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Introduction
Oddly, perhaps inexplicably, the most extreme forms of intellectual giftedness have been the least studied. If one looks for studies of persons with a very high IQ, there is Hollingworth's 1940 case study of children above 180 IQ and little else.¹ If performance rather than potential is the metric, then there seems to be not a single work in English. In 1930, Baumgarten, a Swiss contemporary of Hollingworth, published a study in which nine child prodigies were subjected to psychological analysis through test and interview.² These two works appear to be the sum total of the psychological literature on extreme giftedness, except of course the clinical case studies and biographical or retrospective accounts, such as Cox's estimate of the childhood IQ of prominent individuals living from 145 to 185³.

One purpose of this chapter is to explain why the most obvious and dramatic manifestations of human intellectual superiority have also been the most neglected. The explanation points to the work of Lewis M. Terman and his colleagues as instrumental in transforming the meaning of extreme giftedness even as they were trying to study it. This transformation appears relevant to the virtual nonexistence of extreme giftedness as a field of psychological study. A second purpose is to describe efforts begun recently at Tufts University to learn more about extreme manifestations of intellectual capability.

Interest in extreme forms of giftedness may be seen as part of the more general attempts to rejuvenate the field,⁴ but it is important to distinguish between work with the more moderately gifted, who have in the past received much attention, and work with the extremely gifted, who have not. It could well be that the preoccupation of earlier workers with less extreme forms of giftedness (for example, with subjects whose IQs are in the range of from 125 to 165) was itself a contributing factor to the neglect of the extremely gifted. The concept of giftedness established by the early workers in the field seemed to render unnecessary the study of the most exceptional forms of intellectual expression.

Terman's "Genius”
Ironically, the one who looms most prominent in accounting for the absence of research on extreme forms of giftedness may well have been Terman, a pioneer in the use of intelligence tests and the foremost figure in the study of the gifted.⁵ Although it is difficult to fathom in retrospect, Terman believed that his high-IQ subjects were the geniuses of the future. He believed that an IQ higher than 135 or so was a prerequisite to remarkable achievement in any field.⁶

Terman's subjects did indeed turn out to be remarkable, both for their intellectual accomplishments as well as their mental stability and health. Yet, with hindsight we can see that an IQ of 150 is not necessarily indicative of "genius," as Terman had implied in his writing. Only in 1954, did Terman realize that the label "genius" could not be justifiably applied to his subjects.

The acceptance of the IQ as the metric for giftedness became clearly visible during a search of the literature on topics related to prodigious achievement. A thorough search of volumes 1 through 51of Psychological Abstracts (1927-1974) used such terms as "ability, superior"; "child, gifted"; "precocious, superior"; "precocious, - prodigy"; "student, gifted, superior, talented." Not all terms were present at all times. They had a disconcerting tendency to disappear for a while and then to reappear with a new connotation or as a synonym for a term that seemed formerly to have been only distantly related. Most striking was the ever greater tendency for terms that had been separate entries to be subsumed under the heading "intelligence." From 1936 to 1941, the term "genius" alternated between being listed with other "special mental conditions" and being part of the category "intelligence." Apparently this was a transition period. The year 1941 marked the last separate classification of "genius." Before 1936, it had always appeared under the category "special mental conditions." After 1941, it appeared only in the category "intelligence."

It became clear that no empirical studies had been done in this country (at least none that actually studied child prodigies while they were children) to document the phenomenon of early prodigious achievement. There were a few case studies, the most notable of which was Baumgarten's study of nine children whose achievements had brought most of them to public attention before the age of twelve. The cases include "two piano virtuosi, two violinists, one orchestra leader, one girl dancer, one girl artist, one geographer, (and) one boy chess wonder." With the children's extraordinary accomplishments so clearly established, the purpose of the study was not so much to document and verify the fact of precocity but rather to investigate in what other ways these children differed "in regard to their relation to the art practiced, their relation to their parents, their contemporaries, and their environment."7

A reflection of the change in the meaning of the term "genius') brought about as a consequence of Terman's efforts may be seen in a comparison of the eleventh edition (1910) of Encyclopedia Britannica with the fourteenth edition (1972) .The earlier version referred to "genius” as:

A degree of original greatness which is beyond ordinary powers or explanations, that is, far beyond the capacity of the normal human being in creative work: and it is a convenient term (like Nietzsche's "superman") for application to those rare individuals who in the course of evolution reveal from time to time the heights to which humanity may develop, in literature, art, science, or administrative life.⁸

