SEMIOTICS AND THE DECONSTRUCTION OF CONCEPTUAL LEARNING
by
J. L. LEMKE
What is Postmodernism, and Why is it Saying all these Terrible Things?
Postmodernism is a loose alliance of intellectual perspectives which collectively pose a challenging critique of the most basic assumptions of the modern educational enterprise. What are these perspectives? What do they have to say that can open new doors for educational research and practice? I would first like to sketch a personal view of postmodernist discourse, and then focus on its challenges to the foundations of most modern views of abstract conceptual learning. Going beyond critique, I would like to sketch some alternative, postmodern possibilities.
Modernism, like any intellectual movement, will ultimately be defined from the viewpoint of its successors. Postmodernism is beginning this process by offering a critique, a reaction against some intellectual trends that perhaps began as early as the Renaissance, but certainly became well established by the later 19th and early 20th centuries. This is the foundational period for the discipline of psychology and for educational theory and most of the social sciences, as well as for modern literary and fine arts criticism. Postmodernism is primarily, in its origins, a philosophical critique of the assumptions built into these disciplines in their formative years. The critique is gradually being extended today into the natural sciences, the inner fortress of modernist assumptions about knowledge and reality.
From the postmodern point-of-view, modernism is defined by its belief in objective knowledge, or at least in the possibility of objective knowledge, and by its assumption that such knowledge refers directly to an objective reality which would appear in the same way to any observer. A further characteristic modernist assumption is that knowledge is a product of the activity of the individual mind, fashioning its ideas or mental schemas to correspond with this objective reality.
Postmodernism, on the other hand, argues that what we call knowledge is a special kind of story, a text or discourse that puts together words and images in ways that seem pleasing or useful to a particular culture, or even just to some relatively powerful members of that culture. It denies that we can have objective knowledge, because what we call knowledge has to be made with the linguistic and other meaning-making resources of a particular culture, and different cultures can see the world in very different ways, all of which "work" in their own terms. It argues that the belief that one particular culture's view of the world is also universally "true" was a politically convenient assumption for Europe's imperial ambitions of the past, but has no firm intellectual basis.
Many postmodernists go further and point out that just as Europeans temporarily imposed their view on other cultures by force, so within European cultures, the upper social classes, and particularly middle-aged, masculinized males have dominated the natural and social sciences (as well as politics and business), and so this would-be-universal worldview is even more narrowly just the viewpoint of one dominant social caste or subculture.
Postmodernism traces its roots to the movements of structuralism and its counter-reaction, post-structuralism, mainly in the the French-speaking intellectual community of the 1960s and 1970s. Structuralism is either the last stage of modernism or the immediate precursor of postmodernism. The great spokesman for structuralism in this period was the anthropologist Claude Levi-Strauss (e.g. 1963), who argued that the patterns of human culture, from village architecture to premodern myths, had the subtle regularities of mathematical structures (not quantitative ones, but combinatorial and symmetry patterns as in algebraic group theory). He was joined in this by Jean Piaget, who saw in the developmental movement of childen toward modern concepts of space, time, matter, and quantity a construction by the child's mind of just these same sorts of regularities in the operations it performed to make sense of the world (e.g. 1970, 1971).
The structuralists were often inspired by the successes of modern linguistics, first in using meaning to analyze the seemingly mathematical regularities of the sound systems of language (e.g. Jakobson 1956, 1962), and later in Chomsky's (1957, 1965) use of transformations (the heart of quasi-mathematical structuralism) to illuminate regularities in syntactic rules. Language, culture, and thought were all to be brought at last into the modern fold of mathematically regular sciences.
By codifying the enterprise of modernism, the structuralists made it a more precise target for its critics. The critique can trace its roots, a bit mythologically, back into the Enlightenment (e.g. Giambattista Vico 1774/1968), and with some justification as far back as Friedrich Nietzsche (e.g. 1967, 1989). Those who have been posthumously enrolled in the pedigree of postmodernism include the philosophical phenomenologists (e.g. Edmund Husserl, Maurice Merleau-Ponty, Jose Ortega y Gassett) and the great apostate of modernism, Ludwig Wittgenstein (1949/1958). But the most influential, and first truly post-modern critiques were those by Michel Foucault (esp. 1969/72) and Jacques Derrida (esp. 1967/1976).
