epistemological perspectives on conceptions of curriculum organization and learning

Epistemological Perspectives on Conceptions of Curriculum Organization and LearningAuthor(s): Kenneth A. Strike and George J. PosnerSource: Review of Research in Education, Vol. 4 (1976), pp. 106-141Published by: American Educational Research AssociationStable URL: http://www.jstor.org/stable/1167114 .

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3

Epistemological Perspectives on Conceptions of Curriculum Organization and Learning

KENNETH A. STRIKE GEORGEJ.POSNER Cornell University

To study cognition, one must have some conception of knowledge.

(Kohlberg, 1971)

How should we organize subject matter to be learned? Does learning proceed from the particular to the general or from the general

to the particular? In what ways should the organization of a curriculum depend on the

conceptual properties of the subject matter to be taught? How can we best describe educational objectives? What sorts of learning outcomes should we expect from teaching students

the structure of knowledge? What kinds of concepts do we need to describe cognitive structure? What kinds of concepts do we need to describe cognitive process? What is thinking? What is good thinking? What kinds of concepts do we need to describe thinking? How can we teach someone to think, and how can we tell when he can

think?

The basic tasks of epistemology are to characterize rational inquiry and to describe some of the properties of organized bodies of knowledge. Are the

JONAS F. SOLTIS, Teachers College, Columbia University, was the editorial consultant for this chapter.

The authors wish to thank Robert Balter, Elizabeth Clarke, Lynn DeJonghe, Victor Garlock, Bob Gowin, Kay Koffel, Joseph Novak, Hugh Petrie, Leon Pines, Alan Rudnitsky, Simeon Slovacek, and David Zola for their aid in identifying sources and critiquing earlier drafts of this manuscript, and Nancy Ganoung for her work in preparing the manuscript.

106



Strike and Posner: Conceptions of Curriculum Organization 107

above questions epistemological? Probably the best answer is "in varying degrees." It would be more informative to suggest that the view of the relations between epistemology and educational research which we take has two basic features. First, we believe that there are few, if any, educational or psychological questions-including the aforementioned ones-which can be decided on

purely epistemological grounds (Price, 1973). Thus, epistemology is not likely on its own to get one very far in educational decision making. Second, we believe that there are various research programs or enterprises in education which are organized by theoretical commitments, many of which are epistemological. Thus, epistemological considerations are relevant to an assessment of

many educational and psychological research and development programs. The connection between epistemology and specific research results is often indirect and is mediated by basic orientations of research programs.

In the light of this view of the connection between epistemology and educational research, we have divided this review into two major sections. The first section provides the reader with some philosophical bearings. Here we look at some developments and issues which have characterized epistemology (largely in its Anglo-American varieties) since the 18th century. Obviously our choice of issues is highly selective and is colored by some of the points we hope to make in the second section. Moreover, the epistemological viewpoints considered are varieties of empiricism. They are all committed, in some degree, to the view that knowledge is rooted in experience. The views of how knowl-

edge relates to experience, however, vary widely. Our purpose in conducting this rapid epistemological tour is to identify some of the epistemological issues which have become embedded in educational and psychological research en-

terprises. In the second section, our purpose is to sample research enterprises which

exhibit the issues generated by the first section. Our strategy here, too, is to take the reader on a rapid tour of a diverse set of enterprises. Our reasons for

diverging from the normal review strategy of describing in depth the research in a tightly circumscribed area are twofold. First, our view of the relations between epistemology and educational research indicates that such a strategy is in order. Second, this area is not well explored. It thus seems appropriate to try to sketch the nature of the issues and map out a bit of the intellectual

topography. First, then, some epistemological background.

I. AN EPISTEMIC SKETCH

A. The Humean Background

We begin our sketch with a discussion of David Hume (1957, 1967), since Hume's work in the 18th century posed many of the problems which have



108 Review of Research in Education, 4

influenced the orientation of current work in both philosophy and psychology. Much of Hume's work stems from his radical interpretation of the tradi-

tional empiricist motto "There is nothing in the mind which was not first in the senses." Knowledge, says Hume, originates in experience. More particu- larly, knowledge begins with impressions or perceptions. Impressions, in turn, produce ideas, which are nothing more than mental copies of impressions and differ from them only by being less "forceful and vivacious." There are no ideas which do not have their origins in perceptions. Knowledge, in turn, consists in the association or linking of these ideas according to such principles as resemblance, spatial and temporal contiguity, and cause and effect. To Hume, the mind's sole power is the power to associate or generalize observed relations among ideas. Higher level generalizations are constructed from lower level ones. Hume's empiricism, therefore, is more than a theory of verification. It is a theory of concept formation which requires the general to be constructed from particular experiences.

These central ideas were readily translated into a philosophical-psychological program with the following features:

1. Atomism. The study of the development of knowledge, of the workings of the mind, or of the emergence of behavior patterns begins with the identification of the "atoms of experience," be they conscious states (sense data) or stimulus and response variables.

2. Associationism. The task of both epistemology and psychology is to discover the laws or conditions under which these atoms are connected. The commitment to associationism results, in part, from the fact that the radical empiricism of Hume's program renders illicit the hypothetical explanatory devices (from a substantive mind to cognitive schema or information-processing mechanisms), because they are not objects of direct experience. All that are left are claims of the sort that one item is correlated with or "calls forth" another.

3. Inductivism. The general is always a construct of the particular. This is the case whether we are dealing with skills, concepts, or propositions. Any view of knowledge, concepts, or skills in which the general is somehow prior to the particular turns out to violate the maxim that there is nothing in the mind which is not first in the senses.

Hume's views provide both the historical (Peters, 1965) and philosophical antecedents (Strike, 1974b; Skinner 1950, 1953) of modern associationist and behaviorist psychologies. Modern behaviorisms are derived from a Humean orientation by replacing ideas with the stimulus and response as objects of association, and by replacing introspection with experimentation as the basic concept of scientific observation.

B. Hypothetical Deductive Views

The hypothetical deductive method, an analysis of scientific method whose major proponent has been Karl Popper (1961), can be contrasted with a




Humean view in that it rejects an inductive account of both the origins of scientific ideas and of the verification of scientific claims.

In Popper's view, a scientific theory can be treated as an axiomatized deductive system in which the axioms are the most general and abstract theoretical assumptions of the systems. From these basic assumptions it is

possible to deduce both theoretical claims of lesser scope and, ultimately, empirical claims about the world. Scientific systems differ from the a priori deductive systems of logic or mathematics, primarily in the way their truth is established. The axioms of mathematical systems are assumed to be a priori true. This being the case, the truth of any proposition validly deduced from them is assured. But the axioms of scientific systems are assumptions or hypotheses, which are not a priori true. Thus, their truth is established when the empirical claims derivable from them provide an accurate description of the empirical world.

These aspects of a hypothetical deductive model conflict with a Humean program initially in that they are incompatible with the inductivist view of the origins of ideas. Scientific theories are not generalizations of relations in experience. They are not, as inductivist accounts require, descriptions of sequences in events with an "always" in front. Rather, they are assumptions about the nature of the world from which such generalizations can be derived. Thus, the hypothetical deductive model rejects the inductivist implication that scientific theories are, like pyramids, constructed from the bottom up out of increasingly general claims about relations in experience.

Since advocates of hypothetical deductive models of science are not given to viewing scientific theories as generalizations concerning observed facts, they also are not readily inclined to see questions of scientific evidence as essentially questions about the number and nature of instances required to verify an inductive generalization. It is more appropriate, claims Popper, to think about falsifying a theory than to attempt to collect verifying instances. However, Popper's major argument for preferring an emphasis on falsification over verification is based on a simple logical point: while no number of instances of a given relationship ever entails that a proposition affirming the generality of that relationship is true, a single counterinstance entails that it is false. It follows that it is more profitable to attempt to falsify a theory than to enumer- ate confirming instances. What proves the worth of a scientific theory is its ability to withstand serious attempts to discover counterinstances to it. Scien- tific method thus becomes a matter of proposing bold assumptions about the world, deductively elaborating the empirical consequences of these assumptions, and then trying to find counterinstances. It is a matter of conjecture and refutation, not of constructing generalizations from instances.

C. Recent Developments A basic objection to Popper's falsificationist doctrine is that it is not ade-

quately descriptive of how scientists, even great scientists doing exemplary




work, actually proceed (see Kuhn, 1962). Scientists do not abandon theories, given a single or even a variety of counterinstances. Rather, they execute a variety of ploys to reconcile current theory with recalcitrant data. There is, therefore, a conflict between a naive falsificationist point of view and many paradigmatic cases of quality scientific thought. It would appear to be the case, then, that either the falsificationist doctrine is incorrect, or most scientists behave irrationally much of the time in that they refuse to abandon falsified theories.

