Robert G. Fuller
ADAPT Program Director and Professor of Physics
University of Nebraska-Lincoln
rfuller@unlinfo.unl.edu
www.physics.unl.edu/research/rpeg/rpeg.html

The long haul

The fall of 1976 began with several important changes in the ADAPT program. All of us who had been involved in the instructional aspects of the program felt very encouraged by the intellectual growth of the students, as compared to students we had taught in typical courses. Our feelings had been supported by the evaluation studies. We knew that many of the lessons we had tried had not worked as well in promoting the growth of the students as we had hoped. But we knew how to change those lessons to make them better serve the end of encouraging the use of formal thought by the students. We had all received positive feedback from some aspects of the performances of the students. We had developed a weekly ADAPT faculty lunch meeting to share our lesson ideas and to discuss various aspects of student performance.

The end of the first year of the ADAPT program brought us into close contact with several stark realities of faculty life at large research institutions of higher education in the USA in the 1970s.

1. All six of us teaching in the ADAPT program in 1975-76 received below average pay raises in our departments for the 1976-77 academic year, even though several of us had already received distinguished teaching awards from the University.

2. We had excellent data showing the power of the Karplus learning cycle method in encouraging college students to develop more mature reasoning patterns. Yet few other faculty at UNL were beating on our office doors wanting to know how we did it. In addition most of the ADAPT students returned to UNL for their second year of college. So not only had the ADAPT program showed a way to improve student learning, but, I believed, the attrition rate of students could be significantly lowered by using ADAPT methods for freshmen classes.

3. An excellent way to share the ADAPT values was through faculty development workshops. Our first workshop in March of 1975 had been quite a challenge and was nearly defeated by a spring snow storm in Nebraska. Nevertheless, it had been successfully completed and drew faculty from nearby institutions.

We decided that perhaps one reason why the ADAPT door had not been beaten down by other faculty was that they did not believe strictly Piagetian measures, since those were largely unknown outside of the Piagetian community. What we needed was a nationally normed measure that would be taken seriously by our faculty colleagues who knew almost nothing about Piaget. So Carol Tomlinson-Keasey suggested that we use the Watson Glaser Critical Thinking Appraisal as a pre/post test measure for the second year, in additional to the Piagetian measures. This we did.

We also realized that we had learned many things about teaching from a Piagetian-perspective. We needed to share these learnings with other faculty members. We put together a collection of essays and published them as a book, ADAPT-A Piagetian-based Program for College Freshmen, University of Nebraska-Lincoln(1976). I have included the Table of Contents of that book to give you an idea of the topics we included(see Figure 1).

It seems appropriate for me to conclude this part of the ADAPT history with a quote for the epilogue I wrote for that book:

"In summary, there are two necessary conditions for beginning an ADAPT-like program, a first-rate, tenured core of faculty and a common basis in a scheme for understanding student development. Are these conditions sufficient to assure the long life of pioneer ADAPT-type programs in the frontiers of higher education? If information about ADAPT-type programs is widely shared, then in a few years perhaps an answer can be given to this question."

The academic year of 1976-77 brought some important changes to the ADAPT program. I received an invitation to join Robert Karplus at the University of California, Berkeley for the academic year. Mel Thornton, a mathematics professor, took over the direction of the ADAPT program. Betty Windham, a physics faculty member from William Rainey Harper Community College in Palatine, Illinois, took my place on the ADAPT faculty.

Professor Karplus offered us two opportunities for national exposure. First, he had a standing invitation from the largest circulation physics journal, Physics Today, for an article about his work. I was given the opportunity to write that article and be its senior author. That article, "Can Physics Develop Reasoning?" (Fuller, et. al., 1977) enabled us to get the concepts of Piaget into the language of the physics community. We could give presentations at physics meetings about concrete and formal thought and the process of self-regulation without embarrassment. Second, Professor Karplus had received an invitation from the AAAS-NSF Chautauqua program to lead some short courses for them. He nominated ADAPT for that program and Mel Thornton and I began a stint with the AAAS-NSF Chautauqua program offering "College Science Teaching and the Development of Reasoning" workshops at various Chautauqua centers for the next three years. We offered this workshop in the Midwest, West, and East regions, from 1977 until 1980, at ten different regional centers, for a total of about 240 science faculty members. These workshops featured active learning by the participants dealing with two fundamental aspects of Piaget's work, the concept of stages of development and the process of self-regulation. These workshops were a modification of the ADAPT workshop which, in turn, was based upon the workshop on Physics Teaching and the Development of Reasoning that Karplus, et. al. had developed for the American Association of Physics Teachers (AAPT) in 1975. The Karplus workshop was supported by the AAPT and was distributed nationally for the next few years. The Chautauqua courses taught by Mel Thornton and me gave the ADAPT program a national audience and the program began to receive offers from other institutions to lead workshops for their faculty members.

ADAPT was flying high nationally by the fall of 1978. The faculty were seeing success in the growth of their own students and they were having chances to go as experts to other campuses. The workshops offered on the UNL campus were beginning to bring other faculty members into the ADAPT tent, especially from the English and Anthropology departments. The initial core groups was joined by James McShane and Robert Bergstrom in English and Dani Weinberg in Anthropology. We took turns leading workshops at other institutions. We conducted over 100 workshops for the next decade. The height of attention to the ADAPT program was probably reached when the Chronicle of Higher Education ran a special article on the influence of Piaget on college programs when he died in 1980.

