Productive struggle (PS) has emerged as a critical construct in mathematics education, emphasizing the importance of persistence, cognitive engagement, and conceptual understanding in problem-solving. However, inconsistencies in its conceptual and operational definitions have hindered its effective implementation and assessment. This study…

In this article, I describe the 21 ideas underlying a 42-year search to understand giftedness. I present the ideas roughly chronologically, in the order in which they arose, and discuss how in a career as in science, progress means supplementing or even superseding one idea with the next. In terms of the 21 ideas, I start with a discussion of how…

From the 1990s until 2017 the High Ability and Inquiry Research Group (HAIR) at McGill University in Montreal, received C$1.3M in research funds from Canadian, Quebec, and US agencies to support its research and graduate training in education and educational psychology. Their research encompassed two principal areas, Inquiry in Education and…

Background: Extending Merton's (1936) work on the consequences of purposive social action, the model, theory and taxonomy outlined here incorporates and formalizes both anticipated and unanticipated research findings in a unified theoretical framework. The model of anticipated research findings was developed initially by Carifio (1975, 1977) and…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Research on divergent thinking (mental activity directed to open-end problems for which there is no one correct answer) indicates that the characteristics associated with divergency (fluency of thinking, flexibility of thinking, originality, redefinition, and elaborating) are right brain functions. To assess right brain function and verbal…

Second article of a two-part series focuses on how results of research into learning, creativity, and thinking abilities can be applied to help the individual become more creative. (SL)

Background: Neuroscience is unlikely to produce findings for immediate application in the classroom. The educational significance and practical implications of knowledge about mind and brain inevitably require some level of interpretation, yet the multiplying examples of unscientific "brain-based" educational concepts suggest this process of…

Author examined some logical connections between the creative process and the problem of human relations and argued that though antisocial behavior among creative people is normal and expected, it is neither required nor inevitable. (Author/RK)

The third paper of a series on intellective factors in learning mathematics, critical reviews of research concerned with variables that influence mathematical ability are presented here. (Author/KM)

This study evaluated an attempt to increase the divergent thinking of eighth grade students with a five week experimental treatment utilizing student inquiry. In this treatment, students were shown a demonstration consisting of a discrepant event; students then suggested hypotheses and checked their hypotheses by asking questions, as in Suchman's…

This paper presents a model for examining the cognitive nature of artistic development in children. The model uses Witkin's differentiation theory as a basic construct with which to integrate theories of art criticism/aesthetics (particularly, E.B. Feldman's theory), developmental psychology (Jean Piaget), and linguistics. Witkin's Differentiation…

Mathematical creativity is considered important by many mathematics educators. This literature review gives particular attention to attempts to assess creative ability. Two key aspects emerge related to fixations in problem solving and divergent production, and these might form the basic framework for fostering and rewarding mathematical…

The development of the formal operations and creativity from early to middle adolescence was investigated across high and average levels of school achievement. Two sixth grade classes (sixth-high and sixth-average) and two tenth grade classes (tenth-high and tenth-average) were given formal thinking and creativity tests at separate sessions.…