The common denominator in all these critiques of (except perhaps for those of the phenomenologists, who were recruited rather late) is the analysis of discourse. It is the focus on discourse, and language, that unites structuralists and post-structuralists, but while the structuralists sought the regularities of language, the post-structuralists pointed out how language-in-use, the discourses of philosophers and poets (and, yes, of psychologists and physicists, too), refuse to be contained within the patterns of order we try to impose on them. To the extent that our discourses are our tools, if our tools are -- the modernist would say, in horror, unreliable; the postmodernist, in exaltation, self-organizing -- then the scientific ideals of the structuralists, and of modernism generally, are a chimera, an immature self-delusion we have to grow out of.
Foucault said, in effect, that it was chimerical to imagine that historians could reconstruct a real past; historical discourse is a discourse of the present, serving present ends, making sense for us today out of the archeological traces of past human activity. Foucault undertook to write histories of discourses, including in that term not just language, but all the things people do to make sense of their worlds. He showed, to many people's pleasure, that the very objects of modernist scientific investigation, the very notions of self, nation, language, mind, sex, crime, normality were themselves specific historical constructions, the products, not the objects of human discourse and inquiry. He refocussed attention from the so-called `phenomena' science sought to investigate, to how science (read philosophy, psychology, law, common culture) produced meaningful phenomena through its discourses.
The essential step away from modernism was the new focus on meaning. How does a text mean? How does a graph or diagram tell us something? How do marks on paper (or lighted pixels on a screen) convey to us a complex conceptual meaning? A landscape is a text for a geologist. An apparatus and its readouts is a text in the same sense for a physicist. The principles, and the problems of meaning, are the same. If the meaning of any text depends on how we interpret it in relation to other texts, how can either data or explanation be fixed and stable in its own meaning, much less the basis for objective knowledge of an objective world? Why should we believe that scientific texts are not subject to the same principles of interpretation as literary texts? Why should we believe that primary data can be read from the book of nature without the same problems, or arbitrary conventions, of interpretation that beset the reading of any other sort of "book"? Why should we believe that the practical effects of technologies are legitimate warrant for the objective truth of theories, when the only links between them are yet more texts, more discourses?
Derrida was more playful in his critique, and more direct. Foucault the historian had shown, again and again, exactly how the disciplines created their objects through discourse, and created them very differently in different historical periods. Derrida was a philosopher and sought, in his disruptive readings of classic texts, to show how imperfectly any discourse makes its objects and the world they are supposed to inhabit. Whether a literary, philosophical, or scientific text, Derrida "deconstructed" their constructions of "real objects" of study or narration. He took hold of the key structuralist notion of transformation (A -> B), and showed how unstable any discursive construction of "difference" (A - B) must be. With a rather Zen-like sensibility, he focussed on the absences (B is not A) that all presences presuppose, and on the gaps that must be made to separate things we wish to construe as different. He attacked not just positivism (the naive epistemology of turn-of-the-century science, and still of most contemporary curricula), but "positivities", the notion that things are to be defined by what they are, when in fact discourse can only define something as what it is not. (All categories are based on sets of contrasting alternatives; to be of type Y means not being X or Z.)
Derrida is not widely popular among English-speaking academics -- partly, I think, because they have no patience with the essentially literary genres in which French-speaking intellectuals write philosophy. His deconstructionism, primarily a movement in literary criticism and similar disciplines, is very threatening when applied to the social sciences. It undercuts the possibility of their being positive sciences at all, of their pretensions to "objective knowledge" about the social world. But then deconstruction raises the same epistemological problems for the traditional sciences as well, without negating the usefulness of their technologies. (Once the link between theory and practice is weakened, theory cannot turn to practice for its "proof", but then by the same token practice can go on its merry way whether the metaphysical claims of theory are justified or not.)
There are two other major currents in postmodernism: phenomenology and semiotics. Phenomenology (for major figures, see above) basically chides the scientific view of human life with being too narrow, too mechanical, too little focussed on how people live and make their lives meaningful, too obsessed instead with the artificial objects made by their discourses: kinship systems, cognitive schemata, class struggles. Feminism has found phenomenological perspectives congenial for efforts to construct new discourses of the world rooted in women's experience; intellectual feminists are attracted to postmodernism because it makes it much easier to see how what men define as "the world", "the problems", "the disciplines", are just that, what some men's discourses have defined them to be. (See for example Harding 1986, Haraway 1991, Nicholson 1990.)
The phenomenological perspective does not need to be limited to conceptualizing how the world looks different to men and women; it can be used to examine how it looks different to the young and the middle-aged, to the novice and the expert, the student and the teacher, the ghetto child and the comfortable academic. We each construct our own lifeworlds, and even when we are in the same room, trying to talk to one another, we may still be worlds apart.
