An investigation of selected research projects which focus on intellectual development is presented. The treatment begins with a description of psychological-oriented studies and illustrates the many ways in which studying a second language in school settings contributes to the cognitive development of the learner. (Author/RM)

This book deals addresses how the development of the human capacity for mathematical cognition occurs through educational experience. Chapters include: (1) "The Development of Math Competence in the Preschool and Early School Years: Cognitive Foundations and Instructional Strategies " (Sharon Griffin); (2) "Perspectives on Mathematics Strategy…

This study addressed the problem of how a prospective mathematics teacher's active engagement in a scientific inquiry can deepen the meaning of her extant mathematical concepts. We used a constructivist framework to analyze a 2-hour interview with a prospective mathematics teacher as she solved an open-ended problem of graphing a 3-D landform. We…

This paper studies the modes of thought that occur during the act of solving problems in mathematics. It examines the two main instantiations of mathematical knowledge, the conceptual and the structural, and their role in the act. It claims that awareness of mathematical structure is the lever that educes mathematical knowledge existing in the…

This paper explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at PME-NA about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding we point to the kinds of learning and understanding we may see occurring when…

This report describes a program for improving the transfer of the learning of different techniques used in computer applications. The targeted population consisted of sophomores and juniors in a suburban high school in a middle class community. The problem was documented through teacher surveys, student surveys, anecdotal records and behavioral…

This report describes a study that investigated the relationship between mental imagery and problem solving in physics, specifically in kinematics. A distinction is made between visual imagery and spatial imagery used in solving physics problems. The results of this study indicate that while spatial imagery may promote problem solving success, the…

This paper presents a reasoning taxonomy to explain reasoning objectives, strategies, and habits available to the advanced thinker. It begins by explaining the first part of the taxonomy, objectives of reasoning, including the need for skilled thinkers to reason with a purpose and to understand how the world works so that they can engage with it.…

Discusses some central ideas emerging from a systematic approach to teaching scientific problem-solving skills. Areas considered include: insights derived from naturalistic studies; effective problem-solving methods; problem-solving procedures; characteristics of the knowledge base (focusing on functional conceptual building blocks, knowledge…

Describes the development of a curriculum to improve problem- solving ability when faced with uncertainty by (1) encouraging students to examine their thought processes, (2) presenting fallacious arguments, and (3) providing better tools for decision making. Relevant psychological research, some problems of teacher training, and a small-scale…

Discusses three avenues of problem-solving research: misconceiving natural laws, processing information, and constructing solutions. Suggests that the change in emphasis from problem to problem solver and the key role of "physics" problems are unifying aspects of the research. (JN)

It is suggested that there are three levels of difficulty posing barriers to successful problem-solving performance: (1) entry into the problem; (2) basic skills; and (3) general cognitive skills. The levels are described in some detail and suggestions for instructional methods are given. (MP)