Assuming that the latter conclusion is unacceptable, we then face the question as to where the falsificationist doctrine went wrong. We shall sketch three different objections. First, the falsificationist doctrine rests on the assumption that facts are logically independent of theory. Data, it is presumed, are what they are, regardless of the theories which are maintained by any given observer. Thus any theory can be checked against an objective theory-neutral data base. Against this assumption it is urged that facts are not theory neutral (Hanson, 1958, Kuhn, 1962, Lakatos, 1970). Rather, theories or concepts structure our perceptions such that any and every observation is theory laden.

Second, the falsificationist doctrine assumes that a data base is immediately derivable from a theory. In fact, however, it is usually necessary to supplement a theory with a number of additional assumptions in order to derive any predictions concerning the world. Imre Lakatos (1970) suggests that we may analyze the propositional components of a scientific enterprise into three types: a theoretical "hard core," a set of auxiliary hypotheses (a "protective belt") by means of which the hard core is related to (and defended from) the world, and a set of descriptive predictions derived from the hard core and the auxiliary hypotheses. This analysis provides a formal account of a means whereby a scientist can defend his theoretical hard core against data which conflict with descriptive predictions. He simply denies one or more of the auxiliary hypotheses. Given sufficient imagination, it seems possible to reconcile any moderately plausible theory with substantial negative data by the manipulation of auxiliary hypotheses. Thus, the falsificationist doctrine seems not to give a reliable picture of scientific procedure, since scientists are under no logical compulsion to deny a scientific theory in the face of apparently recalcitrant data.

The third objection to the falsificationist doctrine (see Kuhn, 1962; Toul- min, 1972) is that it is the result (contrary to Popper's claims that it is descriptive of actual scientific procedure) of attempting to impose a formal logical analysis on scientific procedure without benefit of a close scrutiny of what scientists actually do.

These objections have generated a variety of reanalyses of the nature of scientific procedure. Thomas Kuhn (1962) claims that everyday scientific research, termed "normal science," is dominated by a set of interrelated assumptions termed "paradigm." It is the paradigm which determines the nature of problems to be solved and what counts as a solution. Indeed, rational choice




seems possible only within a paradigm, such that when a paradigm itself is in question, choice takes on an inescapable aspect of arbitrariness.

Lakatos (1970) discusses what he calls research programs. If a theoretical hard core can always be reconciled with the data, then the focus of methodology must be on discovering whether or not a line of inquiry organized by a theoretical hard core is progressive or degenerating. Is the program gaining or losing empirical content? Is it anticipating novel facts or accommodating to them by ad hoc assumption? Is it competing well with other research programs?

A third orientation is suggested by Stephen Toulmin, who finds the alternative posed by Kuhn to be overly relativistic. The basic problem of conceptual change, then, is posed as a dilemma. If we follow Popper and provide an account of scientific method which is highly formal, abstract, and universal, we secure an objective foothold for rationality at the price of historical irrele- vance. Such accounts do not effectively characterize actual scientific reasoning. On the other hand, if we elect an option of the sort suggested by Kuhn or by Collingwood (1940), we make rationality internal to a particular point of view and, thus, while rational procedures can be employed within a given rational enterprise, there is no general perspective from which rational enterprises themselves can be evaluated. We are thus landed in a kind of relativism where basic intellectual commitments are necessarily arbitrary. Toulmin believes that recent work in epistemology has presented us with a choice between an irrelevant absolutism and a species of relativism, neither of which is acceptable.

Toulmin's solution to this dilemma can be summarized as follows: First, we must reject the picture of conceptual change given us by Kuhn, which divides scientific work into normal science, where solutions to puzzles are sought within the intellectual confines of a given paradigm, and revolutionary science, where one comprehensive viewpoint replaces another. Conceptual change is evolutionary, not revolutionary. Moreover, itf this is the case, then we are never in the position suggested by Kuhn, where all of our intellectual standards seem to be up for grabs at once. An evolutionary model of change allows us to evaluate any particular conceptual change against an enduring background of rational standards and explanatory ideals. Conceptual change is not a matter of judging between comprehensive views but rather of judging concepts in relation to other concepts, with respect to their adequacy in interpreting problems and fulfilling explanatory ideals.

Toulmin holds that this model is a species of evolutionary theory. Just as changes in the environment and in the development of organisms alter the conditions of competition and thereby bring about changes in organisms and populations of organisms, similarly, changes in intellectual environments alter the conditions under which concepts develop. Concepts adapt to an intellectual environment much as organisms adapt to a biological environment.

These various points of view clearly share with Popper the rejection of the




inductivist implication of a Humean program. However, they differ from Popper, and they tend to have in common the following features:

1. They reject the view that scientific method can be analyzed by inspecting the properties of formal logical systems. One must instead attend to what scientists do. Epistemology, thus, becomes a less a priori and a more empirical enterprise.

2. They emphasize the role of substantive theoretical commitments as op- posed to formal logical rules or standards in scientific judgment. Rationality is often viewed as being internal to some such set of assumptions.

3. As a consequence of the above, they tend to reject notions of a general intellectual method which can be described independently of any theoretical context and which applies to the solution of a diverse range of problems.

4. They tend to view epistemological questions as having more to do with understanding the process of conceptual change, i.e., how sets of concepts develop, decay, and become replaced by other concepts, than as concerning the relations between a theory and some data base.

These views differ from Popper, then, in that Popper presents a view of intellectual method wherein standards of judgment are formal, general, and external to any substantive theoretical considerations. Recent authors, such as Kuhn, Lakatos, and Toulmin, have developed a set of views wherein standards of judgment are to a large degree regarded as substantive and applicable only in a given theoretical context.

This summary should not cause the reader to lose sight of the differences between the views discussed. Generally, on the above points Lakatos is the most conservative and can be regarded as closest to Popper. Kuhn is the most radical. For our purpose, it may be more appropriate to think of these views as arranged on a continuum from a pole providing a formal, general, and content-neutral analysis of intellectual method to a pole providing views which emphasize the role of substantive theoretical commitments in rational judgment. We should note that even Humean views can be arranged on this sort of continuum; they appear at the extreme pole of the atheoretical analyses of method. Consider that while, for Popper, the process of falsification can be described in purely formal terms, theories turn out to be important in guiding research and determining proper areas of exploration. The inductivist view of the origins of theories, however, seems to preclude even this role for theoretical commitments in research.

D. Logic and Psychology Hume's theory is distinct from the other epistemological orientations we

have considered in that it does not distinguish between logic and psychology. No sharp distinction had yet been drawn between the laws of the mind and the norms of inquiry, a distinction insisted on subsequently by both philosophers and psychologists. Thus, notions such as resemblance or contiguity




function in the dual roles of laws of association and rules of valid inference. The distinction between logic and psychology, which can, perhaps, be said to have begun with Immanuel Kant (1929), was first insisted on in the late 19th and early 20th centuries both by psychologists, who wished to make their enterprise an experimental rather than a speculative science, and by philosophers, who wished to insist that the validity of arguments is a matter to be decided on formal a priori grounds and not on the basis of any psychological facts. "Psychologism," the view that the validity of arguments rests on psychological happenings, became a cardinal methodological sin in philosophy.

The essence of the distinction between logic and psychology is as follows: Psychology is concerned with empirical fact. It is supposed to discover actual regularities in phenomena and to construct theories to explain them. Logic is concerned with norms. It is supposed to describe the properties of valid arguments, the conditions under which conclusions are properly drawn from evidence.

The distinction has been put in extreme form. Rudolph Carnap, for example, objects to any mentalist vocabulary in the description of logic: ". . . logic is often characterized as the art of thinking, and the principles of logic are called principles or laws of thought. These and similar formulations refer to thinking and hence are of a subjectivist nature" (1950, p. 39).

However, we are inclined toward the more moderate view of Toulmin:

". . a characterization of logic in terms of justified beliefs, actions, policies, and so on is unavoidable. For if logic is to have any application to the practical assessment of arguments and conclusions, these references are bound to come in" (1958, p. 8).

The difficulty with a radical separation between logic and psychology is that logic is likely to become excessively formalistic and psychology overly mechanistic. The logician is apt to lose sight of the fact that logic may be used as a tool by human beings with actual intellectual problems to be solved. When considerations of formal validity become divorced from considerations of applicability, the result is likely to be logical systems which are too abstract to inform or characterize actual rational activity. The other side of this formal- ist coin is that psychologies may become excessively mechanistic in that they lose sight of their role in providing an empirical account of the ways in which rational activities are conducted. In extreme cases, they may lose sight of the significant distinction between human activities which do and which do not involve the employment of concepts, rules, or rational standards.

