants make category-based predictions about study items and are then given a surprise recognition test that requires discrimination between old and new category members. Exposure duration for study items was either…

Fuzzy trace theory explains why children do not have to use rules of logic or premise information to infer transitive relationships. Instead, memory of the premises and performance on transitivity tasks is explained by a verbatim ability and a gist ability. Until recently, the processes involved in transitive reasoning and memory of the premises…

Research on deductive reasoning in adolescents and adults has shown that errors in deductive logic are not necessarily due to a lack of logical ability but can stem from an executive failure to inhibit biases. Few studies have examined this dissociation in children. Here, we used a negative priming paradigm with 64 children (8-10 years old) to…

Despite the increasing use of the microgenetic methodology to examine change, the techniques employed to analyse microgenetic data remain fairly unsophisticated. This paper reviews the existing ways of analysing such data and describes their limitations. We use two recent studies to illustrate how modelling can avoid these problems and reveal…

Psychologists know that reasoning human beings do not spontaneously follow the rules of formal logic when using implication. Addressing this phenomenon, Piaget employed the concept of "significant implication," which exists when the meaning of a subsequent proposition is "included" in the meaning of an earlier one, and is not…

A group of 60 children from grades K, 1, 3, 4, and 8 were assessed via a battery of Piagetian tasks to determine their stages of cognitive development. They were then asked to interpret a number of metaphors ranging in frequency of occurrence in adult speech from common to rare. (Author/JMB)

This paper presents a system for describing and categorizing various theories of language and thinking. Within this system, theories are described in terms of their position on three basic issues: (1) the direction of dependency between language and cognition, (2) the necessity of that dependency, and (3) the level of specificity at which the…

An eight-phase model of processes involved in mathematics problem solving is presented. At each phase, results from factor-analytic studies are used to suggest abilities relevant and prerequisite for successful completion of the phase. Presentation of the model is followed by a discussion of implications for teaching and research. (Author/MK)

Discusses how one's conception of intelligence and its development profoundly affects the formulation of educational objectives. A mechanistic conception of intelligence leads to the definition of objectives as a collection of fragmented "cognitive skills", while a Piagetian conception attempts to develop children's intelligence as an…

Human infants are predisposed to organize their experience in terms of certain concepts (natural) and not others (unnatural). Three formal, necessary conditions on the naturalness of concepts are offered. The conditions attempt to link the problem of naturalness to principled distinctions between sense vs nonsense, simplicity vs complexity, and…

Offers a theoretical account of moral rationality within a rational constructivist paradigm examining the nature and relationship of rationality and reasoning. Suggests progressive changes through developmental levels of moral rationality. Proposes a developmental moral epistemology that accommodates moral pluralism to a greater degree than does…