The later version defines the modern English usage of the term "genius" as follows:

The word genius is used in two closely related but somewhat different senses. In the first sense, as popularized by Lewis M. Terman, genius refers to high intellectual ability as measured by performance on a standardized intelligence test. The exact intelligence quotient designating genius varies. Terman set the intelligence quotient for "potential genius" at 140 or over, a level reached by about I in 250 of the general population. ...In the second and more popular sense, as derived from Sir Francis Galton, "genius" is used to designate creative ability of an exceptionally high order as demonstrated by actual achievement. In this sense, men of genius are identified by the eminence of their accomplishment.⁹

The word "genius" now carries the combined meanings of high intelligence and achieved eminence. When applied to children, the first meaning, high intellectual ability, is of course the only one relevant, since achievement is years into the future. Genius in the IQ sense is a predictor of later success, an early sign of the mark of eminence. The idea of the IQ index was to be able to know in advance who among the nation's children was likely to go on to achieve eminence.

The meaning of the term "genius," therefore, has been enlarged over the years, chiefly as a consequence of the redefinition of intelligence by Terman and others in the IQ movement. High IQ became almost synonymous with genius, particularly when referring to children. We have not yet, however, come to grips with the actual phenomena that have eluded modern inquiry, namely precociousness and prodigiousness, to which we now direct our attention.

Precociousness and Prodigiousness
Put simply, the intelligence quotient is a measure of precociousness. A high IQ means that a child is able to perform certain mental tasks that are ordinarily performed only by older children. A high IQ, of course, is only one of several possible ways to conceptualize rapid progress or great power in the intellectual domain. Unusual ability in a specific area, such as logic, would be another way. Curiosity about unusual topics, facile use of technologies, demonstrated achievement in a complex field, and so forth, are other ways. For better or worse, however, precociousness became part of the concept of intelligence as we know it. It follows that research on high-IQ children is by definition research on highly precocious children, precocious in whatever IQ tests measure. Virtually no studies of mental precociousness other than high IQ are to be found in the literature of the last thirty years, indicating the degree to which precocity in the IQ sense preoccupied the field. The concept of precociousness has come to be inextricably linked with the concept of intelligence, with the effect that precociousness of a certain sort was already measured by virtue of the measurement of IQ. Precociousness, then, like the concept of genius, tended to be subsumed under the IQ notion of intelligence. But what of the idea of a prodigy? From its earlier definition as "something out of the usual course of nature (as an eclipse or meteor) that is a portent" and "something extraordinary or inexplicable" (again quoting Webster's 1961 edition), a prodigy became defined as "a highly gifted or academically talented child."

The meaning of the term "prodigy" has been camouflaged by a concept of intelligence that seems to include it but really does not. Thus, prodigy came to mean the same as precocious but to an even greater degree.¹⁰ The meanings of the terms "precocious," "prodigy," and "genius" all seem to have been subsumed under the general concept of intelligence as reflected in the IQ index. Prodigies were made part of everyday life, not taken as different in kind from the rest of humanity. Perhaps for this reason it did not seem as necessary to study prodigies as a separate, unique variant of nature.

Piaget and the Developmental View of Intelligence
Fascination with extreme forms of intellectual expression is part of another general shift in point of view about intelligence, a shift that has come about largely because of the influence of Jean Piaget. Piaget views intelligence as an ongoing process of transformation and change. This is in contrast to the psychometric view, which sees intelligence as a relatively unchanging trait of the individual.¹¹ By emphasizing the universal set of changes in thinking that all children experience, Piaget has drawn attention to intellectual development as a growth process that has certain universal milestones and processes through which these milestones are invariably achieved.

An ironic twist is that although Piaget has helped to transcend the IQ view of intelligence, he has not himself been interested in the problem of giftedness at all. Perhaps the reason is that Piaget sees all intellectual accomplishments as caused fundamentally by the same developmental processes, just as Terman had believed that all intellectual differences were caused by different amounts of the trait of IQ.

Thus, as Terman did earlier, Piaget has proposed a set of unifying principles for all intellectual development. These principles, to be sure, are very different from those of Terman's psychometric view. In our work on extreme forms of giftedness the Piagetian framework has been used as a guide. We have extended the frame-work to incorporate child prodigies, although the theory itself must be modified in some respects to do this.