We take the position that a major task of logic or epistemology is to construct a description of the norms which apply (or should apply) in actual cases of inquiry, and that a major task of a "psychology of knowing" is to work out an empirical model of how such norms are applied. We do not hereby mean to affirm that epistemology is in some way logically prior to learning theory, such that learning theory must await philosophical analysis in order




for its problems to be comprehensible (see Toulmin, 1969). Rather, the point is that there is (or should be) a degree of reciprocity between them. For example, an epistemology must be "thinkable," that is, the inferences and manipulations of ideas an epistemology describes must be operations which can actually be performed, and this means that they must conform to whatever constraints on "thinkability" may follow from what we know about what people do in thinking.

Conversely, a psychology of learning must take seriously the fact that some kinds of learning involve the application of concepts or rational norms, and conceptual systems and rational norms are subject to criteria of a nonempirical sort. A psychology which does take this to heart will have some of its questions and problems set by the nature of these norms.

This reciprocity between epistemology and learning theory is nicely illustrated by the concept of generativeness as it is sometimes employed in psy- cholinguistics. The claim that a speaker employed syntactic rule R to generate sentence S requires for its substantiation both formal and empirical evidence. If S is generated from R, R must have a certain logical relation to S. But the question as to whether S was generated from R or from R1, which also has the proper formal relation to S, will have to be decided on empirical grounds. When, as is presumably the case in psycholinguistic research, the questions concern the relations between a complex set of semantic and syntactical rules and a wide range of utterances, the interaction between formal and empirical questions will become complex. The researcher will have to produce a set of rules, R, which is formally adequate in relation to a set of sentences, S, but the selection of R may depend as well on whether the claim that R is used to generate Sis consistent with our empirical knowledge of memory, information coding, decoding, retrieval, and the observable sequences and temporal relations in sentence production. In short, R will be treated as more than an axiom set for which the members of S must be theorems, but as specifying certain cognitive structures and operations which must exhibit their empirical handiwork.

This sort of reciprocity, we believe, ought to be a feature of most research in cognitive learning. It ought also to characterize the interaction between epistemology and cognitive psychology.

E. Epistemology and Educational Research

The discussion to this point has suggested several epistemological issues, which we shall attempt to relate to various lines of educational research in the remainder of this chapter.

Initially, there are two basic sets of issues which divide research programs based on Humean assumptions from those based on the assumptions of a hypothetical deductive orientation. The first group of issues concerns the Humean theory of concept formation. An inductivist view requires general




concepts to be constructed from particular experiences. This view has two noteworthy aspects so far as recent educational research is concerned. First, it seems to require that learning proceed from the particular to the general. This, we will argue, is the central philosophical commitment which divides "bottom up" approaches to curriculum of the sort represented by the work of Robert Gagn6 from "top down" varieties of the sort often associated with Jerome Bruner (Shulman, 1970). Second, the notion that the general is constructed from the particular suggests that the meaning of general concepts is equivalent to the sum of their instances. Concepts, thus, can be clarified by reducing them to the particular instances they summarize. We will claim that this is the philosophical basis of the view that behavioral objectives somehow clarify educational goals.

The second set of issues concerns the relation between epistemology and psychology. We have suggested that psychologies deriving from a Humean orientation are often mechanistic in the sense that they lose sight of the role of psychology in providing models of how people employ concepts or rational standards. We will argue that this difficulty is expressed in educational research in terms of how researchers characterize the cognitive states which are involved in learning or are supposed to result from it. We will thus look at several approaches describing cognitive structure and thinking.

An additional set of issues divides hypothetical deductive views and the views of critics of such an orientation. Here the basic concern is the nature of intellectual standards. Is there anything like a general and formal intellectual method, or are intellectual standards internal to particular theoretical contexts? This set of issues we hope to use to explore some commitments concerning the nature of thinking implicit in literature on the structure of knowledge and on discovery learning.

We will focus, therefore, on work which poses, illustrates, or turns on the following questions:

1. What is the relation between the general and the particular? Are general concepts constructed from their instances, or are the instances derived from general concepts?

2. What are the relationships between the epistemological concepts necessary to describe the structure and manipulations of bodies of knowledge and the concepts necessary to describe cognitive states and processes?

3. What is the nature of intellectual standards? Is there such a thing as a content-neutral intellectual method, or are standards of judgment internal to substantive theoretical commitments?

II. PERSPECTIVES ON PROGRAMS OF EDUCATIONAL RESEARCH

It is unlikely that the epistemological commitments of a research program will determine the results of specific empirical inquiries. If our suppositions




are correct, epistemological commitments will rather be expressed in the basic theoretical commitments of a research program. Our approach here, then, is to focus on the conceptual frameworks in terms of which research is being done. Given the kinds of epistemological issues we have sketched, it will be fruitful to explore three areas.

First, we will look at representative options concerning the structure and organization of curriculum content. Second, we will look at a set of options concerning cognitive structure. Finally, we will look at two different sorts of literature concerning the nature of thinking.

A. Content Structure

Bottom-up Views. An approach to content structure based on the notion of a "learning hierarchy" has been developing for the past 15 years. Gagn6 describes the basic concept as follows: "A learning hierarchy . . . identifies a set of intellectual skills that are ordered in a manner indicating substantial amounts of positive transfer from those skills of lower position to connected ones of higher position" (1970, p. 239).

This notion of a "learning hierarchy" has been the basis of a growing amount of research (Gagn6, 1962; Gagn6 & Bassler, 1963; Gagn6, Mayor, Garstens, & Paradise, 1962; Gagn6 & Paradise, 1961; Gagn6 & Staff, 1965; Kolb, 1967-68; Merrill, 1965; Merrill, Barton, & Wood, 1970; Olsen, 1968; Resnick & Wang, 1969; White, 1974a). The concept has also been the basis for curriculum development in science (AAAS Commission on Science Educa- tion, 1965, 1967; Gagn6, 1966), curricular and instructional theory (Gagne, 1970; Gagn6 & Briggs, 1974), and curriculum evaluation (Gagn6, 1967).

We suggest that the learning hierarchy approach to organizing curriculum content exhibits the central epistemological commitments of a Humean orientation, in the form of the commitments normally found in modern associationist psychologies.

First, the approach is atomistic; that is, it attempts to identify the atoms or simplest elements of learning. In order to design a curriculum, one works backward from complex intellectual skills to discover increasingly more basic units, ultimately to the atom, i.e., the simplest S-R bonds. Second, the approach is associationist; that is, a good deal of the research effort goes into the description of how the "atoms" are linked. A process of "vertical transfer" is used to account for the way "subordinate" skills in the hierarchy enable one to master superordinate skills. Third, it is inductivist; that is, the general is understood as a construction from the particular. Concepts and cognitive skills are constructed ultimately from S-R bonds.

We will examine this approach by considering a recent paper by White (1974c) which attempts to validate Gagne's "basic premise. . . that the ability to perform a class of tasks cannot be acquired unless all of a set of relevant subordinate skills, or elements of knowledge, are already possessed by the learner" (White, 1974c, p. 121).




This study of White, "The Validation of a Learning Hierarchy," attempts to address many of the weaknesses found in previous studies. White identified these weaknesses (1973), suggested ways to overcome them (1974b), and im-

plemented in this study (1974c) a nine-stage process for validating a hierarchy. Steps 1 through 4 are as follows:

1. Define in behavioral terms the element that is to be the pinnacle of the hierarchy. 2. Derive the hierarchy by asking Gagne's question, "What must the learner be able

to do to learn this element, given only instructions?" of each element in turn, from the pinnacle element downward.

3. Check the reasonableness of the postulated hierarchy with experienced teachers and subject matter experts.

4. Invent possible divisions of the elements of the hierarchy, so that very precise definitions are obtained.

In addition, Steps 5 through 9 concern techniques for empirical validation of the hierarchy. This procedure was described by White as providing "the most unequivocal evidence yet obtained for hierarchies" (1974c, p. 135). The results suggested "that verbalized knowledge is not learned hierarchically though intellectual skills are" (1974c, p. 135). According to White, hierarchies validated by this nine-step procedure describe "a complete set of prerequisites-no hidden prerequisites remain unidentified" (1974c, p. 135).

White's study raises a number of questions concerning a learning hierarchy approach to curriculum structure. For example, is it the case that, as required by Step 1, the most general goals in the hierarchy can be translated into a list of behaviors without loss of meaning? This enterprise seems to involve the inductivist assumption that general goals are somehow equivalent to their (in this case) behavioral instances. It has been argued (Posner & Strike, 1975; Strike & Posner, 1974; Strike, 1974b) that this is not the case, and the emphasis on behavioral objectives often results in the confusion of educational goals with the behavioral effects of having achieved these goals. The result is a tendency to trivialize or alter some objectives, especially cognitive ones.

A second issue concerns the assumption on which hierarchies are constructed. Here it is claimed that because items on the higher levels of the hierarchy are constructed out of items on the lower levels (Steps 2 and 4), learning should proceed from the particular to the general-from the bottom up (Gagne, 1970). While we do not wish to claim that this is not the case in some areas (motor skills, perhaps), it seems a suspicious claim when made about ideas or intellectual skills. It does not take seriously the possibility that in some cases the specifics of a body of knowledge can be generated from its more general concepts. Nor does it take sufficiently seriously the idea that general concepts facilitate the retention of their instances.

