During the last half century profound changes in the way knowledge is conceptualized and evaluated have taken place. Work in the philosophy of science and in the psychological and sociological understandings of cognition itself have led to a basic reappraisal of scientific knowledge. Such a reappraisal could not but have repercussions in the field of education, even mathematics education. In this chapter I am reviewing general philosophical reasons that impinge on our conceptions of teaching and learning, as well as some changes of attitude that have already manifested themselves and others that are still in the making. Although I begin with considerations that are specific to the teaching of mathematics and end with an example that is more amply described in another chapter of this volume, my main focus is on the critical interaction between teacher and student and the school as the ambience where this transaction takes place.
We used to feel very confident about mathematics education. We knew what to teach, how to teach it, and why we should do so. Or we thought we did. Things are less certain today as the ground beneath the feet of all educators seems to move. Intellectual upheaval has not commonly been the lot of educators. Even if it had been, they could hardly have been prepared for what they are now experiencing.
The certainties of the past rested on three very grand sets of assumptions, commonly known as theories. The first addressed the “what to teach?” question. Mathematics was seen as a “discipline” and, in virtue of this, had an internal “logic” of its own, its own particular content, and boundaries which divided it from other disciplines. To be doing or teaching mathematics was not to be doing or teaching anything else. The content of such doing or teaching was determined not by individuals, nor in any ordinary sense by institutions, but rather by the discipline itself. Arguments of this kind have been mounted in various forms over the centuries; the most potent contemporary advocate of this view has been Paul Hirst who argues that the disciplines are distinguished from one another by their distinctive use of “categoreal” concepts. Given this, he argues that, It is these categoreal concepts that provide the form of experience in the different modes.
Our understanding of the physical world, for instance, involves such categoreal concepts as those of space, time, and cause. Concepts such as those of acid, electron, and velocity, all presuppose these categoreal notions. In the religious domain, the concept of God or the transcended is presumably categoreal whereas the concept of prayer operates at a lower level. In the moral area, the term ought labels the concept of categoreal status, as the term
intention would seem to do in our understanding of persons. The distinctive type of objective test that is necessary to each domain is clearly linked with the meaning of these categoreal terms, though the specific forms the tests take may depend on the lower level concepts employed.(1)
The second theory addresses the “how to teach?” question. Here things seemed less clear but at least it was generally understood that students’ learning was contingent on teaching (itself roughly defined as “acting with the intention to produce learning”). Students were seldom expected, like Descartes, to work things mathematical out for themselves but rather to have it “take” in their minds, or “pick it up” largely as a consequence of witnessing teachers’ demonstrations and rehearsing examples. The situation, at least in outline, was quite simple. The teacher “knew the material”, the students were “ignorant of the material”, the object of the exercise of “teaching the material” was to have the students “know the material” by processes of learning. This was also, of course, the basis on which the teacher’s authority was said to rest, an important point to which I will return later. The methods of teaching and learning reflected each other. Teachers demonstrated “content”, usually of the theorem or proof sort. Students “worked” the same material. Learning was linked to horticulture as metaphors of tilling, planting, sowing and grafting were employed. Successful learning was detectable by doing: the student had “mastered” the material when he (or less commonly she) could “do” it.
Why one should teach mathematics had the grandest justification. There were various answers beginning with Plato’s magnificent idea that the contemplation of mathematical knowledge not just puts the untrained mind in touch with what is timelessly real but also most perfectly develops the minds of future leaders.(2) Rejecting Plato, one might still have gained comfort from Newton’s view (3) that nature has its own language and that is mathematics, that to unlock God’s works is to know reality through numbers. Even rejecting Newton, one might have taken refuge in faculty psychology seeing the mind as some kind of metaphorical muscle to be grown through repeated exercise on very demanding material like mathematics. In this case the power to reason, developed mathematically (and, in the classical curriculum, by learning classical languages), could “transfer” to any other field, i.e., the person who could reason well in mathematics was seen as being capable of reasoning well in general.
Attacks on all three of these theories have been blistering this century. Thorndike attacked the classical curriculum with the empirical claim that “transfer of training” did not in fact occur and thus the foundation of faculty psychology was no more.(4) The onset of studies in the sociology of knowledge has shown it to be questionable whether disciplines do have lives of their own(5) More recently still, Hirst’s articulation of the forms of knowledge themselves has been attacked so thoroughly that it is doubtful whether it is now credible at all.(6) During these same decades a parallel development has taken place. It is the elaboration of a psychology of cognition in general which is an alternative to the notions of learning mentioned above. This work is most readily identified with the name of Jean Piaget, whose ideas shaped the background of most of the studies reported in this volume. Piaget’s research program, of course, did not develop in a vacuum but rather proceeded at the same time as other, similarly fundamental work in the philosophy of science.