Semiotics, the last of the major currents within postmodernism that I will mention, is a generalization of linguistics. At its narrowest, it is merely a codification of the symbols offered us by our culture, and the formal description of how those symbols are usually combined, be they words, gestures, graphics, foods or clothes. At its most general and most powerful, it is the analysis of how we deploy our cultural resources for making sense of the world: language, depiction, action. It is the systematic uptake of Foucault's challenge: to see how we make our meaning-reality with the symbolic tools available, and how our doing so leads to changes in those tools, our use of them, and the sense we make with them. Because semiotics is the branch of postmodernism I know best, and the branch that offers, I believe, the most highly developed alternative tools for educational research and practice, I want to describe it a little more, and turn its light on the problem of abstract conceptual learning.
Social Semiotics and the Construction of Meaning
Linguistics is important because language is, par excellence, the tool most of us use to make sense of nearly everything nearly all the time. Language is a resource for making meaning. Studying how people use language (i.e. our discourse, in the narrow, linguistic sense) to make the meanings of physics, or economics, or cognitive psychology, in research, in teaching, in writing, in dialogue with colleagues and students, can reveal how these disciplines construe general and special human experience into the categories and relations that characterize their unique disciplinary perspectives (some examples: McCloskey 1985; Bazerman 1988; Lemke 1988a, 1990a, 1990b; Halliday 1988; Halliday & Martin 1993). This is linguistics focussed not on form, but on function (e.g. Halliday 1985). It has more in common with the tradition of grammar-and-rhetoric than with modern formal syntax (though there is a gradual convergence). Linguistic discourse analysis is an applied semantics, a textual semantics, with formal syntax functioning as the legs that carry the dog, but not the tail that wags it.
Some studies of discourse(s) look more closely at the grammar-semantics connection (Halliday 1988, Halliday & Martin 1993); others look more at the semantics-rhetoric connection (Lemke 1988a, 1990a, 1990b), or at the rhetoric-genre connection (McCloskey 1985; Bazerman 1988). If I write a science textbook, my editors and readers expect me to follow certain conventions of format and organization: certain sorts of information are to be included, laid out in a certain way. These are the conventions of the textbook genre. In the course of a chapter I may want to persuade my readers to accept an argument, or I may want to raise some critical questions. These are functions of my rhetoric at that particular point, what I am trying to do for (or to) the reader. If I am going to be persuasive I need to follow the conventions of logic and argumentation that my community of readers probably accept and are used to. As I write my argument, I have to express particular meanings about something. I have to choose my topic and what I want to say about it specifically. These are matters of the semantics of my text. They influence my choice of words and of conceptual relationships that I wish to express. In order to do so, in writing a particular clause of a particular sentence, I also need to bear in mind the rules of English grammar and its syntax.
Studies of discourse are inevitably embedded in studies of social and cultural conventions; they require a social linguistics more than a cognitive linguistics (though both may have their uses). It is not possible to adequately analyze how individuals make sense if you do not know what the typical discourse patterns, the typical sense-making practices, of their community are (their semantic, rhetorical, and genre conventions at least; see for example Lemke 1989). It is particularly obvious that you cannot do so when you see that all discourse analysis is founded, explicitly, or implicitly, on the principle of general intertextuality (Lemke 1985): all meaning is made against the background of other meanings already made and shared in a community.
When I write the textbook chapter, or read one like it, I make sense of it by comparing it, consciously or unconsciously, with other similar texts I have read before. I recognize that it is a textbook and not a research treatise by its genre conventions, so I expect some things from it and not others. I make sense of its content largely because I can fill in its unstated assumptions from other works I have read on the same topic. I make sense of its patterns of argumentation because they are familiar to me from elsewhere. I interpret its use of technical vocabulary based on the specialized meanings I know these words have in this specialty field. And so on.