Moreover, the claim that the lower stages of a hierarchy are not only prerequisite to, but are empirically related to, the higher stages raises puzzling




questions about the relations between the logical or conceptual structure of disciplines and the structure of learning hierarchies (Phillips & Kelly, 1975). Hiemer (1969), for example, claims:

The connection, if any, between the [logical] structure of the content and the design of the associated learning hierarchy seems to be best characterized at the present as a "blur." There is most assuredly an intimate relationship between "what an individual can do" and "what an individual knows," but there is a conspicuous absence of information about this relationship in the literature. (p. 498)

White's suggestion that validation of a hierarchy includes checking its "reasonableness" with teacher and subject matter experts (Step 3) perhaps indicates some sensitivity to the problem, although little light is shed on what counts as "reasonableness." Gagne's remark that learning hierarchies are the best way to describe the structure of any discipline (1970, p. 245) does little to resolve the issue.

The notion of an empirically validated prerequisite is, however, central to the Gagn6-White notion of a learning hierarchy. Empirical prerequisites for White and Gagn6 are treated as the only rational basis for content structure, since they provide the connection between elements in a learning hierarchy. We have argued (Posner & Strike, 1976) that there is a diversity of possible connections between content elements, only one of which is based on empirical prerequisites. For example, content elements may be sequenced on the basis of familiarity, interest, and difficulty, or on the basis of logical properties of the content such as propositional relationships, class relations, logical prerequisites, and level of sophistication of the content. Undoubtedly, empirical tests may indicate that content elements sequenced on one or more of these bases exhibit prerequisite relationships. However, the empirical tests may often obscure the underlying bases for the prerequisite relationship. Consider, for example, that it may be necessary to understand the concept of a set before one can understand the concept of a number. This obviously has something to do with the logical relations which obtain between the concepts of set and number but which will be represented in a learning hierarchy approach as simply an empirical connection. Gagn6's approach will thus mask any relations between prerequisites in learning and the conceptual or logical properties of content (see Phillips & Kelly, 1975).

Such a strategy, by obscuring the diversity of relationships possible between content elements, may also obscure the relationship of content structure to cognitive operations. If the conceptual properties of content are important to the ability of an individual to think, a full description of that content is desirable for investigation of this relationship.

Furthermore, the limited notion of content structure presented by Gagn6, White, and other bottom-up researchers frustrates questions regarding the




diversity of purposes for which one might structure content. For example, one might want to structure content, not for learning efficiency, but rather for the

purpose of altering a learner's cognitive structure so that it is congruent with the logical structure of the discipline. Or one might want to structure the content so that it is consistent with the procedural sequence of tasks followed by workers on a job. The learning hierarchy approach to curriculum building thus seems to be inadequate, both to reflect the conceptual properties of content and to reflect the diversity of human purposes for structuring content.

Top-down Views. As the bottom-up approach reflects an inductivist orientation, the top-down approach reflects assumptions shared by the hypothetical deductive view as well as its recent critics. A defining characteristic of a top-down approach is that it assumes that concepts can generate their instances and are thus not the sums of their instances. This assumption is shared by both the hypothetical deductive orientation and by the recent critics of that approach. Therefore, the conception of the top-down approach does not rigor- ously distinguish between these two somewhat different orientations.

Since the late fifties and early sixties, a top-down approach has been embod- ied in a curriculum reform movement that is often termed the structure-of-the- disciplines approach (Bruner, 1960; Foshay, 1970). Under the leadership of such people as Zacharias (PSSC physics), Bruner (Man: A Course of Study), Schwab and Glass (BSCS biology), Begle (SMSG math), Beberman (UICSM math), and others, this movement has focused on the most fundamental ideas which are supposed to enable the learners to derive particular facts and examples on their own (Bruner, 1966). In contrast to bottom-up curricula, these top-down curricula have been based on conceptual hierarchies rooted in the conceptual structure of subject matter, rather than empirically validated hierarchies of competencies.

Guided by the work of Schwab (1962, 1964a, 19641b), this view tends to reflect the assumption that thinking is more dependent on grasping the "substantive and syntactical structure" of organized bodies of knowledge than on the ability to manipulate some abstract logic or content-neutral intellectual method.

Although actual top-down curriculum development abounded during the sixties, empirical research and evaluation studies have been and continue to be few in number and poor in quality. As Walker & Schaffarzick (1974) point out, most evaluation research on these curricula compares them with tradi- tional types, as though both sorts were intended to accomplish similar objectives. Few studies involve measures appropriate to the new aspirations of these new curricula. (See, for example, Welch and Walberg, 1972, on Harvard Project Physics, and Heath, 1964, on PSSC physics.)

The fundamental insights of the structure-of-the-disciplines movement are that the manipulation of the content of a discipline depends on grasping the structure of the disciplines, and, because of the generative properties of these




structural concepts, one can learn a lot by learning a little. However, the basic defect of much of this work may have been the assumption that a grasp of the structure of subject matter is a sufficient base for curriculum development (Ausubel, 1964).

Paradigmatic of this problem is the Cambridge Conference on School Mathematics. At the outset of planning for the conference it was agreed that "what is or is not worth teaching must be approached, initially at least, in terms of the possibilities that are inherent in the subject matter; the question of what is teachable and what is not depends largely upon the organization of that subject matter" (Cambridge Conference, 1963, p. 2). Once this premise was accepted, a corollary immediately suggested itself: that "only the very top level of expertise is likely to be sufficient to make the necessary determinations" of what is worth teaching (Cambridge Conference, 1963, p. 3). Hence, it was decided to invite to the conference only persons holding university positions or the equivalent.

The structure of the discipline was seen to be so crucial in shaping a person's thought processes that the conference participants agreed that they could

ignore all of the research of Piaget concerning the nature of a child's reasoning, on the grounds that it was irrelevant. "The essence of our enterprise is to alter the data which have formed, so far, the basis of his research. If teaching furnishes experiences which few children now have, then in the future such observers as Piaget may observe quite different things" (Cambridge Confer- ence, 1963, p. 4). Similarly, the group ignored many issues of pedagogical technique, teacher training, and political accommodations as extrinsic to the basic task of "thinking on the nature of the good curriculum."

A number of authors have noted the possible shortcomings in an excessive reliance on the structure-of-the-disciplines approach (Ausubel, 1964, p. 227; Phenix, 1964, p. 54). For our part, while our basic theoretical commitments are supportive of this orientation, we believe at least two points are important. First, the fact that grasping the structure of a discipline is important in under-

standing and manipulating the concept of that discipline provides no illumina- tion for the conditions under which this structure is acquired. Children or adults may be unable to deal with such concepts for a variety of reasons, ranging from innate ability, to cognitive style, to stage of cognitive development. Moreover, we do not find Bruner's "hypothesis" that "any subject can be taught effectively in some intellectually honest form to any child at any stage of development" (Bruner, 1960, p. 33) self-evident, if only for the reason that it is not obvious that any idea can be plausibly represented in a form so as to render it comprehensible to any given stage of development.

Second, while it may be the case that a grasp of the central concepts of a

discipline is necessary for manipulating the detail of a discipline, it is clearly not sufficient. One thus needs to distinguish the logical power of a set of concepts (what the concepts are in principle capable of doing) from the cogni-




tive power of these concepts for a given learner (what a person can do with them). The distinction immediately raises questions concerning the empirical conditions or psychological properties which facilitate or inhibit logical power from becoming cognitive power. We suggested earlier that one task for psychology to perform vis-a-vis epistemology is to develop models of the psychological processes involved in "employing" an epistemology. The above issues seem instances of this task. The fact that such questions were not always asked by structure-of-the-disciplines curriculum developers seems to us to be a basic weakness of the enterprise.

For work related to these issues see Stone (1965), Allendoerfer (1965), Davis (1974), Hawkins (1974) and Taback (1975).

The discussion of these views on the structure of content suggests the following conclusions:

1. The inductivist theoretical context, in which much of the research on content structure has been done, tends to obscure the relations between the conceptual properties of organized bodies of knowledge and questions of instructional sequences. Thus, it subsequently obscures questions concerning the ways in which thinking in a discipline may depend on grasping its conceptual structure.

2. The concept of the structure of a discipline which treats the concepts and organization of disciplines as the conceptual equipment for thinking in the discipline is a more viable position than the view which treats general skills or concepts as constructions of more particular ones.

3. There remains a fruitful research enterprise concerning the ways in which the "logical power" of a set of concepts interacts with the abilities and limita- tions of learners in producing intellectual ability. A second area of interest concerns the most efficient organization of concepts to facilitate their attain- ment.