A revolution began with Karl Popper’s The Logic of Scientific Discovery , which solidified the claim that it was no longer possible to defend any thesis which sought to make scientific knowledge certain. Popper argued that the problem of induction (the discovery of truths from collections of data) could not be solved in any traditional way. Scientific knowledge, therefore, could advance only by refuting rather than confirming hypothese(7). The effect was electric.
Norwood Russell Hanson (8) then focused the debate on the problematic relations between theory and observation. He pointed to the fact that no observation is possible without some theory, for without theory the observer would not know what to attend to. Clearly, Newton’s “I make no hypotheses”, and the neo -Newtonianism which has dominated Western thought ever since, was in serious trouble. Hanson’s dictum that “there is more seeing than meets the eyeball” may as well have acted as the battle cry of a new school of post Popperian philosophers of science. Popper had wanted to protect both the demarcation of science from other kinds of knowledge and the rationality of science by defining its method. This method of “falsificationism”, according to which science proceeds by successively refuting hypotheses and theories and replacing them with new, more comprehensive ones, would indeed allow scientific knowledge to “advance”, in an orderly way, a characteristic not shared by other sorts of knowledge. But this Popperian tranquility was short lived.
Thomas Kuhn, in what must now be counted as one of the most influential(9) proposed a new theory of scientific change. Science, Kuhn argued, does not proceed in an orderly way at all but rather by successive “revolutions”. Building on Hanson’s theory of dependence of observation, his own training in physics and his research on Copernicus, Kuhn saw two different sorts of sciences. “Normal science” was business as usual, the day to day practice of most working scientists who share a high degree of consensus about such issues as what is worth studying, how it should be investigated, what sort of instruments should be used, what an hypothesis is, and the like. But, in addition there is, Kuhn maintained, a “revolutionary science”. Great changes occur in science not because of a gradual, systematic modification of world views but rather because new points of view come to books of the last half century, restructure all aspects of “normal science”. Copernicus and Galileo were revolutionary in this sense. Their work led to a new “paradigm” or way viewing the scientific enterprise. Thomas Kuhn, in what must now be counted as one of the most influential (9) proposed a new theory of scientific change. Science, Kuhn argued, does not proceed in an orderly way at all but rather by successive “revolutions”. Building on Hanson’s theory of dependence of observation, his own training in physics and his research on Copernicus, Kuhn saw two different sorts of sciences. “Normal science” was business as usual, the day to day practice of most working scientists who share a high degree of consensus about such issues as what is worth studying, how it should be investigated, what sort of instruments should be used, what an hypothesis is, and the like. But, in addition there is, Kuhn maintained, a “revolutionary science”. Great changes occur in science not because of a gradual, systematic modification of world views but rather because new points of view come to books of the last half century, restructure all aspects of “normal science”. Copernicus and Galileo were revolutionary in this sense. Their work led to a new “paradigm” or way viewing the scientific enterprise.
The most shocking element of Kuhn’s work, however, was the notion ‘that paradigms are often incommensurable, i.e., they cannot be compared because each involves concepts that are incompatible with the other. The implication was shattering for traditional views of science. If there is no neutral, third position from which to compare two competing paradigms there is no traditionally “rational” way of selecting one over another. Not only were Copernicus and Galileo not “better” than Ptolemy from the point of view of some time -less, value -free, God’s eye position, but there is no such position. Copernicus and Galileo “won” over Ptolemy because of factors outside science; Ptolemy had become unfashionable, Galileo was seen as “the wave of the future”. Thus Popper’s attempt to demarcate science from the rest of human life was defeated. (10)
These developments reached an at least provisional culmination in the work of Paul Feyerabend, a student of Popper and colleague of Kuhn at the University of California at Berkeley. Feyerabend denied that there was anything special about science at all. It has no privileged “method”, no special “objectivity”, no “progress”, no grounds at all to claim to be better than other forms of knowledge or ways of life.(11) Attempts to assert such claims are always rationalization after the fact, rationalization that serves to mask what is really going on. Feyerabend is often understood as being “anti -science”. This is false, and importantly so. He merely argues against the institution of scientific knowledge as unquestionable dogma.