The totemic grandfather of social linguistics and intertextual discourse analysis of this sort is Mikhail Bakhtin (1929, 1981, 1986), a figure who ranks today with Foucault (and perhaps outranks Derrida). Like Foucault, Bakhtin takes a larger view of discourse than simply language in its narrowest sense. Discourse is a mode of action, almost synonymous with meaning-making itself. The units of discoure for both of them are units of meaning, or units of human activity that make meaning (utterances), and not linguistic units per se (clauses, sentences). Their perspective is semiotic. Semiosis is the process of making meaning by deploying the resources of social systems of signs in a community. While linguistic signs (words, clauses, texts) form such a semiotic resource system, so do many nonlinguistic, or only partly linguistic modes of human action. We can make meaning with dance, gesture, and movement; with pictures, diagrams, and typefaces; with songs, meals, and clothes. Most fundamentally, we make meaning with action. Linguistics made the first breakthroughs in the study of how we make meaning by deploying semiotic resources, but the general processes, it appears, apply to all meaning-making activity.
In the sciences, we do not just talk and write. We also act in many other ways that contribute to the special meaning constructions of our disciplines (e.g. Latour 1979, 1987) whether in the laboratory, in the field, in data collection and analysis, or in the economic, social, and political dimensions of the subcultures of our disciplinary institutions. All these actions function in the same way discourses do, to make possible the meanings of the discipline, to construct the objects we say we study. To say that objects or phenomena are social, discursive, actional, semiotic constructions is not to deny their materiality. It is to emphasize that what our theories, our discourses take hold of, are objects or phenomena as meanings, i.e. as we conceive of them, speak of them, measure them. This is not so far from the scientific doctrine of operationalism, that every physical object or quantity is defined by our procedures for observing or measuring it. Semiotics tries to tell us as much as possible about how it is possible to construct such meaning-objects.
I can read a book or I can weigh it on a scale. I can treat it as a symbol to be interpreted semiotically or as a material object to interact with physically. Semiotics is a discourse that tells me how the book's writing and diagrams and language mean something. Physics is a discourse that tells me how books and springs and scale-pointers interact physically, and which enables me to read the scale and interpret it as having a meaning about the weight of the book in the context of a discourse about mass, weight, gravity, force, elasticity, etc.
Every symbol must also be a material object, and any material object is recognizable and interpretable only in relation to some system of semiotic categories. Every act of interpretation of a symbol is also a physical, physiological process as well as being a semiotic practice, an enactment of a cultural system of conventions for making meaning. The material and semiotic aspects of things and processes are complementary to one another. They describe two different systems of relationships that we can construct among objects and processes. One of these is the familiar system of material, physical, chemical, thermodynamic, ecological relations: webs of material interaction. The other is the semiotic system of relationships of meaning: similarity, difference, categorization, ordering, association, etc.
The most basic semiotic relationships are very abstract, but for many purposes one can think of them in terms of a few simple types. Paradigmatic relations are those that tell us what something might have been but isn't: a physics textbook is not a biology textbook, a textbook is not a novel, a book is not a magazine, etc. Paradigmatic relations define contrasting alternatives, meaningful differences within similarity. Syntagmatic relations tell us what parts make up some whole: words that form a single sentence, sentences that form a single paragraph, different volumes that make up a single encyclopedia. Intertextual, or indexical, relations tell us in a broader sense what goes with what: this book is relevant to interpreting that book, this situation or event is a relevant context for that one, etc. The most fundamental principle of semiotics is that meaning is possible only because not all possible combinations of things, events, contexts, are equally likely. The particular odds on various combinations describe the culture of our community: our expectations and our patterns of behavior, including how we interpret meanings and how we interact with our environment.
A postmodern semiotic constructivism such as I have just described (for a fuller account, see Lemke in press) is itself, of course, just another discourse. You can get used to it, use it, enjoy it. Or find another that works better for your purposes. Postmodernism reclaims for science, and philosophy, the intellectual freedom of art. It refuses the power moves of some discourse factions that insist that their discourses are the only possible ones because they are "true". Many different discourses "work". It is not even possible to say absolutely whether many of these discourses are "consistent" with each other or "incompatible". They can be construed as being either, and usually are.
Most people reared in modern positivist traditions, or their commonsense variants, find themselves viscerally upset by the idea of rejecting notions like objective truth and reality. For a long time we have been sold the belief that these notions are indispensable, not only for science, but for morality. Postmodernist sensibility regards these reactions as understandable, but a little childish. Many postmodernists are arrogant; high levels of self-confidence are necessary when disagreeing with the foundations of a large part of your own culture. But postmodernism, semiotics, or social constructivist epistemology, do not require total Faith, or even complete self-consistency (another chimera, read G”del 1962). You can continue to believe that there is an objective external reality out there somewhere, and that truth is the common quality of propositions that correctly describe it, so long as you do not use these assumptions to try to gain power over your opponents in intellectual debate. Many postmodernists believe that such assumptions actually have no other practical function. Agnostics are heartily welcome in this un-church.
