The purposes of this experiment were: (1) to examine the development of categorical representations by comparing the performance of children of various ages to adults, and (2) to compare the internal representations of basic level and superordinate categories. Subjects were 48 children (in second, fourth and sixth grades) and 16 adults. The…

This theoretical paper reevaluates the Piagetian tradition in the study of propositional reasoning. Piaget's assertion that children's logic, prior to the stage of formal operations, is structurally adequate for dealing with objects and their properties, but is inadequate for fully competent propositional reasoning, is challenged on three grounds:…

This paper argues in favor of using interactional strategies in the study of formal operations reasoning. Interactional designs allow a convergent approach to specifying processes underlying the interaction of variables. In contrast, current methodologies contain two inherent disadvantages: they have limited utility in specifying the processes…

The purpose of this study was to provide a more complete understanding of the storage and retrieval processes of developmentally different youngsters. Forty-four second and fourth grade subjects were given a lesson consisting of 25 facts to learn and remember. Half of the group learned the facts in a context containing superordinate statements…

This paper presents a study designed to determine if groups of concrete and formal operational children can be identified through the technique of cluster analysis, using a battery of Piagetian tasks. A Total of 64 subjects, 8 boys and 8 girls from each of the second, fourth, sixth, and eighth grade levels, were selected from a public elementary…

Two experiments compared the cognitive maps (mental representations of the spatial environment) of first graders, fifth graders and college students, and investigated developmental changes in the ability to manipulate cognitive maps mentally. In the first experiment, subjects were asked to move from stationpoint to stationpoint and at each, to…

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

This paper explores one student's attempt to apprehend an abstract mathematical structure (similar to Z[99]). We discuss Karmiloff-Smith's theory of representational redescription as a model for the development of structural understanding and contrast this with existing process-object theories. We use two cycles in Molly's movement from an action…

This paper uses data from two mathematics lessons to explore the nature of progressive discourse and examine critical features of teacher actions that contribute to mathematics classrooms functioning as communities of inquiry. Features found to promote progressive discourse include a focus on the conceptual elements of the curriculum and the use…

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. This article extends the scope of applicability of this…

This paper examines the cognitive process of concept development in preschool children, based on recent psychological research. Rather than attempting an exhaustive review of the more than 7000 articles written on children's concepts of categories, the paper highlights and illustrates four key themes that emerge from recent research: first,…

One of the most basic theoretical areas in the study of visual communication and visual literacy is the nature of representation. Some of the important research in this area is reviewed in this paper, and a model of representation is developed that satisfies many of the philosophical concerns. The paper begins with a discussion on the relationship…

Two studies examined preschoolers' understanding of germs as causes of illness. Previous research suggests that preschoolers know that certain behaviors lead to illness without understanding why or how. In the first study, 22 children between 4 and 5 years old were presented with 12 brief stories describing characters engaged in either dangerous…

The problem of response set is important for questionnaire designers and interpreters, but the public is affected as well if policy is determined on the basis of unsupported conclusions. This study focused on one of the most researched response sets, extreme responding (ER), or extreme checking styles, and its relationship to one dimension of…

Three areas of the classical rhetoric of Aristotle, adapted for the modern discourse of inquiry and demonstration, provide a systematic framework for students to understand thought, investigation, and writing in other disciplines: aitia, kairos, and the enthymeme and the example. Aitia, or cause, has four aspects--the material cause, the formal…