Early Prodigious Achievement as Coincidence
The key difference between the Piaget-inspired view and the IQ-based view is that the IQ view locates the cause of phenomenal achievement primarily within the child. Prodigious achievement is better conceptualized as a remarkable coincidence. The coincidence consists of a human organism with a set of powerful predispositions or qualities that interact in a human environment over a segment of time during which it becomes possible for that individual to express the potential he possesses.

An individual must work at something or in some field, however loosely defined, to demonstrate his or her prodigiousness. Suppose, for example, that Albert Einstein had been born fifty thousand years ago, five thousand years ago, or even five hundred years ago, which could well have happened.¹² Is it reasonable to suppose that Einstein would have achieved his remarkable insights into the workings of the universe if he had been born before the era of science, or for that matter, of history? Perhaps Einstein would have done something remarkable regardless of the age in which he was born, perhaps not. The point is that the transcendent quality of Einstein's achievement was as critically a function of the state of a field of knowledge at a particular point in its own history as it was a function of that talent itself.

Those familiar with Einstein's earliest years may be thinking that he was no child prodigy. Einstein apparently did not speak until he was four or five years of age. But I am not dealing here with all aspects of prodigious achievement. Rather, I wish to draw attention to the crucial importance of the state of a body of knowledge, including its codability and communicability at a given moment in historical time. Of note in this connection is the fact that Einstein's field was physics, in which truly prodigious early achievements, at least as I define them, have not occurred. Einstein was no prodigy, but his field is one in which early prodigious achievement is unheard of. Nonetheless, Einstein's achievements in physics were built upon existing theory and existing facts. Thus, the occurrence of remarkable achievement within a field by a young child depends in part on the existence and transmission of a highly evolved and economically communicable domain of knowledge.

Taking chess as an illustration, the amount, abstractness, and complexity of knowledge required to play adult-level chess is enormous. The probability that an individual would be able to learn enough to play sophisticated chess games by the age of six or seven years, as was the case, for example, with Bobby Fischer and for some of the children in our study, is virtually nil. The chess players in this study, for example, picked up the game with little instruction and achieved considerable skill before the age of six. To deny the obvious gifts of such early achievers requires massive distortion of the facts. But to ignore the importance of a highly distilled and efficiently communicable body of knowledge is equally partsighted. Bobby Fischer learned to play chess when he was about six. From that year on, however, Fischer read hundreds of books about chess, had intensive formal instruction during his teens, and reached the rank of Grandmaster when he was fifteen-a remarkable achievement to be sure, but one which took more than nine years to accomplish.

Thus, early prodigious achievement should be seen as the occurrence in time and space of a remarkably preorganized human being, born during perhaps the optimal period and educated in the precise manner most likely to enable the individual to interact optimally with a highly evolved field of knowledge. In other words, a coincidence occurs, more remarkable even than the awesome talents that make it possible. The subtle, delicate coordination of elements of human potential and cultural tradition is to me even more dazzling than the achievements attributed to various individuals. It is more dazzling because the same processes that are responsible for all human development are responsible for early prodigious achievement, as we shall see in later sections of this chapter.

If it is true that an optimal match of individual talent to specialized environment is highly improbable, then over evolutionary time there are likely to have been many other individuals, preorganized for one purpose but born at a moment in time or in a place where their unique organization had no appropriate environment through which to express itself. Therefore, when we see a natural experiment of the sort we typically refer to as a "child prodigy," what we are actually seeing is an astonishing but predictable coincidence. As with any random process, early prodigious achievement is no more nor less probable than any other combination of human and cultural factors interacting across a few moments of evolutionary time.

Early Prodigious Achievement: A Research Study
For the past two years, three individuals have been studied in our research. All were under the age of ten at the beginning of the study and are without question extremely gifted. These three children meet the demanding criterion of early prodigious achievement set for the study, namely, that each child performs in his chosen field at the level of an adult professional before the age of ten. The study has two aspects: one is educational, the other psychological. The educational aspect deals with the process through which a child prodigy is prepared to practice his craft. As mentioned earlier, even in the most extreme cases on record, intensive education over several years is required in bringing the talented child to full bloom as a master practitioner. To glimpse this process, considerable amounts of time have been spent with the teachers of chess and music composition who guide the three subjects in the study. More than thirty lessons have been observed; about a dozen sessions have been recorded on tape; tournaments, recitals, and concerts have been attended; and the families and teachers of the young subjects have been interviewed.

