Less happily, many who are capable of exhibiting significant understanding appear deficient, simply because they cannot readily traffic in the commonly accepted coin of the educational realm. For instance, there is a significant population that lacks facility with formal examinations but can display relevant understanding when problems arise in natural contexts.

The third organizing theme focuses on the relationship between the creator and work in a domain. Early in life, the creator generally discovers an area or object of interest that is consuming. At first the creator seeks to master work in that domain in the manner of others working within the culture; increasingly, however, the very relationship to the domain becomes problematic. The individual then, willingly or unwillingly, feels constrained to try inventing a new symbol system-a system of meaning-that is adequate to the chosen problems or themes and that can eventually make sense to others as well. In each chapter I examine in detail the ways in which a creator forges a new system of meaning in a distinctive domain; it turns out that surprising commonalities hold across the domains as well.

Nearly all cultures have evolved specific ideas about education, although only in modern times does education prove to be virtually coterminous with formal schooling. Ultimately, the natural paths and forms of development place many children in a difficult bind, as students begin to address the quite different agenda of the schoolroom and the particular structure of the scholastic domains.

Einstein's breakthrough was classic in that it sought to unify the elements of a physical analysis, and it placed the older examples and principles within a broader framework. But it was revolutionary in that, ever afterward, we have thought differently about space and time, matter and energy. Space and time-no more absolute-have become forms of intuition that cannot be divorced from perspective or consciousness, anymore than can the colors of the world or the length of a shadow. As the philosopher Ernst Cassirer commented, in relativity, the conception of constancy and absoluteness of the elements is abandoned to give permanence and necessity to the laws instead.

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all our knowledge, both of time and space, is essentially relative....Position we must evidently acknowledge to be relative, for we cannot describe the position of a body in any terms which do not express relation....There are no landmarks in space; one portion of space is exactly like every other portion....We are, as it were, on an unruffled sea.

given that many items reported by the “establishment press” turn out to be false, and that the same establishment press misses many important stories altogether, why should we attribute any special status to journalists? Why should we hallow, or expect, journalistic truths?

"Berlin suggests that "in the case of seminal discoveries-say of imaginary numbers, or non-Euclidean geometry, or the quantum theory- it is precisely dissociation of categories indispensable to normal human experience, that seems to be required, namely a gift of conceiving of what cannot in principle be imagined nor expressed in ordinary language." Like Newton and Copernicus, Einstein sustained a vision of a unified, harmonious, physically caused world. This dissociation led both to Einstein's genius in the world of physics and his inspirational, but ultimately less successful, forays into issues of world order."

Narrative: telling stories about the topic and the people involved with it (e.g., the story of Charles Darwin for evolution or of Anne Frank for the Holocaust) 2. Quantitative: using examples connected to the topic (e.g., the puzzle of different numbers and varieties of finches spread across a dozen islands in the Galapagos) 3. Logic: identifying the key elements or units and exploring their logical connections (e.g., how Malthus’s argument about human survival in the face of insufficient resources can be applied to competition among biological species) 4. Existential: addressing big questions, such as the nature of truth or beauty, life and death 5. Aesthetic: examining instances in terms of their artistic properties or capturing the examples themselves in works of art (e.g., observing the diverse shapes of the beaks of finches; analyzing the expressive elements in the trio) 6. Hands-on: working directly with tangible examples (e.g., performing the Figaro trio, breeding fruit flies to observe how traits change over the generations) 7. Cooperative or social: engaging in projects with others where each makes a distinctive contribution to successful execution

Consistency: How concerned is this person with consistency? Does this person care about whether stated beliefs, attitudes, and actions are consistent with one another? If so, how can one help this person deal with any inconsistencies? Stance on conflict: How much is this person bothered by the give-and-take of argument? Does this person like to match wits, or is it preferable to avoid sharp exchanges? If one has gone too far, how does one restore calm or equilibrium?

"What is going on here? Why are students not mastering what they ought to be learning? It is my belief that, until recently, those of us involved in education have not appreciated the strength of the initial conceptions, stereotypes, and "scripts" that students bring to their school learning nor the difficulty of refashioning or eradicating them. We have failed to appreciate that in nearly every student there is a five-year-old "unschooled" mind struggling to get out and express itself. Nor have we realized how challenging it is to convey novel materials so that their implications will be appreciated by children who have long conceptualized materials of this sort in a fundamentally different and deeply entrenched way."

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