. . . assume that the pursuit of a theory has led to success and that the theory has explained in a satisfactory manner circumstances that had been unintelligible for quite some time. This gives empirical support to an idea which to start with seemed to possess only this advantage:
It was interesting and intriguing. The concentration upon the theory will now be reinforced,the attitude towards alternatives will become less tolerant.
... At the same time it is evident, . . . that this appearance of success cannot be regarded as a sign of truth and correspondence with nature. On the contrary, the suspicion arises that the
absence of major difficulties is a result of the decrease of empirical content brought about by the elimination of alternatives, and of facts that can be discovered with the help of these alternatives only. In other words, the suspicion arises that this alleged success is due to the fact that in the process of application to new domains the theory has been turned into a metaphysical system. Such a system will of course be very ‘successful’ not, however, because it agrees so well with the facts, but because no facts have been specified that would constitute a test and because some such facts have even been removed. Its ‘success’ is entirely manmade. It was decided to stick to some ideas and the result was, quite naturally,the survival of these ideas.(12)
Feyerabend’s respect for science, and indeed all knowledge, has led him to want science understood for what it is, rather than being misunderstood as a secularized religion. This change of attitude has begun to affect not only the scientific disciplines but also the theory and practice of education and, in the last decade, specifically mathematics education. To appreciate the present changes in that particular field, however, we must look at what is happening to the general notions of knowledge and the ways and means of fostering its acquisition. It is an index of how powerful recent theories and ideologies of science in particular have been in influencing all varieties of knowledge, that the general debate about contemporary epistemological questions in all fields should have been so deeply influenced by the writers mentioned above. And, sadly, it is a reflection of the abject poverty of much that is contemporary educational theory and philosophy, that these recent developments are so seldom mentioned, let alone debated. Educational thought has functioned for decades as little more than a watered down branch of psychology, and indeed that most mindless variety of psychology which has seen a limp behaviorism as an appropriate means for understanding the development of cognition. The nature of knowledge and its development by human persons and institutions has commanded relatively little serious attention by educational thinkers. Hirst’s discipline model of the curriculum has held sway despite decimating attacks.(13) Piaget’s majestic work has been “psychologized” by ignoring its genetic epistemology and focusing on “stages of development” with an attendant elaboration of ideas of “readiness”. By these means a bizarre type of Platonism has been perpetuated. One can only hope thatthe appearance of this, and similar works, signal an end to this situation.
It is now time to face what we do know, and it is this. Educational situations are ethical in their essence. The term “individuals”, with its suggestion of neutral objectivity, must therefore give way to “person”. (14) This used to be a commonplace in earlier times, one which hardly needed to be pointed out and explicated but was taken for granted. To see that this is not the case today is to notice how far our culture has traveled away from meaningful moral discourse. “Individuals” carries a psychological connotation, not a moral one. Psychologists during the last hundred years have succeeded to an alarming extent in redefining the nature of human life, away from the earlier conceptions of us as moral, aesthetic, and political, to conform to the mechanistic world view which had been propagated about the universe since Galileo and Newton. A technology of social and person control has developed around these ideas (see note 16). Freud, Skinner, and others have sought to convince or persuade us that we are no more than the passive products of genetic or environmental and historical circumstances. The implication is that we can and should be molded by “therapeutic intervention” or “social planning”. This sort of thinking has been fostered by a devastating parallel which it then itself encouraged: that we can reasonably consider our lives in a morally neutral context. Thus questions of “psychological health” are seen as technical and have to a great extent replaced moral questions. It is not that the latter could not be answered it is that they hardly make sense in this intellectual climate. Thus education, which is clearly to mean improvement, moral improvement, through the development of cognitive autonomy, was emasculated to mean something like “any learning programmed by the school” or even simply “any learning” (see Peters, note 14). This moral neutrality has the effect of trivializing our experience of ourselves. We can, of course, consider ourselves as machines if we choose to. There are circumstances where this makes good sense: for example when we are on the surgeon’s operating table. But such thinking can hardly be appropriate in all cases: we certainly do not want the surgeon to be a machine during our operation, we want moral consideration and we are right to want it.
