Educators From The United States

"The narrative that emerges in the interpretations developed here presents a critical counter-narrative to the ideological self-understanding of the bourgeois subject as autonomous, rational, self-perfectible in-dividual. The account tells the (his)tory of the subject's often violent political self-disciplining, a self-coercion whose disciplinary methods vary from the extreme of brutal self-repression to the more moderate mode of cautious political self-restraint. The history of the bourgeois subject in Germany appears as the story of a massive repression of certain insights on the part of middle-class intellectuals into the pernicious political and cultural implications of bourgeois socioeconomic praxis."

""Literature" names a discourse in which semiotic elements constantly disrupt the institutional codifications of the symbolic order."

"The individual artist plays the role of a kind of "damaged" vessel into which subjectivity flees in its attempt to escape the reifying effects of bourgeois practice. Artists embody the last outpost of subjectivity, they are neurotic Messiahs, as it were, who represent for all humankind the final hope for salvation from the wholly administered and rationalized world."

"International human rights is an issue basic to the quality of future life and deserving of extensive exploration. The effectiveness of this exploration may be increased by the use of an integrated, multifaceted format which is not only cross-cultural and/or cross-national but also interdisciplinary. Such an approach can reduce the tendency to treat human rights issues in an oversimplified manner."

"The lack of understanding of the history of Blacks in the United States, including the variation of slave utilization, coupled with narrow theoretical orientation of some of the more recent social sciences studies has stimulated the limited conception of the black experience, past and present; this, in turn, paves the way for internal conflict (among Blacks)."

"Human rights have emerged as the most paradoxical subject of international discourse. While it is impossible to find governments baldly advocating the abolition of all human rights, it is also impossible to find a government committed to the full and free exercise of all possible human rights."

"This is great stuff, but does it have to be so complicated?"

"I am such a slow learner that once I understand something I might as well write it down!"

"By the mid-seventies, Elliott had become the foremost expository writer of computer science."

"A modern-day Menabrea"

"In light of the evolutionary links and behavioural similarities between humans and higher animals, it is hard to believe that belief-desire psychology could explain human behaviour, but not animal behaviour. If humans have beliefs, so do animals."

"I have looked attentively at chickens raised in this battery] fashion, and to me they seem to be unhappy and in poor health. Their combs are dull and lifeless except for glaring and unnatural patches of color that appear occasionally … The battery chickens I have observed seem to lose their minds about the time they would normally be weaned by their mothers and off in the weeds chasing grasshoppers on their own account. Yes, literally, actually, the battery becomes a gallinaceous madhouse. The eyes of these chickens through the bars gleam like those of maniacs. Let your hand get within reach and it receives a dozen vicious peeks—not the love peck or the tentative peek of idle curiosity bestowed by the normal chicken, but a peck that means business, a peck for flesh and blood, for which in their madness they are thirsting."

"Literametrics' may become to philology, what 'Biometrics' has already become to the biological sciences."

"Every one knows that the fine phrase "God geometrizes" is attributed to Plato, but few know where this famous passage is found, or the exact words in which it was first expressed. Those who, like the author, have spent hours and even days in the search of the exact statements, or the exact references, of similar famous passages, will not question the timeliness and usefulness of a book whose distinct purpose it is to bring together into a single volume exact quotations, with their exact references, bearing on one of the most time-honored, and even today the most active and most fruitful of all the sciences, the queen-mother of all the sciences, that is, mathematics."

"A discourse, a way of speaking, is considered less scientific, or even rendered ‘unscientific’ exactly to the extent that it includes elements either of the language of feeling or of the language of action and values."

"Each community, each discourse tradition, has its own canons of intertextuality, its own principles and customs regarding which texts are most relevant to the interpretation of any one text"

"We will document a single instance of a widespread and increasingly dominant political strategy in modern society: the transformation of discourses of expert knowledge into discourses of social policy."