The postmodern, semiotic, constructivist view talks about meaning, not about truth. It talks about how discourses define phenomena, not about how phenomena are described by discourses. It always wants to know what people do that makes sense of what we ordinarily call an object or phenomenon. It situates meaning-making practices and the systems of semiotic resources deployed in those practices in the domain of the social, the cultural. Indeed, it sees social and cultural systems exactly as systems of such practices, systems of doings, and not systems of doers per se. The doer, the notion of a human individual, is as much a meaning-construction as anything else. If it is doings, i.e. social and cultural practices, that are fundamental, then as activities these practices consist of processes and participants defined in relation to the processes. Among the types of participant constructed in our culture are ones we call human individuals, but what a human is (an organism, a social individual, an actor or agent) is not necessarily the same from one type of activity to another. We learn how to conflate them, to make them all seem the same, and indeed how to think of ourselves as being constructions of this kind (cf. Lemke 1988b, in press). Human individuals cannot be taken for granted as the starting point of either social or cognitive theories.
As an example of this consider the question of whether and in exactly what sense a student is the same person in class and out of school, in math class and in English class, in small-group work and in whole-class instruction. Of course our culture provides ways to unify these differently behaving individuals, but it takes work to do so, semiotic work. We miss an important perspective on the student if we carry this presumption of unity and consistency too far. If we assume that the student has the same characteristics, the same ability, the same intelligence, even the same personality or interests, in all these different settings and situations, we may be overdoing it. And if we assign a grade to a student, instead of to an event or a performance, what does it really mean, if the student wasn't the same person in each different situation on which we are basing the single grade?
Semiotic Perspectives on Learning and Abstraction
The dominant theory of learning that guides educational practice in our society says that what people need to learn are "abstract concepts," which they can then apply to a wide variety of specific situations. Nearly everyone is convinced that conceptual learning is the most powerful form of learning, and the only problem is how to get more people to be able to successfully learn abstract concepts. The criterion for having learned an abstract concept is being able to apply it in new, unfamiliar situations. The way to teach abstract concepts is to demonstrate how they apply to several different situations until the student "catches on" or generalizes and "gets" the concept at an abstract level. The student will then be able to use the concept wherever it is relevant. -- Do you believe this fairy tale?
What happens in practice? A very, very small percentage of students seem to be "able" to learn abstract concepts in the sense described. If we accept fairly weak criteria of conceptual mastery, say the ability to apply the concept in situations not too different from the ones in which it was taught, but are rigorous about mastery at this level, a reasonable estimator of success across the student population would be the numbers of students who get top grades in courses like algebra or physics. Even most of these students, however, or their counterparts in other disciplines, would not meet the standard of being able to apply the concept `wherever it is relevant'.
Applying the older theory, we could say that either there is something wrong with the students, or something wrong with the teaching (or testing) methods. But the evidence against this prescription for abstract conceptual learning for most students is so overwhelming that surely we ought to consider that there might be something fundamentally wrong with the theory? The closest that traditional educational psychology comes to this is the great "transfer of training" debate. The only conclusion I have been able to draw from all the data on both sides of this is that, in general, the more abstract the concept, and the more unfamiliar the application context or content, the less evidence there is for generalization.
A now long and distinguished tradition of dissenters (e.g. from Cole et al. 1971, Cole & Scribner 1974, to Lave 1988) have argued that higher reasoning processes are context- and content-sensitive, not context- and content-independent. People in this tradition have even wondered whether cognitive processes can be usefully described at all apart from specific social and cultural activities, or at least apart from relatively specific social and cultural strategies for action.
The strongest evidence for conceptual generalization seems to come either from low-level processes (e.g. perceptual shape recognition), where evolution may well have lent a helping hand, or from our persistent introspection which tells (a very, very few) of us that this is what we do in higher-level reasoning. But our introspection is tainted by the theory itself: we have ourselves internalized a common discourse of our academic, intellectual culture which shapes the meanings we give to our subjective experience. Perhaps neither we nor anybody else does any such thing as generalize an abstract concept. Perhaps there is no such thing as an abstract concept.