A very similar situation obtains with teaching and learning. Persons learn not by being given knowledge but rather by constructing knowledge. So the “banking” model of teaching as making “deposits” in the mental accounts of students must be rejected. Rather, the teaching and learning situation must be understood in the following way. First, since we have no privileged access to reality, there is no template of that reality which could be “deposited”, even if we thought such teaching desirable and even if students had an “open account” awaiting such deposits. Second, learning, even learning physical habits such as cleaning one’s teeth and tying one’s laces, always involves a subtly complex negotiation between teacher and student in which both are changed. For the student’s part we must recognize that the learning involves building up knowledge with the means and the material accessible to the student, rather than copying reality. This is another place where the arguments from the contem -
porary philosophy of science are so persuasive (see notes 7-10). “Reality” is not sitting “out there” awaiting appreciation through neutral “observation”; observation is always a theoretical activity carried out by an observer. Nature (itself a theoretical construct) is not waiting to whisper its secrets in our
scientifically cleansed ears. Theories are not mental representations of reality (despite the seduction of that word representations). To observe is to interpret. This does not mean that there is no way we can evaluate such activities. Abandoning the “theory as template of reality” account of things releases us to acknowledge that we could judge the quality of such activities on whatever. relevant grounds we choose. Strong cases can be made for candidates such as purposes (what is the knowledge for?) and moral/social considerations (will this knowledge help us to lead more humane lives?), but the list is endless. The implication is that there is no single “right” or “correct” way of understanding,
and it is time we embraced rather than continued to resist it.
The pedagogical implication is no less far reaching: not everyone learns in the same way. Of course, we all know this to be true but it is a truth which was blurred by focusing on psychological measurement (or, more often mismeasurement) of “individual differences” in order then to ignore, for the most part, what such measurements might reveal. In other words, there has been a peculiar mismatch between our notions of the nature of the learner, the activity of teaching, and the nature of knowledge. This situation has been perpetuated by the third truth to be faced: situations specifically designed for learning (i.e., “schooling”) are the sites of powerful social forces which shape all aspects of what goes on within them. Who and what teachers are is shaped by these forces; how the learner is understood and treated is shaped by these forces; and what is taken to be “knowledge” or “worth knowing” is constituted by these forces. (15) For those who value freedom and autonomy we can hardly conclude that these forces are universally benign. (l6)
It is not just a series of accidents of misunderstanding which have led to the situation we find ourselves in today. Rather, we find schooling serving certain social interests, its self -understanding and practices operating to modify, create, and legitimize some special arrangements and not others. One of the most significant aspects of how these processes work, both within schools and between schools and other social institutions, is that it is often claimed that such processes do not exist. Alternatively, it is claimed that they are an unfortunate and insignificant byproduct of the institutionalization of schooling. Schooling, at its heart a political enterprise, is thus apparently depoliticized. But teaching by its very nature is a political activity; insofar as it is successful it fosters the construction of a specific reality and could hardly, therefore, be a more pervasively political activity. We should now return to the three sets of assumptions with which we began. Mathematics is not a discreet and separate enterprise unrelated to other varieties of knowledge and action. It is a social creation which changes with time and circumstances. All sorts of criteria influence these changes, not the least of which are economic, political and aesthetics. There is no timeless mathematics standing outside history which could be taught. If this seems counter -intuitive then we must face the fact that our intuitions have been well trained.
The point is proven by reference to cross cultural studies. Needham (17) has shown that the Chinese, despite developing a mathematics and physics of great sophistication, never invented the calculus or atomic theory. Nature (and numbers) is not “out there” exerting some kind of mental magnetism which attracts us to “truth”. And within our own culture examples in the history of Western science abound. Galileo’s telescopic research was influenced, and deeply, not just by factors internal to science but also by the needs of Venetian merchants wanting to manipulate market prices, who took advantage of the new “fairground toy” (the telescope) to see the cargos on the decks of ships before they docked. Kepler’s magisterial work would have been briefer had he not been wedded to the notion of spherical celestial motion for religious and aesthetic reasons. Physics, as we understand it, developed in part because the British Admiralty needed an accurate clock, not to promote science but rather to ensure precise navigation; they were in the business of trying to protect shipping in a growing colonial empire.
Secondly, “depositing” is no metaphor of teaching. The teacher who cannot tolerate different ways of knowing is doomed to failure. Most worry about this point seems to spring from a concern for the teacher’s authority; if there is not one “correct” way to teach, what authority does the teacher have? But such a concern rests on a misunderstanding of the question which confuses being “an authority” with “being authoritarian.” Abandoning authoritarianism does not entail abandoning being an authority. Much of traditional mathematics teaching has relied on the former, and this has led to many of the problems in the field today. The mathematics teacher’s authority rests on expertise and maturity, not on the arbitrary exercise of power. So what might an alternative understanding, at the most general level, be? It is refreshing for a philosopher to be able to report in answer to this question that something a good deal more concrete than speculation may now be offered. This very volume comprises several examples of the sort of alternative practice I am advocating to replace the dismal procedures based on the obsolete assumptions outlined above. One of these examples is reported in Paul Cobb, Terry Wood, and Erna Yackel’s paper “A Constructivist Approach to Second Grade Mathematics”. I want to draw your attention to certain features of this work, some more obvious than others, and then draw some general conclusions. But I should point out at once that I consider it no more important or more significant than other contributions to this volume. I am using Cobb et al. as a point of reference because I had the opportunity to read this chapter and to discuss the work with Paul Cobb before I wrote my own piece.