"The biological organism and the social persona are profoundly different social constructions. The different systems of social practices, including discourse practices, through which these two notions are constituted, have their meanings, and are made use of, are radically incommensurable. The biological notion of a human organism as an identifiable individual unit of analysis depends on the specific scientific practices we use to construct the identity, the boundedness, the integrity, and the continuity across interactions of this unit. The criteria we use to do so: DNA signatures, neural micro-anatomy, organism-environment boundaries, internal physiological interdependence of subsystems, external physical probes of identification at distinct moments of physical time -- all depend on social practices and discourses profoundly different from those in terms of which we define the social person."

"All meaning is intertextual. No text is complete or autonomous in itself; it needs to be read, and it is read, in relation to other texts."

"We are constantly reading and listening to, writing and speaking, this text in the context of and against the background of other texts and other discourses."

"Many people have been taught a social habit, a discourse, for speaking about meaning, which considers only the role of the individual organism, or the individual mind, in the process of making meanings... Mentalistic discourses, by creating a separate realm and locating meanings there, are not useful for understanding the material and social aspects of meaning-making. Mentalistic discourses depend on a common sense view of the separation of mind from body, and individual from society, which has ideological functions in our society. Particular aspects of these discourses deflect attention away from the social, cultural, historical and political dimensions of the meanings we make."

"We need a social theory that sees all social phenomena, including itself, as being partly the product of how people in a community deploy semiotic resources: how we mean, and what we mean, by every meaningful act."

"Our visual discrimination is far better than our linguistic system at dealing with complex ratios and continuous variations in space, line, shape, and color."

"Minds are formed by our social interactions in a community and a culture."

"The language others speak to us, from childhood, shapes the attitudes and beliefs that ground how we use all our powers of action."

"The role of discourse in society is active; it not only re-confirms and re-enacts existing social relationships and patterns of behavior, it also renegotiates social relationships and introduces new meanings and new behaviors."

"Science teachers have a special responsibility to study the nature of science as a discipline, how it works, how it is described by sociologists, historians, and philosophers from different points of view…. Science education cannot just be about learning science: Its foundation must be learning about the nature of science as a human activity."

"[Teachers] emphasize the human side of science: real activities by real human beings, both today and in specific periods of history. Personal characteristics of scientists, with which students can identify, should be emphasized rather than making scientists seem superhuman or alien."

"When I speak about discourse in general, I will usually mean the social activity of making meanings with language and other symbolic systems in some particular kind of situation or setting."

"Instead of talking about meaning making as something that is done by minds, I prefer to talk about it as a social practice in a community. It is a kind of doing that is done in ways that are characteristic of a community, and its occurrence is part of what binds the community together and helps to constitute it as a community."

"It is dangerous to society to have students leave school believing that science is a perfect means to absolute, objective truths, discovered by people of superhuman intelligence. Apart form the danger that scientific “findings” could be used to justify wrong social polices, an impersonal, inhuman view of science alienates many students from the subject. If we are to encourage students of all kinds to take in interest in science, and use it for their own purposes, we need to show it as it really is."

"Meaning is a much more fundamental notion than truth, indeed more fundamental even than the notion of "reality" itself. The basic argument [of the essay] was that claims about truth or reality are meanings made by people according to patterns that they have learned, and that trying to understand how and why people make the meanings they do is more useful than fighting over the truth of their claims."

"Learning science means learning to talk science... Talking science means observing, describing, comparing, classifying, analysing, discussing, hypothesizing, theorizing, questioning, challenging, arguing, designing experiments, following procedures, judging, evaluating, deciding, concluding, generalizing, reporting ... in and through the language of science."

"In terms of language, we do know what a scientific theory or conceptual system must be: it is a thematic pattern of semantic relationships in a subject, one that is reconstructed again and again in nearly the same ways by members of a community."

"Science has often presented itself, intentionally or unintentionally as a "truer" or even the true way of talking about the world. In science classrooms, except for rare occasions, this is the way science is taught and presented. Not as a way of talking about the world, but as the way the world is."

"The basic point-of-view is that science is a social process."

"A genre is maintained by the conventions of a community, and in most cases serves specific functions within the system of practices of particular institutions of that community."

"Science does not speak of the world in the language of words alone, and in many cases it simply cannot do so. The natural language of science is a synergistic integration of words, diagrams, pictures, graphs, maps, equations, tables, charts, and other forms of visual and mathematical expression... [Science thus consists of] the languages of visual representation, the languages of mathematical symbolism, and the languages of experimental operations."

