Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

The focus of the article is on the complex cognitive process involved in learning the concept of "straightness" in Non-Euclidean geometry. Learning new material is viewed through a conflict resolution framework, as a student questions familiar assumptions understood in Euclidean geometry. A case study reveals how mathematization of the straight…

Researchers have examined inductive reasoning to identify different cognitive processes when participants deal with inductive problems. This article presents a prescriptive theory of inductive reasoning that identifies cognitive processing using a procedural strategy for making comparisons. It is hypothesized that training in the use of the…

The intent of this paper is to sketch a conception of problem-finding and delineate the role of problem-finding in the solution of problems. (Author)

The history and evolution of the concept of intuition is traced through philosophical intuitionism and positivism to contemporary psychology. The theoretical and empirical psychological research relating to intuitive experience and intuitive behavior is also traced, and relations between intuitive problem solving and previous data concerning…

Performance of 10 adult trainees in a workshop for mentally retarded persons and that of an equivalent mental age group of third-grade children was observed in a toy construction task. Performances were videotaped and coded for executive activities that proved to be a powerful influence in discriminating between the groups. (Author/DB)

Children should be faced with high level questions in the classroom in order to develop their ability to think creatively. (CK)

Suggests a method for helping students approach problems and initiate the problem-solving process. The system is a self-dialogue involving five questions: (1) what is the problem? (2) what are you to find? (3) what are the givens and the desired outcomes? (4) what is the appropriate formula? and (5) what decision is needed? (JOW)

Ninety-two males aged 17 to 20 were interviewed and categorized in terms of four identity statuses: identity achievement (IA), moratorium (M), foreclosure (F), or identity diffusion (ID). Individuals in the IA and M statuses performed better than those in F and ID statuses on the Watson-Glaser Critical Thinking Appraisal, which was used as a…

Examines Sherlock Holmes's reasoning processes and approaches to problem solving and applies his seven principles to students to help them with problem solving. (HTH)

Discusses (1) neobehaviorist theory and analysis of response probability, (2) discrete models of qualitative changes in knowledge and stages of processing, and (3) programmed simulations of the detailed structure of knowledge and cognitive processes. Comments on the prospects for developing significant new understandings of learning during the…

An investigation of the effect of the direction of search on the problem-solving performance of junior high school algebra students reveals a relationship between the number of correct responses and solution time to the number of possible "blind alleys" and memory load. (Editor/LH)

In three experiments, differences in EEG alpha activity between 30 gifted and 30 average individuals were studied. Results support the hypothesis that higher alpha power during information processing displayed by gifted individuals may derive from the nonuse of many brain areas not required for the problem at hand. (SLD)