Although it is too early to report many findings from the educational phase of the project, a few things stand out strikingly:

1. The children are taught by remarkable teachers, each a master of his field and a master teacher.
2. Each teacher has a distinctive style; the styles are different, but there is a coherence to how each teacher carries out his plan of instruction.
3. All curricula (in chess, music, and I believe in mathematics as well, although I have had less experience in the latter field) recapitulate in some sense the history of the field. For example, in chess both masters guide their students through the games of all the world champions of chess, often going back 150 years.
4. The teachers are at least as passionate and committed to the field in which they work as are their pupils; they are also enormously dedicated teachers, reflective and vigilant about their instruction.
5. None of the teachers was a child prodigy himself.

There is much that these highly specialized teaching situations can tell us about teaching in general. The psychological aspect of the research is intended to shed light on early prodigious achievement as a developmental phenomenon, while at the same time illuminating certain aspects of developmental processes in general. For this purpose, it is necessary first to show that early prodigious achievement is indeed developmental, sharing certain attributes with other developmental phenomena. The research project illustrates the point that early prodigious achievement is a developmental phenomenon, but not quite the kind of phenomenon that Piagetian theory would tend to suggest.

Some years ago Kluckhohn and Murray wrote: "Everyone is in certain respects (a) like all other men, (b) like some other men, and (c) like no other man."¹³ These observations can be used as a point of departure from which to show how early prodigious achievement is (a) like all other developmental phenomena, (b) like some other developmental phenomena, and (c) like no other developmental phenomenon.

Ways in Which Early Prodigious Achievement is Like All Other Developmental Phenomena
The main way in which early prodigious achievement is akin to the Piagetian stages of intellectual development-and therefore like all other developmental changes-is that both are achieved through a sequence of broad levels of mastery. Piaget uses the-term "development" (in contrast to "learning") to refer to those aspects of psychological change that occur spontaneously and take place in a universal sequence of hierarchically ordered stages or levels. The first two qualities-spontaneousness and universal achievement-are not necessary for bestowing the label "developmental," but these are two of the qualities that are central to Piaget's formulation.

The Piagetian universal sequences of developmental change are but one set of developmental phenomena, although a crucial set to be sure. There are numerous others. All regions of developmental change share certain properties with the Piagetian sequences but are distinct in some ways as well. Things that are typically referred to as "developmental" are things that all of us eventually acquire. One of the real contributions of developmental theory and research, in particular that of Piaget, has been to draw attention to those qualities that all human beings share. The central premise of my way of viewing early prodigious achievement is that it, too, is developmental, despite the fact that few persons will experience the incredible rapidity of achievement that is the hallmark of the prodigy.

The assumption that early prodigious achievement is developmental rests on the belief that the processes of transformation and change in early prodigious achievement are analogous to processes of transformation and change in more universal and inevitable aspects of human behavior.

That is, in early prodigious achievement all the qualities of the more usual developmental changes are seen except for these two. As noted above, there is nothing universal about early prodigious achievement. (This is obvious enough, since the phenomenon is so strikingly different from more typical trajectories of mastery in a field.) And, the achievement of precocious mastery is not "spontaneous" in the sense that Piaget tends to use the term. Early prodigious achievement will not occur in the absence of specialized resources and intensive efforts on the part of master instructors in the field, that is, without education.

Ways in Which Early Prodigious Achievement is Like Some Developmental Phenomena
Early prodigious achievement is not inevitable, to say the least, nor does it occur spontaneously. Perhaps some would want to dispute the second point; Mozart is often cited as a case of genius without instruction. To see a child of nine or ten years composing pieces that defy formal distinction from a mature composer's works is indeed awe inspiring. But these works did not spring from the mind of the child without extensive preparation and intensive instruction; even Mozart grew up in a home where music was played, discussed, and perhaps even composed.

After many hours of observation with prodigious children and their teachers, one is struck by the tireless efforts that go into the acquisition of one's craft. To draw attention to the lack of spontaneousness in the achievements is not in any way to dilute the impressiveness of the talents of the children; they are staggering. But to attribute the achievements of these children solely to the natural gifts they possess is to ignore a crucial part of the process. Early prodigious achievement is therefore distinguished from more universal developmental acquisitions in being a relatively rare occurrence that requires the catalytic efforts of specialized, more experienced individuals and the availability of a body of knowledge in a form that can be readily communicated. Early prodigious achievement is most distinguished from other phenomena by how well education works.