Put that way, we recognize that "abstract concepts" are not the sort of thing to which our culture assigns much of a "reality" status anyway. Do abstract concepts exist? We would probably say that, no, perhaps the phenomena they refer to, or describe, do, but the concepts themselves are just a shorthand way of talking about rather complex cognitive processes. The postmodern semiotician, of course, will see the very notion of "abstract concepts" as born of the discourse of cognitive psychology (and its predecessors), and regard what goes under that name as just a set of conventions for using particular linguistic forms (often in conjunction with nonlinguistic actions of various sorts). Some of us (myself included) question the usefulness of even the notion of cognitive conceptual processes as such, wondering what, at least in the present discussion, cognitive theories can say about human reasoning that linguistic discourse analysis does not describe more precisely and with greater economy of theoretical means (especially remembering that the data of this area of cognitive psychology are, by and large, contextualized verbal reports in the first place; see Thibault 1986; Lemke 1989, 1990a; and even Geertz 1983).
In education we often proceed to teach something by first `breaking it down into simple parts or steps' then teaching the steps and expecting students to be able to perform the whole. In the teaching of skills (famously, bicycle riding), it is well known that this is not effective, but in the teaching of most academic intellectual skills it is still routinely adhered to. Constructivism points out that this sort of reductive analysis into parts is only possible as a post-hoc activity. It is only after we have mastered the whole that we can understand how it can be artificially divided into parts. The parts are not `natural', they are not there as a given prior reality. The parts are constructed by local conventions that depend on a prior facility with the whole. You cannot learn wholes through their parts. And the reason is that they don't have these parts! What you can do is learn how wholes are conventionally analyzed into parts, learning what precise kinds of part-whole relationships need to be constructed.
In academic education we also assume that students can learn abstract principles by induction from examples and by descriptions of abstract properties and relations. But just as skills do not necessarily have specific "parts" apart from how we choose to analyze them into these parts, so also an abstract principle is not necessarily visible in its "examples" until we learn how these examples are conventionally construed as instances of the same general principle. It is not necessarily true that the principle is "there" in the examples to be seen by anyone. Many students don't see these imaginary properties of examples even when teachers try their best to point them out.
In a classroom episode I analyzed a few years ago (Lemke 1990: 144-148), students could not "see" a wave moving on a long coiled spring in the way the teacher did, despite the teacher repeatedly demonstrating it right in front of them. They had to learn to "see" it in a new way, mediated by special technical distinctions named by specific terminology. They had to learn to use language, in conjunction with vision and motor action, to reinterpret experience in a new way, to "see" something that for the teacher was simply "there" in front of them.
For the purposes of learning and social behavior, we do not simply "see" photons registering on our retinas; we "see" meaningful patterns created by the higher centers of our brains according to the habits and conventions of our culture. The way in which these patterns are constructed is still somewhat mysterious in neurological terms (see Edelman 1992), but the social evidence for the process clearly shows the role of language and other systems of symbols. Learning to use a semantic distinction, such as that between "longitudinal" and "transverse" wave, or that between "motion of the medium" and "motion of the disturbance," as part of language is an integral part of learning to make and use the conceptual distinction.
We expect students to `catch on', to formulate abstract generalizations that will then apply to new and unfamiliar examples. We expect that they will `transfer' the abstract principle to new settings. But why? Mainly because our own cultural traditions, from Platonism to positivism, assume that the situations in which the principle applies really are "the same" in some respect that we can learn to recognize.
But for the postmodern constructivist there are no inherent similarities except the ones that a culture, a community constructs as meaningful, as significant against the background of an infinite number of possible categorizations, and constructs always, again, post hoc, i.e. after each instance is encountered. What our semiotic practices, such as the use of semantic distinctions coded in language, do is to enable us to fit instances into prior categories, or to create categories to encompass known sets of instances. We must invent a way to fit each new type of instance into an existing category, and insofar as the category is defined by the practices that assign its members, we actually change the category (i.e. add new categorization practices) for each new type of member.
This can only be done post hoc. Only instances that we already know how to type as members of a category will accomodate `transfer'; genuinely non-trivial new instances cannot be automatically typed because they do not already have the categorially critical features -- those features must be constructed for them. They do not automatically `fit' the category; they must be fitted into it. That requires work, social work. It cannot be done by an individual, because it must be done by the conventions of a community. It is ultimately as much or more a social than a `cognitive' process.
As an example, consider one of the most widely generalized concepts of natural science, "energy". The history of science shows clearly that each new `form' of energy (sound, heat, light, etc.) had to be defined in just such a way that it could be assimilated to the existing concept of energy. In fact, as each new form of energy was added, the concept itself, insofar as its meaning can be described as the sum total of all its possible uses or operational definitions, changed. The concept also changed insofar as it is defined by the set of operations for applying it to various phenomena.
