Both science and history are moving targets. Scholars in the twenty-first century are much more aware than those of earlier generations that scientists operate under the influence of powerful metaphors (science as exploration, discovery, documentation, thrust and counterthrust), and that both the scope and the tools of history undergo continual changes. Still, most scientists and most historians would concur that the broad strokes I've sketched, when viewed from sufficient distance, are accurately rendered—that is, that science and history are each in pursuit of statements that represent the truths ascertained by their respective disciplines

"Children not only think better as they mature; they also become capable of thinking about their own mental processes. Memory capacity may not expand in any real sense, but children (and adults) learn how to boost their recall by various strategies, ranging from the ways in which they group or store things to the kinds of tally systems they utilize on paper or in their heads. Children also learn to think about their own problem-solving activities: How can I best handle a new challenge? Which system or which tool would be useful? Who can I turn to for help? What is relevant and what is irrelevant to a problem I am trying to solve or a principle I am seeking to discover or master? Often these lessons are learned by watching others reflect on their memories or their thinking processes, by mastering practices common in the culture, or by following oft-repeated adages; even left pretty much to their own devices, however, in seems reasonable to assume that nearly all youngsters will improve somewhat in the "metacognitive" areas between the age of seven and adulthood (which itself begins at markedly different ages across cultures)."

Type of Audience When one is dealing with an audience that is large and heterogeneous, one is dealing with the unschooled mind. Expertise cannot be assumed. Simple stories work the best. On the other hand, when one is dealing with individuals who share knowledge and expertise, one can assume a mind that is schooled and relatively homogeneous with respect to other minds in the group. Stories or theories related to such groups can be more sophisticated, and counterarguments can and should be addressed directly.

Why, one may ask, should we care about erasing these gaps? And, in particular, why is it important that natural or scholastic understandings give way to disciplinary understandings? To my mind, the answer is simple: The understandings of the disciplines represent the most important cognitive achievements of human beings. It is necessary to come to know these understandings if we are to be fully human, to live in our time, to be able to understand it to the best of our abilities, and to build upon it. The five-year-old knows many things, but he cannot know what disciplinary experts have discovered over the centuries. Perhaps our daily lives might not be that different if we continue to believe that the world is flat, but such a belief makes it impossible for us to appreciate in any rounded way the nature of time, travel, weather, or seasons; the behaviors of objects; and the personal and cultural options open to us.

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In a typical approach, historiometric investigators like Simonton review large bodies of data to determine the decade of life in which creative individuals are most productive. Such studies have led to the findings that maximal productivity typically occurs between ages thrity-five and thirty-nine, but that profiles differ appreciably across disparate domains of knowledge: thus, poets and mathematicians reach an apogee in their twenties or thirties, while historians or philosophers may peak decades later.

By the time the child has reached the age of seven or so, his development has become completely intertwined with the values and goals of the culture. Nearly all learning will take place in one or another cultural context; aids to his thinking will reside in many other human beings as well as in a multitude of cultural artifacts. Far from being restricted to the individual's skull, cognition and intelligence become distributed across the landscape.

Between the conception of the idea of this special relativity theory and the completion of the corresponding publication, there elapsed five or six weeks. But it would be hardly correct to consider this as a birth date, because earlier the arguments and building blocks were being prepared over a period of years, although without bringing about the fundamental decision.

Thanks to his own thought experiments, his formal education, and his study of authors like Foppl, Einstein already had identified the set of issues that would occupy him for years to come: the relation between electricity and magnetism, the putative role of the ether, and conceptions of space and time, as formulated by a philosopher like Kant or a scientific thinker like Maxwell. Einstein later recalled:

What made the greatest impression upon the student, however, was less the technical construction of mechanics or the solution of complicated problems than the achievements of mechanics in areas which apparently had nothing to do with mechanics: the mechanical theory of light, which conceived of light as the wave-motion of a quasi-rigid elastic ether and above all the kinetic theory of gases.

If we cannot today implement an education that yields full understanding, we can certainly do a much better job than we have done up to this point. The process of achieving such an education ought to be challenging and enriching, far more so than the implementation of the less ambitious education with which we have been saddled — even in places where students are required to work on their assignments until the wee hours of the morning. Important clues for the achievement of such an education come from venerable sources such as the traditional apprenticeship; equally important clues come from new sources of evidence, ranging from recently developed technologies like videodisks to newly evolving institutions such as children's museums.

As David Feldman has shown, the prodigy must exhibit promise in an area that is valued by the culture and in which children’s relevant behaviors are at least noticed. If graphic expression is not valued in a culture, if children’s scribbles are routinely disregarded and discarded, there will be no drawing prodigies. By the same token, when a culture begins to attend to children’s precocious performances in a domain — as has happened with visual artistry in contemporary China — one may discover unexpected gifts.

To begin with, the child of five, six, or seven is in many ways an extremely competent individual. Not only can she use skillfully a raft of symbolic forms, but she has evolved a galaxy of robust theories that prove quite serviceable for most purposes and can even be extended in generative fashion to provide cogent accounts of unfamiliar materials or processes. The child is also capable of intensive and extensive involvement in cognitive activities, ranging from experimenting with fluids in the bathtub to building complex block structures and mastering board games, card games, and sports. While some of these creations are derivative, at least a few of them may exhibit genuine creativity and originality. And quite frequently in at least one area, the young child has achieved the competence expected from much older children. Such precocity is particularly likely when youngsters have pursued a special passion, like dinosaurs, dolls, or guns, or when there is a strain of special talent in areas like mathematics, music, or chess or simply a flexibility, a willingness to try new things.

No less than human beings, human institutions exhibit constraints. Schools or factories or offices may be malleable, but they are not infinitely so. Economies of scale, vexations of human relations, bureaucratic histories, diverse and changing expectations, and pressures for accountability burden all significant human institutions. In the past, serving a smaller and less diverse clientele, schools faced certain problems; today, in a rapidly changing world, where the schools are expected to serve the multiple needs of every young individual, the limitations of this institution are sometimes overwhelming. If one wishes to bring about change in schools, it is important to understand their modes of operation no less than one understands the operations of individuals within them. Accordingly, following the investigation of constraints on human knowing, I consider some limits governing educational institutions, most especially schools. A focus on children and schools brings us face-to-face with a third dimension: the question of which knowledges and performances we value. If one considers school strictly as a place in which certain criteria are to be met (say, for the purpose of certification), it matters not what use one can subsequently make of the skills and knowledge acquired there. One could readily tolerate schools where understanding was considered irrelevant or even noxious. But if one wishes to argue that school should relate to a productive life in the community, or that certain kinds of understanding ought to be the desiderata of education, then the research results I have described are consequential.

Current scripts — form: Individuals differ in the symbol systems, formats, or intelligences in which they habitually encode their mental representations. To the extent possible, it is desirable to determine which “forms of representation” are favored by an individual and to embed new concerns in those familiar forms. So, for example, if a person favors graphic demonstrations, these means should be employed when feasible. If, on the other hand, the person is influenced by the human embodiment of a desired perspective, the mind changer should try to model or embody the desired changes.