Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

Science education is viewed from a framework that integrated sources of knowledge with the traditional processes of scientific inquiry. Sciencing is then described, and how it could be implemented with young children is discussed. (MNS)

How mathematics subject matter can be enhanced through the scientific reasoning method, how this integration can be achieved, adaptations needed for a modified approach, and resulting attainments are all considered. Prime numbers using the Sieve of Erastosthenes are the vehicle through which the approach is described. (MNS)

The goal of this article is to identify and disseminate several important messages from recent research on formal thought. Reasoning by adolescents, measurement of Piagetian formal reasoning, the importance of additional factors, stages, and working memory are discussed. (MNS)

This discussion is primarily designed to increase teachers' awareness of Piaget's theory of cognitive development and implications for mathematics in the middle school. It is hoped such awareness will compel instructors to adopt strategies that help pupils gain more from mathematical experiences, by providing impetus for innovation and…

An overview is provided of 50 years of research on naive theories in human biology. A set of recommendations aimed at confronting student misconceptions and facilitating conceptual change about the structure and function of the human body is presented, with five lessons described. (MNS)

As calculators and computer use increases in mathematics education, more educators are recognizing a shift in emphasis from computation to problem solving. Ways to generate problems that can be used to develop pupil creativity and insight are suggested, and process-oriented instruction is promoted. (MP)

Discusses the organization and retrieval of information. Describes the tip-of-the-tongue state during mathematics problem solving. Provides five rules for a deep level of processing of new concepts. (YP)

Provides examples of if-then and combinatorial reasoning situations that have proved successful with college students and can be used with secondary school students. Proposes that practice with these problem solving processes can eliminate the need to memorize formulas that students may not understand. (ML)

Helping children to bridge the gap between physical materials and symbolic representations is the focus of this article. Examples are drawn from numerical topics, with several hierarchies illustrated. (MNS)

Guessing is seen in all forms to be a creative and critical process which has practical and scientific utility. The goal of science in early childhood is viewed as having children make better guesses. Ways of instruction that create and develop an atmosphere for guessing are detailed. (MP)

Cognitive processes, characteristic of the early childhood learner, and potential benefits of learning through incorrect responses are discussed. Science and mathematical concepts viewed to be within the early learner's capabilities are noted, and ways to make such concepts more visable and viable within early childhood settings are detailed. (MP)

Discussed are science activities appropriate for middle school students. Considerations include the degree of abstractness of the concepts and the need for increased class time for explaining, discussing, and integrating students' activity experiences. (DS)

Reports a study to examine the role of context on the ability to interpret graphs. Graph tests involving 2 ecological contexts were presented to 14- and 15-year-old students (n=23) in the form of an interview. Results indicated how students used their contextual knowledge in interpreting the graphs. (MDH)

This study investigated the effects of combining interactive microcomputer simulations and concrete activities on the development of abstract thinking in elementary school mathematics. Students in grades 2-4 were assessed on tasks involving designs and patterns. (MNS)