Developmental phenomena that are not universal and that require instruction can be given the label "cultural."¹⁴ Examples are map understanding, mathematics, music, art, and so forth. Early prodigious achievement may be seen as a special occurrence within a certain cultural developmental domain. It is cultural because early prodigious achievement depends upon the existence of a culturally evolved set of techniques for transmitting the principles and practices of the domain. It would have been unfortunate, for example, for a chess player of Bobby Fischer's stature to have been born before there were chess boards, chess pieces, and chess books. The existence of a body of knowledge and a technology to transmit it made possible Fischer's achievements in chess.

Thus, early prodigious achievement shares features with other cultural developmental phenomena. It is certainly not universal, yet it is an accomplishment that is not altogether unique either. The level of mastery of the field is not unprecedented; it is the speed of mastery that is so remarkable. Early prodigious achievement is also not spontaneous, and this too it shares with other cultural and developmental phenomena. The rapidity of accomplishment is indeed striking, and we shall consider this quality next, but no matter how astounding the relative speed, it is still the case that years of intense preparation are required for even the most talented individuals to achieve distinction in their respective fields; creative works, of course, generally take longer.

With regard to prodigious individuals themselves, those few cases where psychological measures have been taken reveal that even in extraordinary instances of early prodigious mastery, individuals share general developmental qualities with their age peers. Early prodigious achievement, then, is like some other developmental achievements, namely cultural ones; likewise, individuals who achieve remarkable mastery are in some respects developmentally similar to other children their age.

In 1976, a battery of four general developmental measures was administered to our three subjects-two eight-year-old chess players and a student of music composition who had just turned ten years of age. Our aim in this facet of the research was to assess the general developmental progress in cognition of each of these children in relation to his age peers. One other aspect, which is also pertinent to the "stage" notion, is the extent to which remarkable precocity generalizes across developmental domains. As with other aspects of the phenomenon, there is little empirical precedent to guide us. Most of the available information is anecdotal. The evidence from Baumgarten's research, while unsystematic by today's standards, seems to support the notion that early prodigious achievement represents a reductio ad asurdum of Piaget's notion of decalage: why this is the case is made clear by the pattern of our results.

The four measures given were (a) Piaget's five chemicals task, a test of the level of acquisition of various concrete and formal logical operations;¹⁵ (b) a role-taking test devised by Flavell and associates at the University of Minnesota, the aim of which is to test social/cognitive development by assessing the level of ability to take another's point of view;¹⁶ (c) a map-drawing exercise (an adaptation of Piaget and lnhelder's layout diagram task), which gives a general estimate of the level of the coordination of spatial/ logical reasoning;¹⁷ and (d) a psychometric measure of level of moral judgment and reasoning, prepared by Rest and based on Kohlberg's stages of moral development,¹⁸ A summary of the results is given in table 1.

TABLE 1
Summary of Data on Three Prodigious Achievers

Notes:

1. Jean Piaget and Barbel Inhelder, The Child's Conception of Space (London : Routledge and Kegan Paul, 1956), first published in 1948; Samuel Snyder, David Feldman, and Cheryl LaRossa, " A Manual for the Administration and Scoring of a Piaget-based Map-drawing Exercise," in Tests and Measurements in Child Development: A. Handbook (II), ed. Orval Johnson (San Francisco, Calif.: Jossey-Bass, 1976), pp. 268-69.
   
2. James Rest, "Manual for the Defining Issues Test: An Objective Test of Moral Judgment Development," mimeographed (Minneapolis: University of Minnesota, 1974). This instrument was not designed for use with children younger than thirteen to fourteen ears of age. It typically yields higher scores than are obtained from Kohlberg Interviews.
   
3. John H. Flavell, .The Development of Role-taking and Communication Skills in Children (New York: John Wiley and Sons, 1968), pp. 42-55.
   
4. Barbel Inhelder and Jean Piaget, The Growth of Logical Thinking from Childhood to Adolescence (New York: Basic Books, 1958), pp. 105-122.

Table 1 indicates that the three subjects all fell well within the usual range of performance for their age on each of the four measures. To be sure, these children are all very bright and do well in school; likewise, they do relatively well on the developmental measures we have administered. But in none of the general developmental regions was their progress remarkable in comparison with the extraordinary levels they have achieved in chess and music. In this respect, then, these individuals, who have shown extreme early prodigious achievement in the fields of chess and music composition, fall, within the typical range of variation in general developmental levels of logic, role taking, spatial reasoning, and moral judgment.