The first thing to note is that this is conceptually well grounded work. Cobb et al. have addressed the central core of literature in not only contemporary cognitive psychology but also contemporary philosophy of science.(l8) In other words it is work which, despite the modest tone of its reportage, has broken out of the normal framework of discourse in mathematics education and is in fact radical in the literal sense of that word, it returns to fundamentals. It is no wonder, then, that its results are such dynamite! Secondly, it is real schoolingresearch that is reported here. Cobb and his co -workers have not been satisfied with what normally passes for “educational research”, i.e., the “laboratory trials” or the “lab school”. Rather they have sought to situate their work in what is, at once, the most exciting, challenging and relevant of all settings, a real school with all that entails: real pupils, real grades, real teachers, real parents, real administrators, real school board, etc. It also means that the results described in this report have real credibility.
It is clear that questions of authority are central in this work. There are two major areas. First, there are questions related to what we might describe as the “authority of the material”. Second, there are questions related directly to the teacher’s authority. Clearly these interact in powerful and subtle ways. In the first case Cobb, his collaborators, and other similarly oriented researchers have abandoned many of the safe notions on which much mathematics education has rested. While it is still individual persons who are learners, they are understood as participants acting and learning within the social constraints of a classroom. Both what is learned and how it is learned are contingent to some extent on a redrawing of the boundaries between the individual learner, the teacher, and the whole group (including the teacher). This, of course, has a direct impact on the authority of the teacher.
That this is inevitable only becomes the more obvious when we note how some of the other “safe assumptions” have also been abandoned. In this classroom there is no one way to “best” solve a problem. The teacher really does not “know best” all the time. But further, there are no “problems” in the traditional sense either. The teacher does not pluck “problems” from the
“logical structure of mathematics itself” and try to “insert” them into pupils
“minds”. Instead, the problems usually arise from within the experience of the pupils and the particular social setting generated in the classroom. The class -
room is a constrained situation; people are there for reasons; work has to be done; the teacher is “in charge”, is responsible and knows more. But none of this entails the traditional mathematics education practice or its justifications. The irony here rests in the fact that the traditional authoritarianism of mathe -
matics teaching was phoney whereas the authority exercised in Cobb’s et al. classroom is real just because it depends on a proper recognition of the individual’s construction of knowledge within a social setting and the practical requirements of maintaining such a setting.
This work (and indeed this whole volume) raises a number of other impor -
tant issues only the most general of which I can address here. I want to call it the issue of credibility. The authors seem to assume that the reason schools attempt to teach mathematics is that they want all children and adolescents to
learn mathematics, that a mathematically competent general population is a long -range social goal of contemporary schooling practice. But there is now a
daunting and unignorably potent literature which suggests that public schooling does not exist, and was never established, to promote the fullest cognitive autonomy for the whole population. In the light of recent historical and sociological analysis this seems simply another false assumption.(19) Just as schools do have an educational mission they also have what has been described as a “cooling out” one too.(20) They are in the business of selecting, classifying, certifying and manipulating the expectations of their pupils in both direction (21) Schools are, to put the matter plainly, sites of social conflict (22)
and these conflicts shape the contours of the educational and miseducational activities in which they engage. All this is as true of the preschool and elementary school as it is of the rest of the system.(23) Of course to point this out is not to offer a critique of the reportage by Cobb et al. It is to note that work of this sort will finally need to be situated in a more general theory, first of schooling (which links curriculum, teaching and learning with the political discourse of which they are in fact part) and, secondly, with a theory of education (in which the ethical structure of schooling is comprehended).
