Research in the psychology of mathematics education has been confronted with the fact that people blatantly fail to solve tasks they are supposed to be able to solve correctly given their available domain-specific knowledge and skills. Also researchers in cognitive psychology have encountered such phenomena. In this paper, theories that have been…

Successful learning sometimes requires that the learner abandons or rejects one or more prior concepts, beliefs, or intuitive theories. Such "nonmonotonic changes" are widely believed to have a low probability of occurring spontaneously and to be difficult to promote with instruction. A theory of nonmonotonic cognitive change should explain both…

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…

This discussion of metalearning theories and thinking skills in relation to instructional design highlights other papers presented in this journal issue. Topics discussed include properties of skills; problem solving; the concept of psychological sets in contrast to the concept of skill; and the organization of previously acquired systematic…

An attempt is made to link the domain of mathematics and the natures and abilities of mathematicians to that which is perceptual, presentational, and implicit. (MP)

A theory of adult cognitive development which includes two post-formal operational stages is described. The paper is divided into three sections. The first section provides background for discussion of the theory. A case study in which various employees in a hypothetical organization react to a problem is provided. Examples of pre-logical,…

Representational competence develops as individuals learn that objects, events, and places can be represented in some form. Irving Siegel's studies of classification competencies showed that underprivileged children have difficulty sorting pictures into meaningful groupings. However, both privileged and underprivileged children construct…

Discusses the relationship between situated cognition and anchored instruction in response to criticism of a previous article. Topics addressed include school versus nonschool settings; learning by observing models; "real-world" problem solving; transfer of training; and future work. (26 references) (LRW)

This fourth in a series of edited transcripts based on a conference at Utah State University compares Gagne's Conditions of Learning with Merrill's Component Display/Design Theory, and suggests a merging of the two. Topics discussed include content structures, learning hierarchies, learning theories, learner control, problem solving, cognitive…

The purpose of action learning is to learn through devising solutions and strategies in response to problems and implementing them through deliberative action. To understand the relation between action and learning, learners and facilitators need sufficient understanding of both concepts, but they are handicapped by lack of adequate theory and…

Explains how the instrumental enrichment program helps adolescents and adults develop higher order thinking and problem-solving abilities. (Author/MLF)

Many students are not skilled "thinkers" or "problem solvers." Extensive research has been conducted to describe the mental processes involved in problem solving in the hope of establishing a theoretical basis for training students to become more adept at reasoning. Certain problems become evident, however, when reviewing literature for designing…

Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

Discusses the role of instructional design in the development of learning theory. Topics discussed include the acquisition of knowledge and skills; models of teaching; the teaching and acquisition of concepts; influences on retention; and the integration of procedures, principles, and concepts for solving problems. (20 references) (LRW)

Argues that thinking and problem solving should be taught as part of an interactive process between these cognitive abilities and the acquisition of domain-specific knowledge, rather than as add-ons to knowledge. (CMG)