Either the children were accelerated in their mental structures such that their thinking was generally advanced beyond their years, or their performance was remarkable in their fields through the unusually facile use of, say, concrete operations. Otherwise, we are left to explain how acceleration could occur within a relatively limited region of thought while the child's general level of thinking seemed to remain age-appropriate.

From our preliminary results to date, it appears that the rate of transformation of structures for our subjects is highly domain-specific, yet it is hard to argue that the children were not using adult formal thought in their fields of accomplishment. Indeed, we chose these fields in part because there seemed to be as little question about the demands they make as any other fields we could think of. One-problem, then, is to determine if early prodigious achievement represents a simple acceleration through the same levels of achievement in a field that any other individual would pass, or alternatively, if the child literally skips levels and enters at a more advanced point in the sequence. Indeed, is the sequence itself really as similar to the more typical sequence as it appears to be?

It should be noted that the cases described were chosen for their special talents in specific domains. This was done primarily to show that there are instances of precocity within a domain that are difficult, if not impossible, to explain within existing cognitive-developmental theories such as Piaget's. If a child's performance at chess, for example, is at a level that clearly utilizes formal operational logic (Piaget's most advanced stage), then theory would require that the child have these mental processes available to solve at least some other problems. Furthermore, the theory posits that certain domains are more "resistant" to the application of various mental structures than others. If so, it follows that less resistant tasks should be solved earlier. Yet we know that our prodigies violate these principles. They perform in a highly resistant domain at an advanced level long before they do so in any other domain; also, their performance in general developmental domains is not markedly different from their age peers. Thus, they "violate" Piagetian theory by moving rapidly within a single domain that should be very resistant to mastery.

Although not looking for such individuals, we have encountered two or perhaps three cases of what are best labeled "all-purpose" prodigies. These individuals seem to be remarkably precocious across several domains. One child of eight is extremely advanced for his age in all natural sciences (including science fiction), music, geography, mathematics, and has vast general knowledge. Clearly this sort of child is much different from the "special purpose" prodigies who make up the bulk of our cases. The intellectual power of these all-purpose cases seems omnibus, and their presence is also characteristically more aversive to others. Such individuals are often perceived as arrogant, mechanical, technocratic, intense, erratic, peculiar, or bizarre. They represent a fascinating form of intelligence in their own right, but for the present purpose of our research, which is to examine developmental theory in terms of certain selected extreme cases, the all-purpose prodigy is of less interest because he is less discrepant from what theory would predict. These cases would not, for example, have caused sufficient problems with existing theory to require me to invent the idea of coincidence. Once invented, however, coincidence seems to account for both special and all-purpose prodigies more adequately than other available explanations.

Early Prodigious Achievement as a Unique Developmental Phenomenon
Whatever the resolutions to the above sorts of issues turn out to be, it should be clear that they are uniquely expressed in early prodigious achievement. For in no other phenomenon does the fact of the achievement itself seem to run so counter to our notions of general psychological transformation. How could it be that a child can not only comprehend and discuss, but can produce original compositions of the subtlety and complexity of a mature composer, yet find Piaget's five chemicals problem to be difficult to solve? And how can a chess player who regularly wins tournaments against mature adult players show moral judgment and reasoning typical for that of an eight-or nine-year-old child? It should be abundantly clear that early prodigious achievement represents a developmental phenomenon that has distinctive and unique qualities, qualities that may lead to some new insights about developmental processes in general.

We have taken so much care in showing how early prodigious achievement bears resemblance to other developmental phenomena because these aspects of the phenomenon are less obvious. The folklore surrounding such legendary prodigies as Mozart, Francis Galton, and Norbert Weiner derives much of its impact from their ability to master a field and produce works of quality at a very early age. This is, to be sure, what is so compelling about prodigiousness. Now we turn to look at its full force, without trying to dilute the uniqueness of the achievement by drawing parallels and analogies to other developmental regions.

Our conceptualization of early prodigious achievement as coincidence points to the need to understand the reciprocal relations among intrinsic human talents, culturally evolved qualities of a field or craft or discipline, and traditions pertaining to the formal transmission of knowledge. To ignore one set of these factors is like watching a player piano: despite what it looks like, the piano does not play itself. Reciprocally, every great performer at the piano is playing music, which has a history of its own, and that performer is playing his music on an instrument, which has a history too. To understand achievement one must understand the joint histories of all the participants, and this is especially true where really remarkable achievement occurs.