4. The work done on top-down curricula typically reflects the view that it is the substantive aspects of disciplines which are important in thinking within the discipline, rather than any more abstract and subject matter-neutral intellectual method.

B. Cognitive Structure

The view that subject matter should be organized according to some sorts of structural features of the discipline needs to be linked to a view of an- ticipated outcomes. Two obviously related claims are (1) that the structure of subject matter is somehow mapped in cognitive structure, and (2) that this resulting cognitive structure results, in turn, in certain cognitive capacities, such as improved problem-solving ability.

These claims pose some rather difficult conceptual, theoretical, and measurement problems. Included among these problems are:




1. What sorts of concepts are required in order to characterize cognitive structure?

2. How do these concepts differ from or relate to those necessary to characterize content structure?

3. What sorts of evidence are appropriate to verify claims concerning cognitive structure?

4. How do claims concerning content and cognitive structure relate to cognitive capacity?

We will pursue these questions by looking at three types of approaches to conceiving and characterizing cognitive structure. First, we will discuss the work of David Ausubel. Second, we will look at some recent attempts of "associative mappers," as represented in the work of Richard Shavelson. Finally, we will look at some approaches from the information-processing literature.

A usubel. The concept of cognitive structure may be most familiar to educational researchers in the form it takes in the work of David Ausubel (1963, 1964, 1968). Ausubel characterizes what he calls the psychological structure of knowledge as "an organized residue of inclusive subsumers and those elements of related subsumed materials that have managed to resist the process of memorial reduction or assimilation, plus the residual products of forgetting; namely, the original subsuming ideas which have completely assimilated their subsumed materials" (1964, p. 225).

Ausubel's notion of cognitive structure is dominated by the view that material is more readily learned when it is meaningful than when it is not. The intuitive notion of meaning here is that the material should be rendered comprehensible to the learner by relating it to his current state of knowledge. The technical explication of this concept is in terms of the notion of subsumption. Ausubel claims that there are two sorts of subsumption. Derivative subsumption occurs when the material to be learned is an example of a concept in the learner's cognitive structure or when it is derivable from a concept in the learner's cognitive structure. Although Ausubel does not say so, we can postu- late for the moment that derivative subsumption might be explicated by one or both of two sorts of logical relations: class inclusion or deduction. (We thus treat the notion that content is an example of a concept as equivalent to the claim that an object is a member of a given set, and the notion that one concept is derivable from another as equivalent to the claim that a permissible inference between propositions obtains.) On this rendering, X is subsumed under Y, when either Xis a member of set, Y, or when Xis a conclusion derivable from premises Y Correlative subsumption occurs when the meaning of learned material is an extension or elaboration of previously learned material, but the meaning of the new material is not fully contained in the existing cognitive structure. Correlative subsumption here seems to be simply partial or incom- plete derivative subsumption.




From our perspective, Ausubel's view of cognitive structure has two strong points. First, the emphasis on the import for learning of being able to form a rational connection between what one is learning and what one already knows appears to us as sound (see, however, Barnes & Clawson, 1975). It also

appears to be an important antidote to the increasingly popular mechanistic views of learning. Second, Ausubel's insistence (1964) that effective curriculum organization should attend to the current cognitive organization of the learner, as well as to the logical features of the subject matter, is an important correc- tive for the excessively a priori approach to curriculum development which we have suggested is extant in some structure-of-the-disciplines approaches. Ausubel has noted that the logical power of a set of concepts is not likely to be transformed into cognitive power for a learner who is not sufficiently cognitively mature to manage the set of concepts.

The fundamental theoretical weakness of the theory is the narrowness and vagueness of the concept of meaning. The concept of subsumption, which exhausts Ausubel's notion of meaning, is not well explicated in terms of the kinds of logical relations involved. We have suggested that subsumption may involve both the notion of class inclusion and the notion of deduction. But even this degree of precision is our construction of Ausubel's view. No attempt is made by Ausubel to render the concept more precise in terms of the extant notions of set theory or deductive logic (or any other notions), which seem to be promising tools for characterizing the precise nature of the subsumptive relationships. As a consequence, the theory is often excessively vague (subject matter contains meanings which are "nonarbitrary and substantive") or meta- phorical (subsumed material is said to be "anchored").

Subsumption is also too narrow a concept to explicate the intuitive notion of meaningfulness. In effect, the explication of meaningfulness in terms of subsumption amounts to the claim that the only ways to relate new material to old are to see the new concept as a member of a currently understood class or to see it as a conclusion derivable from a currently grasped proposition. This view seems to ignore the import of semantic and syntactical rules in explicating the notion of meaning and, indeed, it fails to appreciate that there are other options whereby the new can be related to the old. Surely, for example, one can relate new material to old by analogy or contrast as well as by subsumption. Moreover, new ideas may well be rendered meaningful by seeing that they explain known facts, solve current problems, or fulfill a variety of intellectual specifications.

We should note that there are passages in Ausubel's writing which suggest that he would regard the notion of subsumption as pliable enough to incorpo- rate many of the above examples. But, then, it seems that, in lieu of an attempt to provide precise specifications of the variety of logical relations involved in the subsumptive relationship, such an expansion of the concept would more likely produce theoretical vacuity than theoretical adequacy. In short, we find



124 Review of Research In Education, 4

Ausubel's central concept obscure. And it is obscure not just because Ausubel insists on writing in a private idiom-that is a problem in communication, not theory-but because the logical properties of the subsumptive relationship remain unspecified.

Associative Mappers. A second approach to characterizing cognitive structure (Geeslin, 1973; Geeslin & Shavelson, 1975; Johnson, 1967, 1969; Shavel- son, 1971, 1972) extends earlier efforts to map associative structures by means of word association tests (see, for example, Deese, 1962). Shavelson (1974), for example, describes a set of techniques which analyze cognitive structure and which permit comparison with the results of other methods for analyzing content structure.

The technique for describing content structure is a strategy whereby a diagram of a sentence containing two or more of the concepts of a given discipline is used to obtain a measure of the "distance" between concepts in a text. A set of rules is employed for turning a sentence diagram into a directed graph (or "digraph"), in which the structure of the basic concepts in a sentence is represented by a set of lines connecting the concepts. The distance between two concepts is the number of lines in the shortest path connecting them. The conceptual structure of a text concerning a given subject matter can then be represented in a "super digraph distance matrix," which in turn can be rendered as a hierarchical arrangement of the text's concepts.

In Shavelson's research cognitive structure is characterized by three techniques: (1) a word association test, in which (for mathematics) subjects are asked to think like mathematicians and write down words which are related to cer' .iin mathematical concepts; (2) a card-sorting test, in which concepts are sorte& into piles labeled similar and dissimilar; and (3) a graph-building test, in which subjects are asked to connect similar concepts by lines. All three techniques allow the development of proximity measures between key concepts. The results of the three techniques for assessing cognitive structure are thus cast in a form which allows them to be compared with the analysis of content structure.

Shavelson's basic hypothesis about these measures is:

If the three measures of cognitive structure tap similar significant aspects of the organization of key concepts in the curriculum developers' (subjects') memories, the representations of cognitive structure obtained with each measurement method should be quite similar to each other and should correspond closely with the representations of content structure. ...

Shavelson's data indicate that for a set of subjects working with a set of mathematical concepts, significant similarities of these sorts do in fact occur. He concludes that "meaningful representations of structure can be obtained"




(1974, p. 120) and that "such measurement methods might be used to evaluate the extent to which a curriculum communicates the structure it has been developed to communicate" (1974, p. 120).

However ingenious Shavelson's techniques are, there is a problem in using associationist or quasi-associationist techniques to study cognitive structure, especially when cognitive structure is supposed to result from learning content structure. This problem is suggested by the cryptic remark by Deese (1962) that associative meaning is not logical, for the structure of a discipline, if it is anything, is logical. The essence of the structure-of-the-disciplines movement is that a discipline is more than a body of accepted propositions. A discipline is also comprised of a set of concepts and logical structures which enable the learner who has acquired these to employ the discipline in thought. Bruner puts the point nicely, noting that:

. . . the tools of the mind are not only certain kinds of response patterns, but also organized, powerful concepts that come out of the field he is studying. There is no such thing, to be sure, as the psychology of arithmetic, but the great concepts of arithmetic are part of the tool kit for thinking (1971, pp. 71-72).

These observations suggest that two kinds of constraints ought to be applied on properties of a discipline picked out as important structural properties. First, these structural features ought to be something which would be recognized as significant and essential features of the conceptual organization of a discipline, something which, if altered, would change the nature of the discipline in an important way. Second, the structural features identified ought to be part of the conceptual equipment requisite for the performance of some intellectual task. That is, there should be some prima facie evidence that learning the particular structure will increase the learner's intellectual power.

