Modern schoolchildren are the new digital generation and their preferences for working with information are based on of the dominant sensory modality which can be visual, auditory, and tactile/ kinesthetic. Therefore, to organize effective mathematics teaching it is necessary to use a personalized system of teaching techniques, instructional…

How people see the world, even how they research it, is influenced by beliefs. Some beliefs are conscious and the result of research, or at least amenable to research. Others are largely invisible. They may feel like "common knowledge" (though myth, not knowledge), unrecognized premises that are part of the surrounding culture. As we…

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…

Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving…

This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements. In order to investigate this, a quasi-experimental non-equivalent comparison group design…

The purpose of this study was to design a unit on percent for adult remedial students based on the principles of Piaget's theory and to evaluate the effectiveness of the unit as a means of improving one characteristic of formal operations, the ability to use porportion. The subjects consisted of 89 undergraduate remedial mathematics students at a…

This pamphlet reviews five reports that highlight an emerging consensus among researchers about the value of systematically incorporating cognitive instruction into the elementary school curriculum. First is a comprehensive framework by Robert J. Marzano and C. L. Hutchins for an integrated approach to thinking skills that has been developed and…

This study investigated the relationships between Piagetian logical reasoning abilities with an information processing capacity, and first-grade children's performance on verbal addition and subtraction problems. An analysis of simple arithmetic problems indicated that several reasoning abilities identified by Piaget are needed to achieve…

Investigates uses of interactive geometry software to enhance students' understanding and reasoning about two-dimensional shapes. Describes basic principles that underlie high-quality geometry instruction. Presents examples that illustrate how appropriate use of dynamic software can enhance students' geometric reasoning. (KHR)

When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…

The National Institute of Education has supported new research and synthesized existing information to provide teachers and administrators with direction for cognitive instruction. Efforts have been made to identify kinds of thinking and learning conducive to success in particular subjects and to offer useful research-based ideas to teachers. (TE)

We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970).…

The purpose of this study was to test the effect of several cognitive development capacities on first-grade children's ability to learn basic concepts and skills of linear measurement. The cognitive capacities of interest were logical reasoning ability and information processing capacity. The hypotheses predicted that children who had not yet…

The focus of this research was the conduct and analysis of six hours of clinical interviews with sixth and ninth grade students to investigate how they learn geometry in light of the van Hiele model. In chapter 1 an overview of the project and its four major goals is given. The theoretical model is described in chapter 2. In chapter 3 the…

Described is a study in which seventh graders used LOGO in place of receiving geometry instruction. It was hypothesized that angle recognition estimation and construction would be higher for the LOGO group. Reports that a difference was found favoring the LOGO group. Provides a short history of the LOGO language. (MVL)