Perhaps the most striking quality in the children in our study as well as other cases is the passion with which excellence is pursued. Commitment and tenacity and joy in achievement are perhaps the best signs that a coincidence has occurred among child, field, and moment in evolutionary time. No event is more likely to predict that a truly remarkable, creative contribution will eventually occur. Early prodigious achievement thus is related to creativity if in no other way than because precocious mastery provides more time and more opportunity for an individual to reach the limits of his craft, to confront the unknowns, to go beyond the frontiers of the discipline he has mastered. But one thing is clear. No matter how remarkable are the feats of child prodigies, these feats are not achieved without intensive, prolonged, educational assistance.

Addendum
For a more contemporary treatment of the topic of domain specific extreme giftedness, please see Nature's Gambit: Child Prodigies and the Development of Human Potential (Teachers College Press, 1991). - David Henry Feldman, June, 2001.

References

1. Leta Hollingworth Children above 180 IQ (New York: World Book Co., 1941).

2. Franziska Baumgarten Wunderkinder psychologische UnterSuchungen (Leipzig: Johann Ambrosius Barth, 1930).

3. Catherine Cox, The Early Mental Traits of Three Hundred Geniuses (Stanford) Calif.: Stanford University Press, 1926). After completing the preparation of this chapter, I learned of an important work on child prodigies that had not previously come to my attention: Geza Revesz, The Psychology of a Musical Prodigy (Westport) Conn.: Greenwood Press, 1970). This volume was originally published in 1925, in New York by Harcourt, Brace and Co. and in London by Kegan Paul, Trench, Trubner, and Co.

4. Kathleen Montour, "William James Sidis, the Broken Twig," American Psychologist 32 (1977): 265-79.

5. Lewis M. Terman et al., Genetic Studies of Genius, vols. I-V (Stanford, Calif.: Stanford University Press, 1925-1959).

6. Paul Witty and Harvey Lehman, "Nervous Instability and Genius: Poetry and Fiction," in Psychology and Education of the Gifted: Selected Readings, ed. Walter B. Barbe (New York: Appleton-Century-Crofts, 1965).

7. Baumgarten, "Vunderkinder psychologjsche Untersuchgen, p. 4.

8. Encyclopedia Britannica, 11th ed., s.v. "genius."

9. Ibid., 14th ed., s.v. "genius."

10. Cox, The Early Mental Traits of Three Hundred Geniuses.

11. David Feldman, “Universal to Unique,” in Essays in Creativity, ed. Stanley Rosner and L.E. Abt (Croton-on-Hudson, N.Y.: North River Press, 1974)

12. Sherwood L. Washburn and F. Clark Howell, "Human Evolution and Culture," in The Evolution of Man, ed. Sol Tax (Chicago: University of Chicago Press, 1960), vol. 2, PP. 33-56.

13. Clyde Kluckhohn and Henry Murray, "Personality Formation: The Determinants," in Personality: In Nature, Society, and Culture, ed. Clyde Kluckhohn and Henry Murray (New York: Alfred A. Knopf, 1948), p. 53.

14. Feldman, "Universal to Unique."

15. Barbel Inhelder and Jean Piaget, The Growth of Logical Thinking from Childhood to Adolescence (New York: Basic Books, 1958), pp. 105-122.

16. John H. Flavell, The Development of Role-taking and Communication Skills in Children (New York: John Wiley and Sons, 1968), 42-55.

17. Jean Piaget and Barbel Inhelder, The Child's Conception of Space (London: Routledge and Kegan Paul, 1956), first published in 1948; Samuel Snyder, David Feldman, and Cheryl LaRossa, "A Manual for the Administration and Scoring of a Piaget-based Map-drawing Exercise," in Tests and Measurements in Child Development: A Handbook (II), ed. Orval Johnson (San Francisco: Jossey-Bass, 1976), pp. 268-69.

18. James Rest, "Manual for the Defining Issues Test: An Objective Test of Moral Judgment Development," mimeographed (Minneapolis, Minn.: University of Minnesota, 1974).

Permission Statement

Reprinted with permission of the author.

This article is provided as a service of the Davidson Institute for Talent Development, a 501(c)3 nonprofit dedicated to supporting profoundly gifted young people 18 and under. To learn more about the Davidson Institute’s programs, please visit www.DavidsonGifted.org.