Changes in values, beliefs and the demographics o f A m e r i c a n s o c i e t y h a v e n o t b e e n a c c o m p a n i e d b y c o n s i s t e n t c h a n g e s in definitions and practices relat can be presented to s u p p o r t t h e b e l i e f t h a t a f u n d a mental paradigm shift is occurring or has occurred, programs. Research and literature are reviewed to support the thesis that that new identification procedures, new curricular and instructional programs, appropriate criteria for evaluating identification procedures, and changes in beliefs and stereotypes are needed to resolve the problem of underrepresentation and to accomplish needed changes. A conceptual framework, definition of giftedness, and an identification process consistent with the definition are discussed A desig n for develop ing app ropri ate methods and critria to evaluate identification procedures and for monitoring and evaluating changes in beliefs and stereotypes are provided.

A new definition of giftedness is proposed based on a review of the constructs of intelligence, creativity, and problem solving. A research design employed in a series of studies of giftedness in children and adults is presented, along with a summary of important results. Finally, implications of the design for both research and practice are outlined.

Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary students. The author investigated this relationship by separating performance in openended and closed situations. Findings of the study indicated that the cognitive abilities explained 32.3% (open-ended) and 48.2% (closed) of the variance in mathematical problem solving performance as a whole. Mathematical knowledge and general intelligence were found to be the only variables that contributed significant variance to closed problem solving performance. General creativity and verbal ability were found to be the only variables that contributed significant variance to open-ended problem solving performance.

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In the Cultivating Diverse Talent in STEM project, funded by the National Science Foundation in the United States, new assessments were developed, field tested, used to identify students with exceptional talent in science, technology, engineering, and mathematics (STEM), and compared with existing methods (grade point average [GPA], letters of recommendation, self-statements). Students identified by both methods participated in an internship program in laboratories of scientists on the campus of an R1 university in the Southwest. Existing methods limited the diversity of students identified. Significant differences were found between students identified by the new methods (M2) and existing methods (M1) in GPA, ethnicity, and parent level of education. Ethnicity differences may be due to the ethnic makeup of the partner schools, but differences in GPA and parent level of education cannot be attributed to the location of schools. Although GPAs of M1 students were significantly higher (3.71) than those of M2 students (3.07) and M1 students came from higher income groups and schools in higher income areas, the M2 students scored higher on all the performance assessments of creative problem-solving and at similar levels on concept maps and mathematical problem-solving. Studies of the usefulness and psychometric properties of the new assessments are needed with different groups and in different contexts.