Shavelson gives no reason to suggest that the method for specifying content structure specifies any structural property of a body of knowledge which is of any conceptual interest from the perspective of that subject matter or which adds to the intellectual power of the learner. Indeed, it is not at all obvious what sort of thing is picked out by Shavelson's measures. When we have mapped out this sort of concept hierarchy, what is it that we know about the concepts or the relation between the concepts in the hierarchy? First, it is not clear what we are mapping the structure of. Is it a text, the memory of the author of the text, a discipline, or all three at once? And, if we are not in some way mapping a discipline, why should we be interested in the enterprise? Further, what sort of property is the distance between concepts? Shavelson (1974) indicates that distance has to do with how concepts are defined. Why the definitional structure of a text or a subject matter is important is not clear. The question needs attention.




Information-Processing Theory. Another approach to describing cognitive structure is that of artificial intelligence and information-processing theory. This type of research, while often remote from the concerns of educators, is included because it exhibits what we believe to be an adequate conception of cognitive structure. Thus, it offers promise of future exploitation by educational researchers.

Newell (1973) states some of the assumptions of the enterprise:

. .. the important organizing notion is that of an information-processing system, not that of an artificial intelligence system .. . Programs. . . are created as psychological theories, not to demonstrate that at least some mechanism can do the task. Thus, the whole study of information-processing systems constitutes theoretical psychology-if one views man as such a system. (p. 42, italics added)

While we believe that the claim that information-processing systems (IPS) constitute theoretical psychology is too strong, much of the artificial intelligence literature, especially when concerned with notions such as the structure of belief systems or problem solving, is noteworthy in several respects. First, our view of the relations between epistemology and psychology is supported, in that a grasp of the conceptual structures of ideological systems or problem- solving contexts (content structure) is prerequisite for producing successful programs which stimulate behavior. If a program is a model of cognitive structure, the implication is that the concepts necessary to describe cognitive structure are much the same as those necessary to describe content structure. It is noteworthy that simulation in most areas (chess, for example) is as much a matter of understanding the properties of the subject matter as it is a matter of studying behavior.

These points are nicely illustrated in the work done on modeling belief systems. We will look at two examples. The first concerns the nature of neurotic belief systems (Colby, 1973), and the second concerns political belief systems (Abelson, 1973). (Neurotic and political belief systems do have substantive content reflected in a cognitive structure. They are not, of course, organized bodies of knowledge. The argument is, thus, an argument by analogy.)

Both types of work treat a belief as an affirmation of a proposition (Colby uses the term conceptualization). A belief system is understood as a set (or repertoire) of propositions concerning a given topic or area which are interconnected or interrelated by an inference structure. To successfully simulate a belief system, it is necessary to solve a set of problems concerned with a program's ability to generate a wide enough range of well-formed and appropriate responses to an adequate variety of inputs. But the heart of simulation is to characterize the inference system which leads a person to respond to input in a way which allows him to be recognized as, for example, paranoid or as




a "true believer." In both sorts of enterprises attempts at simulation can be looked at as involving the particularization of a theory of the general sorts of cognitive processes which characterize a person of a given type. Colby describes part of the theory of paranoia which underlies one attempt at simulation:

S. . a paranoid Self is differentially sensitive to terms which refer to concepts of self-concerns and self-worth. It is also sensitive to terms pointing to "flare" concepts, i.e., concepts related at various conceptual-semantic distances, to the concepts in a delusional network. Expressions which touch on flare concepts in turn tend to activate the delusional network. (1973, p. 267)

A particular program must, of course, have a particular delusional network (e.g., the belief one is being watched by the Mafia). Colby thus characterizes part of a particular paranoid "inference structure" as follows:

The process of checking for and responding to a flare concept involves (a) a quantitative hierarchy of eleven concepts, weighted again as part of initial conditions in order of their relevance to the model's fears concerning the Mafia and (b) a direction graph in which each flare concept points to another flare concept as part of a strategy designed to lead the interviewer along paths to the topic of the Mafia. (Thus, for example, horses - horse racing --+ gambling -- bookies -- underworld -- Mafia.) (1973, pp. 273, 274)

Insofar as a particular program is an instance of a theory of paranoia, a successful simulation (success is understood as the ability to generate a set of responses which would be classified by experts as paranoid) is both the description of part of the cognitive organization of a particular (hypothetical) paranoid person and confirming evidence of a general theory of the structure of paranoia which the program instantiates.

Abelson (1973) provides a description of his attempts to simulate the belief structure of a "true believer" in right-wing politics. The structure of a belief system here is constructed as a set of levels of increasing complexity and a set of rules by which structures at a given level are combined to yield structures at a higher level. The levels are labeled Elements, Atoms, Molecules, Plans, Themes, and Scripts. These levels, in effect, pass from the belief system's lexicon (elements) to scenarios which map characteristic responses to the features of a type of political happening (e.g., a "Cold War Script").

These various levels can to some degree be thought of as "formation rules" for organizing or inspecting belief systems. Lower levels develop a general abstract system for conceptualizing human actions and interactions, indicating, for example, the structural relations in which purposes can stand to actions. Higher levels describe typical patterns of interaction. One Theme, for example, alienation, is characterized, "Actor F is a negative interested party to one or more goals of E, and wants to prevent them, but has no means of




so doing" (Abelson, 1973, p. 322). Themes, in turn, may be combined into Scripts of varying degrees of complexity, the more complex of which describe standard or permissible sequences of events for various political agents or entities and which correspond roughly to an ideology. Part of the "Cold War Script" goes: "There is a great struggle taking place between the Free World and the forces of Communism, which the Communists fully expect to pursue until they control the world. Liberal and left wing dupes who dominate many Free World governments are playing into the hands of Communist designs" (Abelson, 1973, p. 331; symbols omitted).

A belief system of this sort operates essentially by search procedures conducted at various levels. "The system shifts back and forth between levels, either looking for something that fits a specification, or for a specification that fits a something" (Abelson, 1973, p. 338). For example, particular political happenings must be organized by an individual who ascribes to the appropriate political ideology into a pattern which reflects or is consistent with the "Cold War Script." The system thus generates descriptions of events which are "well formed" at several levels, ranging from the basic organization of action to complex ideologies.

A further noteworthy implication of some recent work in information processing is that insofar as a view of intellectual method is concerned, the evidence does not support the notion of a general intellectual method. The concepts necessary for problem solving in a given area tend to be specific to that area. This is implicit in the work on belief systems and is nicely illustrated in recent work by Newell and Simon (1972) on problem solving in logic, cryptarithmetic, and chess. They summarize their work in four conclusions (pp. 788, 789).

1. A few, and only a few, gross characteristics of the human IPS are invariant over task and problem solver.

2. These characteristics are sufficient to determine that a task environment is represented (in the IPS) as a problem space, and that problem solving takes place in a problem space.

3. The structure of the task environment determines the possible structure of the problem space.

4. The structure of the problem space determines the programs that can be used for problem solving.

The discussion of these various approaches to cognitive structure suggests the following conclusions:

1. The notion of cognitive structure is central to educational research on learning subject matter, in that a coherent view of cognitive structure is necessary in order to understand what is learned, how it is learned, and what can be done cognitively with what is learned.




2. The approaches to cognitive structure we have reviewed do not exhibit a successful integration of conception, measurement, and practical concerns. Ausubel's account has considerable intuitive appeal, but the central concepts are obscure. Shavelson has devised some ingenious measures of cognitive structure which may prove fruitful, yet it is unclear precisely what the measures are measures of, or why we should be interested in measuring whatever is measured. The information-processing models reviewed seem to exhibit the most adequate conception of what cognitive structure is, but they are at the same time most remote from the direct concerns of educators.

3. An adequate view of cognitive structure should do at least three things. First, it should provide a coherent account of the relations between the conceptual features of subject matter and the representation of subject matter in cognitive structure. Second, it should account for the role of what is already known in the learning of new material. And, third, it should account for the intellectual capacity of people who have learned a given subject matter.

4. In our view, the key to success in each of these three criteria is the first. A view of cognitive structure capable of making sense of various cognitive operations must treat cognitive structure as a representation or embodiment of the conceptual features of the subject matter.

5. The range of concepts necessary to describe cognitive structure will thus be as diverse as the range of concepts necessary to describe the organization and manipulation of diverse bodies of subject matter. Work in several areas suggests that this task will require considerable conceptual diversity.

6. Finally, we must note that if the complexity of describing and measuring cognitive structure is grasped, the futility of attempts to describe educational goals involving cognitive structure in a behavioral language becomes clearer.

C. The Conceptualization of Thinking The previous section should have made it clear that the questions concern-

ing how cognitive organization can be described and how thinking can be described are virtually the same question. It follows that the separation of the discussion of cognitive structure from that of thinking is a function of organi- zational convenience rather than being attributable to a significant difference in topic. The questions in this section are much the same as in the last. They concern the sorts of concepts necessary for describing the cognitive processes involved in thinking. Here we will pursue two more aspects of this investigation, however. First, we will look at some classical treatments of thinking from an associationist perspective. Second, we will look at some work on discovery learning and teaching.

