In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order…

Meanings of "surprise" are wide and include uplifting and engaging facets like wonder and amazement on the one hand as well as ones that may be of the opposite nature like interruption and disrupt on the other. Pedagogically, educators who use surprise in class activities are focusing on students being "taken aback" by a situation, hopefully…

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…

A total of 308 undergraduates performed 2 word tasks and a gestalt closure task in a study of intuition. Subjects could respond discriminately to coherence they could not identify and were led by this perception to form a hunch or hypothesis. Clues to coherence evidently activate problem-solving networks. (SLD)

The study concerned (1) identifying component processes of discovery and rule learning; (2) describing differences in learning outcomes produced by the two instructional methods, and; (3) optimizing learning. It was believed that understanding the effects of aptitude, instructional methods, and their interaction is important in the study of…

Seven principles are presented for improving creative thinking, based on assumptions of creativity as a perceptual shift resulting from a metamorphic mental image. Principles include (1) the future initiates and pulls creative thought; (2) initial fact finding is best postponed; (3) problem redefinition is often retrospective; and (4) metaphors…

A SYSTEMATIC EXPLORATION OF THE COGNITIVE PROCESSES INVOLVED IN THE PRODUCTION OF A DRAWING WAS CONDUCTED. A SITUATION WAS DESIGNED IN WHICH A SAMPLE GROUP OF ABOUT 30 ARTISTS COULD BE OBSERVED AT WORK. BEHAVIOR WAS RECORDED AND THE PROGRESS OF THEIR WORK PHOTOGRAPHED. OF THE BEHAVIORS OBSERVED, SIX WERE TAKEN TO REFLECT RELEVANT STAGES IN THE…

Studies of creativity have generally dealt with the creative act, typically defined as the statistically infrequent approach to problem solving. A study was conducted to determine whether a relationship exists between problem discovery and originality of the written product, and whether problem-finding behavior may be observed in student writers.…

A REVIEW OF THEORY AND EMPIRICAL RESEARCH ON "THE LEARNING BY DISCOVERY HYPOTHESIS," AND RELATED LITERATURE ON CONCEPT-LEARNING AND PROBLEM-SOLVING, WAS PREPARED FOR A CONFERENCE IN NEW YORK CITY, 1965. RECENT CURRICULAR ACTIVITIES IN THE SUBJECT AREA WERE DESCRIBED. ATTEMPTS WERE MADE TO IDENTIFY INDEPENDENT AND DEPENDENT VARIABLES AND…

A study of the meanings of "generation," a popular term in current rhetorical jargon, reveals important developments in the art and theory of rhetoric. As now used, it refers without clear distinction to rule-governed, heuristic, and trial-and-error procedures. The rule-governed procedures of transformation grammar are being employed to…

Two studies were conducted, one using 80 university students and the other 140 fifth through seventh graders, to examine the relationship between problem-solving strategies (leaping and flexibility) and measures of insight and scholastic aptitude. Relationships among insight, leaping, and quantitative scholastic aptitude were found. A…

Based on a study dealing with problem-finding behavior of artists as the first step in the creative process (Getzels and Czikszentmihalyi), this study on the empirical nature of problem-finding included middle school students from a suburban-rural area in Western Pennsylvania. Eight students identified through three measures as creative were…

Describes grade-appropriate weekly activities designed to appeal directly to students by giving them open-ended questions. Activities may be worked on individually, in pairs, or in small groups. This particular set of activities focuses on stories from literature involving measurement, earning money, marketing a product, and setting up a…