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…

In this review, it is suggested that language influences the young child's thinking and behavior at an age earlier than commonly reported. Three areas are discussed: concept formation, communication, and problem solving. (CS)

Article considered different ways in which subjects at different age levels solved a musical task involving melodic permutation. The differences in responses to the musical task between age groups were judged to be compatible with Piaget's theory of cognitive development. (Author/RK)

Presents suggestions for opening the minds of children to new concepts and for teachers, who must encourage their pupils to desire to learn about the world. (RK)

Presented is a multiple option curriculum model for current arithmetical programing in development of quantitative concepts for three groups of handicapped children: mentally handicapped, emotionally disturbed, and learning disabled. (Author/CB)

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)

This article presents the Practical Action Teaching Model and discusses its four phases: identification of the practical problem, practical reasoning or deliberation, action, and reflection. It incorporates intrinsically motivating, practical, value-based student problems that call for critical and creative thinking and offer opportunities for…

Presents transcripts of freshmen engineering majors solving elementary physics problems to examine some limitations of formula-centered approaches to problem solving. Although students use formulas successfully, the qualitative conception of the underlying physical situation is weak. Results from written tests indicate that this phenomenon may be…

This study considers two problems related to cognitive development: "Is development hierarchical?" and "If so, what are the mechanisms involved in the process of development?" Analysis of the results of an experiment lead to differentiation of stages of development, and problem-solving strategies at each level are discussed.…

It is argued that a young child's perceptual skills form the basis for all future conceptual and mathematical learning. An experiment supports the argument. (MP)

An activity in which children can learn the concept of the sizes of planets in comparison to the size of the earth is described. Activity questions are included. (SA)

Reports a study of the quality and extent of understanding of certain well-known theoretical concepts which are held by prospective teachers (N=173) of chemistry in Yemen. Results indicate that teacher understanding ranges from a partial understanding with a specific misconception to no understanding. Contains 25 references. (DDR)

Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…