Associationist Views. The discussion of associationist views of thinking will be organized around a problem. The discussion to this point has suggested that thinking is something that is done with concepts or rules. Assuming such a view of thinking provides a prima facie challenge to the very possibility of




a coherent associationist view of thinking, for two reasons. First, a standard methodological commitment of orthodox associationist views is peripheralism (Strike, 1974a). Psychological laws are supposed to connect intersubjectively observable events, and this is often held to exclude psychology from dealing with the black box of the mind. Cognitive models, of course, deal with the insides of the black box. Second, the notion of an association is the basic mechanism of behavioral production for the associationist, and associations and cognitive acts appear to be different and incompatible explanatory mechanisms. Thus, associationist psychologies have a significant problem to solve in conceptualizing thinking. The phenomenon of thinking seems to require a theory employing rules and concepts, but associationist views seem to preclude such concepts. The question concerning associationist views of thinking is, then: How can an associationist theory accommodate the nature of the phenomenon? For illustrative purposes, we will treat a subset of this question. Formal reasoning (e.g., theorem proving in the propositional calculus) requires the recognition of the logical form of propositions and the manipulation of these propositions according to formal rules of inference. Concerning formal reasoning our question thus becomes: How can an associationist theory accommodate logical form?

There appear to be three types of responses to such a problem. First, the phenomenon of thinking can be reconceptualized so as to avoid having to characterize it in rule-following terms. Second, logical form can be treated as properties of stimuli and behavior. Rule-following acts then are replaced by associations between stimuli and responses of the requisite type. Third, one can construct associationist analogs of rule-following activity.

Maltzman (1965) provides a paradigm of the first view. The theory is presented as a theory of problem solving, and Maltzman explicates it by means of an extension of Hull's theory of a family habit hierarchy. The keys to this theory are the concepts of divergent and convergent mechanisms. A divergent mechanism is one in which a particular stimulus has varying tendencies to elicit alternative responses. That is, more than one response has been conditioned to a single stimulus. These responses may be ranked in a hierarchy on the assumption that the strength of the conditioned responses differ so that there is an order of dominance among the responses. A convergent mechanism is similarly one in which alternative stimuli have varying tendencies to elicit the same response. Divergent and convergent mechanisms can become linked together to provide "a family hierarchy," and several family hierarchies can be combined to produce "a compound family hierarchy." It will be sufficient for our purposes to think of a compound family hierarchy as a set of habit chains arranged in some order of dominance. Problem solving or thinking can then be described in terms of the way in which the order of dominance among these chains changes. Maltzman provides the following account of the concepts of productive and reproductive thinking:




The occurrence of reproductive thinking in situations where only a single problem is presented is also the consequence of the factors outlined. As a result of past training the dominant habit family in the compound hierarchy contains the correct response. Solution of the given problem depends upon extinction of the initially dominant incorrect responses within this one hierarchy. In productive thinking, on the other hand, a habit family initially low in the compound hierarchy must become dominant before a correct solution can be attained. This occurs as the result of the extinction of the dominant incorrect response hierarchies. Once the appropriate habit family is dominant a solution will occur, provided that the correct responses within that hierarchy in turn become dominant. (1965, pp. 572-573)

The question to ask concerning this view is whether it is, in fact, a view of thinking in any sense of thinking which relates to human reasoning. The notion of a solution to a problem is understood as ant action which alters a situation, rather than the assertion of the truth of a proposition. The theory as it stands provides no way to talk about judgments of truth or falsity or processes of weighing evidence. Therefore, however plausible Maltzman's account may be as an account of problem solving, it is not a plausible account of thinking in the sense of thinking which relates to reasoning. The question of logical form is thus avoided.

Skinner (1953, 1957) at times seems to hold the view that logical form is a stimulus property. The following are illustrative remarks:

S. . the logical syllogism is a way of arranging stimuli. The logician possesses a verbal repertoire in which certain conclusions are likely to be made upon the statement of certain premises. . . . (1953, p. 250)

The logical and scientific community also sharpens and restricts verbal behavior in response to verbal stimuli. (1957, p. 420)

In engaging in verbal behavior which is logical and scientific the speaker slowly acquires skeletal intraverbal sequences which combine with responses to a given occa- sion. (1957, p. 422)

Skinner's view has the merit of being, in fact, about thinking, since it does take account of the existence of logical rules. Moreover, by putting logical form into the stimuli, the theory appears to handle logical form in a way consistent with both peripheralism and associationism. A difficulty, however, is that the theory seems to merely transfer many of the difficulties in developing a behaviorist account of reasoning into difficulties for a behaviorist account of perception. How exactly does one see logical form? Logical form is not exactly a property like red. Indeed, if one considers what are the empirical properties by means of which one would recognize the logical form of a set of propositions, the complexity of the processes by which one learns to recognize logical form should become obvious. Thus, the ploy of treating logical form as an




aspect of stimuli does not appear to remove the need for centralist accounts or information-processing systems as much as it transfers the theoretical pres- sure for such accounts to the psychology of perception.

Berlyne (1965) provides an instance of the third view. Reasoning is ex-

plicated by means of a series of levels of complexity of S-R bonds. The flavor of the theory may be obtained by characterizing the third and the sixth levels. The third level, symbolization, occurs when external S-R bonds become replaced by internal S-R bonds which are links between fractional responses (subvocal or perceptual) and which can, in turn, become linked together in longer internal chains. These represent symbol sequences. The sixth level, ratiocination, occurs when the organism has learned to perform "only such symbol sequences as fulfill certain conditions ('rules of logic') which are necessary to insure their stability and consistency" (Berlyne, 1965, p. 53).

Berlyne's view, like Skinner's, has the merit of adequately grasping the importance of the notion of rules and logical form for explicating the phenomenon of thinking. Here too the adequacy of the construction of the theory can be doubted. (It is not clear, for example, how chains of fractional responses could be consistent or inconsistent or accord with or violate rules of logic.) However, Berlyne's treatment of reasoning abandons the two features which we have suggested as central to associationism. Peripheralism is abandoned in the third level, where a class of theoretical and unobserved (unobservable?) entities is postulated. The box does not become less black by putting little S's and R's into it. Associationism is abandoned in the sixth level, where the symbol sequences are treated as the expression of rules rather than associations. Berlyne may have intended that we view these symbol sequences as in accord with rules rather than rule following (see Melden, 1961, for the distinction). However, this view is implausible in that it is virtually impossible to see how a person could produce a series of symbols in accord with logical rules without being engaged in following those rules. In short, Berlyne's theory contains only vestigial remains of the central commitments of an associationist viewpoint, and these remains appear to be a theoretical liability rather than an asset in constructing a theory of reasoning.

Thus it appears that none of the associationist views inspected provides viable approaches to the phenomena of thinking. The particular sorts of defi- ciencies exhibited suggest that theories only approach an adequate conception of the nature of thought by abandoning, explicitly or indirectly, central associationist commitments. (An expanded version of this line of argument can be found in Strike, 1974a.)

Educational enterprises involving a conception of thinking constructed on associationist assumptions are few, and where they exist the actual connection between the concept of thought exhibited or implied and the associationist background is tenuous. The approaches are often better considered as eclectic. Gagn6 (1970) weds thinking to an associationist hierarchy of skills without




benefit of argument. The curricular progeny of this view of learning often present plausible characterizations of thinking skills, but, as suggested, the legitimacy of the underlying theoretical structure is at best suspect. Likewise, the Bereiter and Englemann (1966) program to teach thinking to disadvantaged children is often thought to be rooted in associationist assumptions. Yet the skills the program intends to teach are very nearly the transformation and quantification rules of propositional logic. There is no reason to assume that whatever associationist assumptions the authors may have are reflected in or reflectable in the concept of thought exhibited. The "associationist" literature in education thus offers some reasonable conceptualizations of some thinking skills, but it provides little reason to believe that these concepts are or can be firmly rooted in associationist theory.

Discovery Learning. Perhaps the most common observation in recent re- views of discovery learning (Strike, 1975; Wittrock, 1966) is that it is far from clear what discovery learning is. Here we propose a twofold classification of the literature on discovery learning which we hope has the dual virtues of not being overly arbitrary and of shedding some light on the connection between discovery learning and thinking.

