This paper reports a study that sought to explain student understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of data analysis, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examined the differences in the problem-solving activities of solvers who…

This study examined the problem-solving behaviors, strategies, and achievement of college students enrolled in a one-semester college algebra and statistics course, with respect to the content areas of quantitative literacy, connections between algebraic and graphical representations, and mathematical modeling. Four instructional units of this…

This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…

This paper describes the characteristics of graphic techniques, such as networks, pattern notes, semantic maps, and graphic organizers, that can be used to acquire knowledge of relationships between concepts in a content area. The implications for research and instructional design are considered, and nine types of these techniques are described…

The outcomes of collaboration provide an incomplete and potentially misleading picture of cognitive change, one that is clarified by examining the collaborative processes themselves. Results from a study illustrate the dangers of focusing solely on the consequences of collaboration and emphasize why the analysis of collaborative processes is…

Three models have been proposed to account for the relationship between the principle of commutativity and the development of more economical addition strategies, which disregard addend order. In the first and second models, it has been proposed that either discovery or assumption of commutativity is a necessary condition for the invention of…

This article presented some of the research on learning processes and illustrated how different modes of thinking can be applied in teaching some topics in secondary mathematics. (Author/RK)

It is the purpose of this paper to identify the topic at hand and to test it against a number of accepted works - the intent being to determine if, and how well, creative drama squares with research evidence on good teaching and learning practices. (Author)

Soar, an architecture for problem solving and learning based on heuristic search and chunking, has been applied to a variety of tasks during the development of the Soar project, the goal of which is to build a system capable of general intelligent behavior. The hypothesis being tested in this aspect of Soar research is that chunking, a simple…

The notion of buggy procedures has played an important role in recent cognitive models of mathematical skills. Some earlier work on student modeling used artificial intelligence methods to automatically construct buggy models of student behavior. An alternate approach, proposed here, draws on insights from the rapidly developing field of machine…

Because research indicates that specific cognitive deficiencies do exist for hearing-impaired individuals (though the normal range of intellectual potential exists among the hearing-impaired as a group), Instrumental Enrichment (IE), an approach developed originally in response to the need for mediated learning experiences for culturally…

The purpose of this paper is to demonstrate methods for developing cognitive processes in adult students. It discusses concept formation and concept attainment, problem solving (which involves concept formation and concept attainment), Bruner's three stages of learning (enactive, iconic, and symbolic modes), and visual thinking. A curriculum for…

In order to investigate the nature of metaphoric generation, comprehension, and appreciation, 8 different groups of 16 subjects were asked to rate each of 20 terms within each of 8 categories (United States historical figures, modern world leaders, mammals, birds, fish, airplanes, land vehicles, and ships) on 21 scales such as "warlike…

Relates J.P. Guilford's model of problem solving to the negotiation of a reference question. (PF)

This analysis of solutions to the Tower of Hanoi Problem underscores the importance of subject-by-subject analysis of "What is learned" in understanding human behavior in problem-solving situations, and provides a technique for describing subjects' task performance programs in detail. (Author/BJG)