The work I have cited implies such a direction. Its authors, as do others who contributed to this volume, force us to think through an alternative epistemology (which is a constructivist one) and pedagogy. This shift of perspective suggests that we should teach mathematics for many reasons. Beyond the obvious ones (getting a job, etc.) mathematics is essential to the contemporary sciences. But there are at least two further reasons, and they are subtly connected. One is that mathematics is part of that great treasure trove of human understanding which this culture has constructed in its history and by which we can know ourselves. Like the works of the finest poets, philosophers, artists, and scientists, the creations of mathematicians show us the human potential (at least in the West) operating at full strength. No less is the educational right of every student. The other is that mathematics is fun. Or at least it can be. Why it is often not, should exercise the wits of all those who seek to understand, not just mathematics teaching but the phenomenon of schooling itself.
NOTES
* Paul Feyerabend and Ernst von Glasersfeld read drafts of this paper. I am grateful to them both for their suggestions and to the latter for his gracious editing .
1 . See the now classic “Liberal Education and the Nature of Knowledge” and Hirst’s other related papers in P.H. Hirst, Knowledge and the Curriculum. London: Routledge and Kegan Paul, 1974.
2. See Plato’s Republic.
3. See F.E. Manuel, A Portrait of Isaac Newton. Washington, D.C.: New Republic Books,1979.
4. See the treatment of Thorndike in C.J. Karier, Scientists of the Mind , Urbana, IL: 5. See my “Curriculum and Knowledge Selection” in L.E. Beyer and M.W. Apple (eds.), University of Illinois Press, 1986. The Curriculum: Problems, Politics and Possibilities. Albany: SUNY Press, 1988.
6. Ibid .
7. See K.R. Popper, The Logic of Scientific Discovery. London: Hutchinson, 1959. Conjectures and Refutations: The Growth of Scientific Knowledge . London: Routledge and Kegan Paul, 1963. Objective Knowledge: An Evolutionary Approach. Oxford, U.K.: Oxford University Press, 1972 .
8. N.R. Hanson, Patterns of Discovery. Cambridge, U.K.: Cambridge University Press, 1972.
9. T.S. Kuhn, The Structure of Scientific Revolutions (Second Edition). Chicago: University of Chicago Press, 1970.
10. This argument is elaborated in Imre Lakatos’ classic “The Methodology of Scientific Research Programmes” in his Collected Papers, Vol. I. Cambridge, U.K.: Cambridge
University Press, 1978. 11. Feyerabend’s writings are now voluminous but see P.K. Feyerabend, Against Method:
Outline of an Anarchistic Theory of Knowledge . London: New Left Books, 1975 .
Science in a Free Society. London: New Left Books, 1978. Collected Papers (two
volumes). Cambridge, U.K.: Cambridge University Press, 198 1. Farewell to Reason. London: Verso, 1987.
12. P.K. Feyerabend, “How To Be A Good Empiricist - A Plea For Tolerance In Matters Epistemological”. In P.H. Nidditch (ed.), The Philosophy of Science . Oxford, U.K.: Oxford University Press, 1968.
13. It is ironic that Hirst’s magnum opus (op. cit.) was published during the period of most
furious debate over Kuhn and Feyerabend’s work, yet they are not so much as mentioned by Hirst. See my “Should Debbie do Shale?”, Educational Studies, Vol. 13, No. 2, Summer, 1982.
14. See R.S. Peters, Ethics and Education. London: George Allen & Unwin, 1966. 15. For excellent introductions to this literature which is now vast, see J.A. Scimecca, Education and Society. New York: Holt, Rinehart and Winston, 1980, and J. Spring, American Education: An Introduction To Social and Political Aspects (Third Edition). NY: Longman, 1985.
16. The relations between social forces, the constitutions of persons and institutions, and the nature of knowledge is discussed in detail in my The Educational Panaticon:
Schooling After Foucault, (in progress).
17. Needham and W. Long, Science and Civilization in China, Vol. 4, Physics and Physical Technology Part I, Physics, Cambridge, U.K.: Cambridge University Press, 1962.
18. Paul Cobb, private communications 1986 and 1988. (The sort of literature I have in mind is represented in Notes, 7,8,9,10 and 11 above ).
19. See C.J. Karier, The Individual, Society and Education: A History of American Educational Ideals (Second Edition). Urbana, IL: University of Illinois Press, 1986.
20. See B.R. Clark, “The ‘Cooling-Out’ Function in Higher Education”, American Journal of Sociology , May, 1960; 569-76.
21. See P.C. Violas, The Training of the Urban Working Class. Chicago, IL: Rand McManny, 1978.
22. See J. Spring, Conflict of Interests: The Politics of American Education. NY: Longman, 1988.
23. See M.W. Apple, Ideology and Currriculum. Boston, MA: Routledge and Kegan Paul, 1979 (especially Chapter 3).