The first group of literature we shall term "concept formation" studies. Here the task is typically formulated as the learning of some principle or generalization. The procedure often entails contrasting the effects of a teaching method in which the subjects are told the principle or generalization with those of a method whereby they are expected to "discover" the principle or generalization inductively by being presented with a number of instances which exhibit it. More sophisticated studies often manage to compare several degrees of variation concerning the information given about the principle or generalization to be learned. The dependent variables in such studies are normally retention and transfer. Perhaps because mathematics tends to have a handy variety of clear-cut principles which bear nicely comprehensible relations to their instances, most of these studies focus on the teaching of mathematical concepts. After reviewing a number of older studies of this type-for example, McConnell (1934), Katona (1940), Swenson (1949), and Anderson (1949)-Scott and Frazer (1970) observe:

The general, though by no means universal, finding of these studies appears to be that discovery methods are not superior to rote or drill methods when the criteria is immediate learning or short-term retention, but become superior when the criterion is either long-term retention or transfer. (p. 15)

They add that when variations in amounts of guidance and verbalization are introduced, "complex interactions between stimuli and as yet undeter- mined variables appear to occur" (p. 24). Studies later than those reviewed by Scott and Frazer (for example, Worthen, 1968) are often more sophis-




ticated, but they exhibit similar conceptual properties and roughly comparable results.

Concerning this body of literature, a number of properties are of interest. First, it is normally assumed that the student does not know the generalizations to be acquired, but the generalization is exhibited in and can be obtained rather directly from the instances. Thus, these studies tend to be inductivist, although they are inductivist in a way which is more reminiscent of Aris- totelian induction than induction as described by the British empiricism of the past two centuries. (See Strike, 1975, for the distinction.) Second, these studies tend to make the primary task of the subjects the formulation or conceiving of the generalization involved. Moreover, rarely is the student expected to provide any evidence to suggest that the generalizations formulated are true. These studies thus tend to understand discovery as "conceiving that p" rather than "find out p to be the case." (Strike, 1975, argues that the second of these two senses of discover is the basic one, although he would not infer that studies oriented to conceiving are noxious as much as that they might be better called something else other than discovery.) Perhaps one reason this distinction appears not to have been attended to in the literature is the focus of so many of these studies on mathematics, where to formulate a principle is often to "see" that it is true. Some mathematical propositions have the property of self-evidence. Conceiving and verifying are thus sometimes less distinct in mathematics than is the case in empirical enterprises.

The second orientation to discovery learning is best expressed by Jerome Bruner:

It is my hunch that it is only through the exercise of problem solving and the effort of discovery that one learns the working heuristics of discovery, and the more one has practice, the more likely is one to generalize what one has learned into a style of problem solving or inquiry that serves for any kind of task one may encounter-or almost any kind of task. (1965, p. 618)

We shall call this the "practice makes perfect" view. The view can plausibly be said to be exhibited in educational theories of many progressive educators (Dewey, 1916, 1933; Kilpatrick, 1951), as well as more recent authors like Suchman (1961). This view suggests that in a given instance of discovery learning there are two sorts of things to be learned, not one. The first is the generalization or principle to be discovered; the second is the method of discovery. The practice-makes-perfect orientation implies that learning the methods of discovery is the paramount objective. Thus, the thing to be discovered is not the central thing to be learned.

Second, the proposal that students learn how to discover suggests the relevance of epistemology to specifying what students are supposed to learn. Insofar as it is the task of epistemology to describe what counts as rational




procedure, epistemology is the general theory of discovery. Thus, it is necessary to have an epistemology to decide what kinds of skills a person who is learning by discovery is supposed to be learning. One has merely to contrast the views of Plato (in Meno, 1949; Republic, 1945; and Theatetus, 1957) and Dewey (1916, 1933) on the nature of discovery learning to see the effects of different epistemologies on the conception of discovery skills. For Plato, a sort of rationalist armed with a doctrine of innate ideas, discovery is a dialectical process intended to enable a person to formulate explicitly what he already knows implicitly. For Dewey, learning by discovery is a matter of proceeding according to the scientific method. The difference in skills to be learned is a difference in epistemological theory.

In a similar way, epistemological assumptions are likely to dominate teaching strategy. The concept of acquiring discovery skills by practice suggests a process whereby a skill which is already possessed in a rudimentary form is perfected by employing that skill. The teacher's task, then, is to arrange the environment so that the appropriate skills can be employed in a meaningful way. This view of discovery learning treats discovery learning as a means whereby people are taught how to think. What counts as thinking skills and what counts as a context for practicing them are largely epistemological issues.

Given our concerns in this paper, the most problematic part of the practice- makes-perfect view is the assumption that there is a generalizable style of problem solving. Much of the literature on discovery learning-Dewey (1916) is paradigmatic-seems committed to two interconnected views. The first is that there is a single intellectual method common to all intellectual endeavors. If this is not the case, then there is not a general style of problem solving which can be taught; there are only styles of problem solving. No one set of discovery skills should be expected to transfer to problems of a markedly different sort. The second view is that the method appropriate to a given domain can be readily distinguished from the content of that domain. A challenge to this view is, we believe, more serious than a challenge to the first one. A plurality of intellectual methods implies restrictions on the extent of transfer which should be expected from any effort at "inquiry training." It does not necessarily challenge the basic assumption that practice makes perfect. But if the method of an intellectual domain cannot be effectively distinguished from the content of the domain, the practice-makes-perfect hypothesis must be reformulated in some way so as to relate it to a theory concerning the relations between the acquisition of concepts and propositional knowledge and the acquisition of intellectual skills. Acquiring intellectual skills, in this view, is not like acquiring psychomotor skills. One has to know that as well as to know how in order to acquire intellectual skill, and this strongly suggests that practice is not a sufficient account of the process of acquiring intellectual skills. This problem has been discussed by philosophers of education (Scheffler, 1965), but to our knowledge it has not been explicitly treated in an empirical context.



136 Review of Research In Education, 4

These questions about the practice-makes-perfect view of discovery learning are, of course, essentially the issues concerning the viability of formal and external epistemologies rephrased in a context concerned with teaching. The moral is, perhaps, that this dispute will have immediate relevance to any educational endeavor which desires to teach someone how to think.

The discussion of associationist views of thinking and of discovery learning generates conclusions analogous to several of the conclusions in the preceding discussion of structure:

1. It seems necessary, in describing thinking, to employ those concepts needed to characterize the manipulation of the concepts and propositions of subject matter. Mechanistic accounts of thinking which do not use such concepts are not viable.

2. The range and sort of concepts necessary is a function of the conceptual diversity necessary to describe the methods of dealing with various disciplines.

CONCLUSIONS

We can hardly claim at this point to have adequately surveyed the major points of contact between epistemology and educational research. One we have largely ignored is the area of cognitive development and genetic epistemology, in which fruitful contact has been made between philosophers and psychologists (Mischel, 1971). A second area is the emerging literature on cognitive style and individual differences.

Our efforts herein have been organized around two basic themes. The first concerns the relations between epistemology and psychology. We have suggested that, at least in some cases, cognitive states and processes can be regarded as the "embodiments" of the kinds of logical and conceptual features which characterize organized bodies of propositions. Thus, the sorts of concepts used to describe the structure of content and the nature of inferences are important in developing a sophisticated and precise descriptive vocabulary for talking about cognitive structure and cognitive operations. This view seems to be important in formulating the nature of the relations between educational content and its cognitive effects, in developing a view concerning how certain educational objectives should be described, and, thus, for developing a theoretical framework in terms of which a technology for measuring objectives can be developed.

Our view here also leads us to a healthy suspicion of approaches to research which tend to replace these kinds of descriptions with more mechanistic ones. In particular, we believe that inductivist and associationistic research orientations reflect epistemological assumptions which have been rendered quite dubi- ous by much of the recent research, and pure associationistic views are sufficiently at odds with current views in epistemology to make it difficult to take both seriously. It is, of course, clear by now where our sympathies lie. We are




thus concerned about the increasing popularity of associationist-rooted enter-

prises among educators, because associationist views lead to a problematic orientation both to questions concerning the nature and organization of content and to questions concerning the nature of cognition and the language in which educational objectives should be formulated. We believe history will judge many contemporary educators to have boarded an intellectually sinking ship.

Our second major theme concerns the particular epistemological orientation to be taken in considering content structure and, pursuantly, cognitive states and processes. We have suggested that some recent views can be arranged on a kind of continuum according to their opinions on the nature of basic standards of intellectual judgment, where one pole of the continuum emphasizes standards which are formal and external to the content of any discipline and the other pole emphasizes standards which are substantive and internal to content. We have not sought here to stake out a firm position on this issue, although our preferences are for a moderate position of the sort represented by Lakatos. The outcome of these debates, however, is important to such questions as how one construes the organization of the content of disciplines and the view one takes of the nature of thinking. Thus it is also important in considering theories dealing with the teaching and learning of disciplinary content or good habits of thought.

A final point, not much discussed but hopefully exhibited in this paper, is that many philosophers and psychologists have been moving toward conceptions of their disciplines and tasks which make possible a fruitful sort of interaction which has the potential to shed light on important educational concerns.

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