No one can be expected to `generalize' from a notion of kinetic energy to the concept of potential energy, or to be able to anticipate the proper definitions of various forms of nuclear energy from a knowledge of heat energy or electromagnetic energy. What do all the forms of `energy' have in common? not even how they are measured, not even their `operational definitions'. You have to learn to call them all "energy" and learn that what this means is that, properly defined or measured, they can all play the same role in particular calculations or arguments, all fill the same slot in particular theoretical discussions. Our community has developed conventions for fitting each variation on the theme of energy into a common semiotic pattern (i.e. a general set of statements, whether linguistic, mathematical or graphical). That development has been the work of centuries. It can be recapitulated, but it would be foolish to imagine that it can be anticipated by individuals because it is somehow `there' in nature to be seen. In fact, you have to be carefully taught how to look to see `it' (i.e. to construct it) or how to `show' it to (construct it for) others, or even how to argue that others should accept what you show as evidence for what you claim.
The implications for education of this reconceptualization of what abstract concepts are is radical and profound. In this model generalizations are culture-specific: of all the possible similarities of two events, two moving springs, two "systems with energy", our culture has historically opted to pay attention to just certain ones, which it has evolved methods (semiotic methods: linguistic, experimental, graphical, mathematical) for constructing. Even if you believe that the similarities are "there" in the sense that it just wouldn't work for practical purposes (whose purposes? how practical?) to construct ANY old similarity, there are still an awful lot of possible similarities that CAN be constructed between two events or two systems in nature. Learning our culture means learning which ones we do construct, how we construct them, and what good they are for our practical purposes.
But if these particular similarities are not "obvious" ones, if we have to learn how to "see" (i.e. construct) them, then the process of learning "an abstract principle" or "an abstract concept" or generalization is really the process of learning how to construct specific sorts of similarities among specific classes of instances. In terms of classical logic this means that categories are learned "extensionally" by learning what their members are and why they are members, rather than "intensionally" by learning a set of features which are common to all members of the set. Those "same" features have to be constructed DIFFERENTLY for different members of the set. We probably do this by stages or degrees, first learning how to "see" some sorts of phenomena as "waves", then how to see other sorts as being similar, then how to see still other sorts, etc.
When we come to a new and unfamiliar class of phenomena, we can propose that these too are waves, but it is ultimately a matter of social consensus whether our proposal is adopted or not (for whatever reasons). If history has already made this decision for us, and the criteria of the culture for validating that decision leave no leeway for reconsideration, there is really no way to expect us, the students, to second-guess this history. We just have to be told. We have to be let in on one more set of specific procedures for how to make this new class of examples look like the others, how to construct similarities between it and other classes of examples.
Perhaps those of us, a small minority, who are positioned within our culture in such a way as to have acquired habits for guessing (or reasoning) that are most similar to those of the people who made these determinations historically (sc. upper-middle class, masculinized, middle-aged Northern European males), we are more likely to guess "right", i.e. to decide as our forbears did. This does not make us more intelligent or more able at abstract thinking. It only signals that we have been cut from the same cloth. (Such habits are largely unconscious, and the product of experiences in all aspects of our lives, not just school experiences. For a theory of them as embodied dispositions, see Bourdieu 1990; for gender and class differences in how children and students make meanings with language in interactions with mothers and with teachers see Hasan 1986, 1990, 1992 on semantic orientations.)
Another important implication of this reconsideration of the nature of abstract conceptual learning is that the value of studying something "similar" to our ultimate object of interest is called seriously into question. In academic learning we have acquired the habit of teaching by simulations and simulacra, rather than by giving our students first-hand experience of "the real thing".
In science education, for example, we expose students to science textbooks instead of, say, to scientific text; to science teachers instead of to scientists; to school laboratories instead of to scientific and technological workplaces. Simplified equipment, simplified procedures and processes, whether intellectual, conceptual, or manual will not suffice. They may have a function as adjuncts to learning, once students have already participated in the actual social practices being taught, but we cannot expect them to function, as they do now, as substitutes for such direct participation. It is only after we have learned how, say, science and technology operate in our communities in real laboratories and workplaces that we can intelligently participate in the construction of correspondences and similarities between what happens there and what happens in science classrooms or school laboratories.
