Teachers need to assist students in understanding what they read in science textbooks. Presents effective reading as a basis for good problem solving skills. (DDR)

Back-of-the-envelope problems call for approximate calculations of quantities that can be related to information in a person's knowledge but are not solved precisely. These problems provide an opportunity for the study of processes and the role of general knowledge in ill-defined problem solving. Subjects with advanced and intermediate knowledge…

This paper represents one portion of an ongoing effort to elaborate on pedagogical principles based on structural-developmental (largely Piagetian) theory and research. Here, a concept of "problem structure" is developed as a means for identifying physical factors that contribute to children's ability to apply experimental reasoning.…

Reported are early results of a research program that aims to improve children's mathematics learning by developing attitudes and strategies that support processes of interpretation and meaning construction in mathematics. Considerable research shows that many children learn mathematics as symbol manipulation rules, without meaning. Collaborative…

Mathematics is generally regarded as a well-structured discipline by educators and cognitive scientists. This leads to the analysis of the suggestion that practitioners begin investigating possibilities for teaching mathematics as if it were an ill-structured discipline, with more than one interpretation for mathematical statements. The paper is…

In an experiment using a conditional logic task, subjects were given a set of cards defining a particular conditional relationship. The subjects were required to determine the rule and predict the outcomes of the rule. Rule structure was varied by providing subjects with either a suggested rule, a partial rule, or no rule for each set of cards.…

The relationship of cognitive development to learning science is considered. Views of thinking from both a psychological and a scientific standpoint are compared in order to shed light on current science teaching practice. Metacognition and problem solving are discussed. (Author/MT)

This study investigated whether good novice problem solvers have their knowledge arranged around problem types to a greater extent than poor problem solvers have. Twelve problem types (see appendix) were distinguished according to underlying physics principles and 65 knowledge elements were printed on cards for university students to sort.…

This paper presented various issues about pedagogical and cognitive aspects of problem solving and explored ways to lessen the heavy cognitive load of a problem solving task. It established a problem type schema for students at different levels. It recognizes the role of modern technology as a cognitive tool that promotes learning mathematics with…

Teaching/learning trends include (1) incremental (information explosion); (2) stationary (biology of cognitive processes); and (3) iterative (recurring debates over teaching methods). Effects are externalization of knowledge structures, the importance of "importance," and instructional "enabling," failure of teachers and students to confront real…

Examines the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry. Indicates that high achievers build schemas that are qualitatively more sophisticated than low achievers, which in turn helps them construct representations that are conducive to understanding the…

Explores the relevance of hierarchies to information processing. Suggests that participants in all conditions create hierarchical representations as they work, and those in nonlinear conditions use this structure to guide their exploration of the material. An important function of hierarchies may be to define relationships between concepts.…

The relation of knowledge for solving problems to understanding of general principles in a subject-matter domain is discussed. Theoretical representations, called "conceptual competence," are presented to represent principles that are believed to be understood implicitly by individuals. Implications for problem-solving procedures can be…

Constructivist theory argues that students construct knowledge for themselves and that each knows the world in a different way. The problem for education is how students can construct an "objectified" knowledge. Outlines an integrative framework for the description of information and problem-solving procedures and a problem-solving…

Used a microgenetic method to examine knowledge acquisition as a process by coordinating existing theories with new evidence. Subjects were 17 community college students (ages 22-47) and 15 fourth graders. Assessed knowledge acquisition in problem solving in both physical and social domains. Found multiple strategies for, and varying levels of,…