"Multimodal presentations have an inherent critical potential to the extent that we learn how to use the images to deconstruct the viewpoint of the text, and the text to subvert the naturalness of the image."

"Scientific language that is correct and serious so far as teachers and students are concerned must follow these stylistic norms:"

"Ecosocial Dynamics concerns ecosocial systems and networks, i.e. those ecosystems, including all material components, for which semiotic practices are essential to characterizing the dynamics of the material processes which constitute the system through their networks of mutual interdependencies."

"Human communities are ecosystems. Ecosystems are biological, chemical and physical systems. The physics, chemistry and biology of complex self-organizing systems can tell us much that is useful about human communities: about the conditions necessary for the existence of human communities, about the properties human communities 'inherit' because they are special cases of more general kinds of systems, particularly ecosystems."

"The mystique of science is an essential tool for technocratic rule. Through it we are all taught that science, as the paradigm of all expert knowledge, has an objective, superior, and special truth that only the superintelligent few can understand. Science education, like it or not, does a great job in foisting these myths on most of us."

"The medium of printed scientific text is first of all a visual one."

"Although Cardan reduced his particular equations to forms lacking a term in x^2, it was Vieta who began with the general formx^3 + px^2 + qx + r = 0and made the substitution x = y -\frac{1}{3}p, thus reducing the equation to the formy^3 + 3by = 2c.He then made the substitutionz^3 + yz = b, or y = \frac{b - z^2}{z},which led to the formz^6 + 2cz^2 = b^2,a sextic which he solved as a quadratic."

"The problem of the biquadratic equation was laid prominently before Italian mathematicians by Zuanne de Tonini da Coi, who in 1540 proposed the problem, "Divide 10 parts into three parts such that they shall be continued in proportion and that the product of the first two shall be 6." He gave this to Cardan with the statement that it could not be solved, but Cardan denied the assertion, although himself unable to solve it. He gave it to Ferrari, his pupil, and the latter, although then a mere youth, succeeded where the master had failed. ...This method soon became known to algebraists through Cardan's Ars Magna, and in 1567 we find it used by Nicolas Petri [of Deventer]."

"The law which asserts that the equation X = 0, complete or incomplete, can have no more real positive roots than it has changes of sign, and no more real negative roots than it has permanences of sign, was apparently known to Cardan; but a satisfactory statement is possibly due to Harriot (died 1621) and certainly to Descartes."

"He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam."

"[Zuanne de Tonini] da Coi... impuned Tartaglia to publish his method, but the latter declined to do so. In 1539 Cardan wrote to Tartaglia, and a meeting was arranged at which, Tartaglia says, having pledged Cardan to secrecy, he revealed the method in cryptic verse and later with a full explanation. Cardan admits that he received the solution from Tartaglia, but... without any explanation. At any rate, the two cubics x^3 + ax^2 = c and x^3 + bx = c could now be solved. The reduction of the general cubic x^3 + ax^2 + bx = c to the second of these forms does not seem to have been considered by Tartaglia at the time of the controversy. When Cardan published his Ars Magna however, he transformed the types x^3 = ax^2 + c and x^3 + ax^2 = c by substituting x = y + \frac{1}{3}a and x = y - \frac{1}{3}a respectively, and transformed the type x^3 + c = ax^2 by the substitution x = \sqrt[3]{c^2/y}, thus freeing the equations of the term x^2. This completed the general solution, and he applied the method to the complete cubic in his later problems."

"Cardan's originality in the matter seems to have been shown chiefly in four respects. First, he reduced the general equation to the type x^3 + bx = c; second, in a letter written August 4, 1539, he discussed the question of the irreducible case; third, he had the idea of the number of roots to be expected in the cubic; and, fourth, he made a beginning in the theory of symmetric functions. ...With respect to the irreducible case... we have the cube root of a complex number, thus reaching an expression that is irreducible even though all three values of x turn out to be real. With respect to the number of roots to be expected in the cubic... before this time only two roots were ever found, negative roots being rejected. As to the question of symmetric functions, he stated that the sum of the roots is minus the coefficient of x2"