Curriculum designers (rarely teachers, and almost never students) are typically people who have already learned how to construct these conventional similarities between textbook language and the working language of a discipline, between classroom demonstrations and actual phenomena or working professional procedures, between teachers of a subject and those who practice it outside of schools. They can do this because, hopefully, they have actual firsthand working knowledge of professional practices outside the context of education (in the contexts of production and use). But many teachers and most students do not have such experience. Curricula which assume that they do not need it, that it is sufficient to form abstract concepts based on inherently similar textbook and classroom examples, are based on fundamental epistemological fallacies. These similarities, too, must be constructed by learned cultural procedures; they are not inherent in the instances. They are not "the same as", and they are "like" the real thing for us only AFTER we learn how to compare them TO the real thing.
Yes, humans do pattern recognition. But but we must learn to think of it not as "pattern recognition", but as pattern construction. Since we construct patterns in the context of a culture, a community, and its pervasive habits of making some kinds of meanings rather than others, we do learn to make some patterns, construct some kinds of similarities rather than others, in ways peculiar to our own community. We do this in very small steps, learning to add each new category of examples to all the others in a special new way, building up toward being able to see the similarity in all that our traditions have taught us to painstakingly construct. We do not do it in great, impossible abstract leaps. There are no guidewires of self-evident similarities to lead us only to safe landing-sites when we leap for such conclusions.
Can we learn to leap further? at least in retracing the paths made step-by-step by our cultural predecessors? (Or better think of this as a developmental recapitulation of our historical phylogeny, not driven by from the inside alone, but also by the environment with which what is inside us evolved to cooperate). Some very few of us do seem to take longer leaps and land more or less where our cultural traditions say we should. One way of understanding this is as a process of "meta-construction," in which we are guided by a learned sensitivity to the cultural habits of meaning-making that are all around us. (At least they are all around us if we are middle-class, male, etc.)
By meta-construction I do not mean what is misnamed "meta-cognition" and is really no more than self-monitoring, glorified, like self-regulation and self-discipline, by the value system of a particular, influential subculture in our society. I mean, rather, the sort of process originally envisioned (for dolphins, in fact) by Gregory Bateson (1972): that we construct patterns of patterns. Having seen how our culture constructs some kinds of similarities rather than others, according to some kinds of principles rather than others, some of us come to embody in our neurological and behavioral dispositions a successful model of these patterns, and through it we invent new similarities, on old grounds, that can be understood and accepted by others and integrated into the meaning-making practices of our community. That is, everybody thinks we must be very smart.
So, for example, when we seem to "catch on" to an abstract principle, when we guess right about how to apply a generalization to a new class of instances, we may not in fact have acquired a flexible intellectual tool at all. We may simply be following a kind of learned habit of a higher order, making what is truly just an "educated guess". When schools and teachers praise and reward those who have this knack, we are discriminating in favor of the already socially privileged, because the only way you can have this knack is by catching on to the meaning-making habits of the dominant groups in our society and its history. If we call it intelligence, and assume it is an immutable characteristic of the individual, we will never take the trouble to teach these meaning-making procedures, step-by-step, to all the others.
At some level, most members of a community do learn, though not consciously, to construct such higher-order patterns. We can tell whether something seems culturally "alien" or not (perhaps this is even the basis of the much debated "grammaticality judgments" of native speakers about language). But the pattern-of-patterns we learn to construct are those of "our culture" in the narrow sense: the subculture we live in every day. That is not the same culture for all of us in our diverse and heterogeneous society. Even so, very few of us seem to learn to use this facility at all consciously to make new patterns, or to do what we value so much (and see so little) in education: anticipate the conventional way to make a particular pattern that has evolved in the history of our culture, before you are shown how. This facility exists, but we have misused it as evidence that what we have called abstract conceptual learning is the norm. It is almost as rare as genuine intellectual creativity, and for exactly the same reasons.
Too many of us pride ourselves that we have this facility because we have, finally, eventually, and after much struggle, re-constructed after-the-fact ways of making all these similarities seem natural. Often we achieved this only years after it was taught to us by methods which assumed that we should have easily been able to catch on, to "see" the inherent similarities that were there in front of us, so evident to our teachers, who had themselves similarly struggled for years to see them. Most of us can remember blaming ourselves for not being able to "see" abstract relations that our teachers assured us were "there" and which they were confident we "should" be able to catch on to after two or three examples. Many of us perpetuate this fallacy and its painful frustrations with our own students.
Postmodernism, constructivism, and social semiotics are not here to make our lives tough. Modernism, positivism, and abstract conceptual learning theory have already done that. We deserve a break. And so do our students.
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