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Is leadership an innate quality of the person? Can it be taught? Or is it simply a feature of small group behavior and organizational structure? Or perhaps just a naive notion that allows us to attribute the cause of daily events to .our fellow humans rather than the less personal and, consequently, less identifiable factors of world economic activity and multinational maneuverings.Starting with a few general comments on leadership, this paper then notes the historic origins of its inclusion as a type of giftedness in the American government's definition of gifted and talented. Given this federal perspective, the construct is considered from a gifted point of view and then from a leadership frame of reference. In these two sections, selected concepts and research findings are reviewed. This is followed by a short section speculating on the implications of the marriage of these two areas of study on the identification and education of potential leaders in our schools.For the purpose of this paper leadership is regarded as a phenomenon embedded in the matrix of events which combine to form such complex social processes as political, economic, and religious movements. A leader is understood to be that person invested with the responsibility to maintain and change both the incidental and basic fabric of such movements. Such an individual is distinct from someone whose charge is fundamentally the maintenance of whatever group or organization he or she serves. So organizational supervisors and middle management personnel, who have so frequently served as the subjects of research on leadership, are not seen as true leaders. Within this presentation leadership implies eminence, an eminence characterized by social action. This action eminence serves to distinguish social leaders from people who have attained eminence through thoughtful reflection and production. There is no question that such gifted individuals attained leadership within their fields of work. However, theirs is primarily a reflective form of leadership. Within the following pages I will be looking at the action leader, speculating about the nature of this type of talent. My remarks will focus on both what we do and do not know about this subject. The Beginnings of a CategoryIn 1972 the United States Commissioner of Education published a report on the status of gifted and talented education in America. Perhaps the most significant portion of that paper was the attempt of its authors to establish a definition of giftedness that would reflect the multidimensional approach to the phenomenon which had emerged during the previous decade, while at the same time making the definition useful for future policy and planning of federal program development. Taking perhaps the simplest explanatory approach available, the report established a taxonomic strategy for defining giftedness, isolating a series of supposedly distinct categories of gifts and listing them as separate operational entities. As the definition evolved leadership emerged as a natural component. The c...

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We apply a method of positive quadratic forms based on polynomial inequalities to establish sharp explicit bounds on the envelope of Hermite polynomials in the oscillatory region |x| < (2k – 3/2)1/2.

The author presents a convincing case that large-scale studies do not necessarily yield useful information for describing the phenomenon we call giftedness, or for identifying related cause-and-effect factors. Alternatives for studying gifted indivduals using methods such as case studies and single subject designs are explored and discussed.When we do research on giftedness we intend to accomplish two things: 1) to better describe the phenomenon and 2) by locating cause/effect relationships connected to that phenomenon, more adequately explain its nature and our effect upon its overall character and development. In research on the gifted and talented we usually employ large samples in the pursuit of these objectives. Survey, correlational and quasi-experimental designs are typical of our research strategies. Such designs allow us to do parametric statistical analysis (statistics which assumes that the data distributes itself normally along the bell-shaped curve) of our data and, therefore, to be reasonably confident when we generalize our findings from our research sample to some larger population of high performing individuals.However, the aim of all our research need not be to seek such generalizations. At times, our efforts should be simply to better understand and explain the particular circumstance in which we find ourselves. For this research our usual nomothetic (large sample) methods should take a back seat to solid, idiographic (single subject) investigation.An appreciation of such single subject designs is particularly important to us as investigators in the applied field of gifted education. This is so for two reasons: 1) the very nature of this exceptionality means that we are attempting to describe and explain the unusual, the atypical, the unique, and 2) our ultimate concern must extend beyond knowledge generation to the educational and psychosocial well-being of the individuals with whom we work.The value of single subject methods is furthered by certain corollated circumstances. In our efforts to better understand the phenomenon of exceptional ability and extraordinary achievement we seldom have the opportunity for random selection from large subject pools, two conditions necessary for the utilization of these nomothetic methods. Usually our subjects are few in number or even unique, as is the case in the study of prodigies (Bamberger, 1982) and genius (Montour, 1977). And when we interact with the academic or personal life of one of these individuals our ultimate concern must be with the effect of our educational or psychosocial interventions on that person. Single subject research methods are ideally suited to meet the demands of these circumstances, through the application of case study procedures (Frey, 1978) and the utilization of intensive experimental designs (Kratochwill, 1978).A View to Greater Knowledge However, research efforts in the area of the gifted and talented persist in transposing nomothetic (large sample) designs and methodologies into the study of this special population. Ofte...