David Moshman
University of Nebraska-Lincoln

When I joined the faculty of the UNL Educational Psychology department in August 1977, I replaced Carol Tomlinson-Keasey, who had been among the founders of the ADAPT program. Although no one ever mistook me for Carol, we were in many ways quite similar. Both of us had interests at the intersection of developmental, cognitive, and educational psychology, both of us were Piagetian in our general theoretical perspective, and both of us had done research on the development of formal operational reasoning. It was thus natural that I replaced Carol not only within my department but as what Bob Fuller often called the "guru" of the ADAPT program.

Coming to UNL, I was delighted to find myself on a campus where faculty in a variety of departments and disciplines were knowledgeable about Piaget's theory of formal operations and devoted to fostering formal operational reasoning. I was even more surprised and delighted to find that the educational efforts of the ADAPT faculty were firmly rooted in the constructivist epistemology that lies at the heart of Piaget's theory. Let me explain why a constructivist approach to education is, in my view, the main legacy of the ADAPT program.

Do advanced forms of reasoning emerge from our genes or are they learned from our environments? This initially seems a reasonable question, but it turns out to be deeply misleading. The question is a special case of the nature vs. nurture question that has historically been central to the study of psychological development. Psychologists who stress genetic determination are known as nativists; those who stress learning from the environment are known as empiricists. With regard to advanced reasoning, a nativist might construe formal operations as a structure of reasoning that is programmed to emerge in early adolescence in all normal human beings in all normal human environments. An empiricist, in contrast, might construe formal operations as a set of thinking skills to be taught and learned.

Contemporary psychologists recognize that both genes and environments play important roles in development and that the effects of each depend on the other. Thus it is misleading to set them against each other and force a theoretical choice between them. This suggests an interactionist view of the development of formal operations. It might be argued, for example, that formal operational reasoning is a set of thinking skills that must be learned from one's environment, as an empiricist would suggest, but that such learning can only take place after one has reached the necessary level in a genetically-directed process of maturation.

Although interactionism recognizes the importance of both genes and environment, Piaget believed that an interactionist view is not sufficient to explain development. What is missing, he argued, is the active role of the individual. New forms of reasoning, in his view, are constructed by the individual through processes of reflection and coordination. Constructivism does not deny that the human genome makes it possible for human beings to construct advanced forms of reasoning that cannot be constructed by members of other species. It insists, however, that advanced forms of reasoning are not programmed in the genes, waiting to emerge when the time is right. Similarly, constructivism does not deny that some environments encourage and support the construction of advanced forms of reasoning, whereas others do not, nor does it deny the critical role of social interaction in such construction. Constructivism insists, however, that advanced forms of reasoning are not simply internalized from our physical and social environments.

In the period since ADAPT was founded, psychological research has raised serious questions about Piaget's stages of cognitive development. With respect to the stage of formal operations (Inhelder & Piaget, 1958), it appears that the theory fails to address many important forms of advanced cognition, especially those that transcend formal logic (Moshman, 1998, 1999). During this same period, however, constructivist views have flourished both as explanations of psychological development and as approaches to education (Moshman, 1998, 1999; Phillips, 1997).

If the ADAPT faculty had taken a nativist perspective on formal operations, there probably would never have been an ADAPT program. They would simply have accepted that college students develop as their genes direct. If the ADAPT faculty had taken an empiricist perspective on formal operations, they might have devoted themselves to teaching the specific formal thinking skills that Piaget discussed. Appreciating the significance of Piaget's constructivist epistemology, however, the ADAPT faculty have formulated creative educational strategies that encourage students to construct new forms of reasoning, probably including forms of reasoning that go far beyond Piaget's conception of formal operations.

In its systematically constructivist approach, ADAPT highlighted what has turned out to be the most enduring aspect of Piaget's theory. In this respect it was a program ahead of its time. Over the course of ADAPT's history, and in part through the efforts of the ADAPT faculty, constructivism became part of the educational mainstream.

Orlando Lourenço University of Lisbon, Portugal

Armando Machado Indiana University, USA

The reader probably remembers that in 1996, Alan Sokal, professor of physics at New York University, submitted a paper titled "Transgressing the boundaries: toward a transformative hermeneutics of quantum gravity" to Social Text, an American cultural-studies journal. Although the paper contained chock-full absurdities and obvious non-sequiturs, it was readily accepted and published. When the hoax was finally revealed it provoked a firestorm of reaction in both the popular and academic presses.

We could not help but remember this story when we read Grobecker's article "Redefining mathematics 'disabilities'" recently published in The Genetic Epistemologist (1998, Vol. 26, #4, pp. 1-10). In the paper, Grobecker argues for a constructivistic, Piagetian approach to mathematics disabilities in place of the dominant, information-processing approach. Using a Piagetian, logical-mathematical task, the fish task (Piaget, Grize, Szeminska, & Bang, 1977), Grobecker presents some data on the development of logical-mathematical structures in children with and without learning disabilities in mathematics, and then concludes that "to adequately address the real complexity of learning problems, the field of special education needs to reassess what constitutes cognition and learning and the relationship between these two mental processes" (p.8).

Before we explain the connection between Sokal's parody and Grobecker's article, and to prevent potential misunderstandings, let us identify what is not at issue here. First, we applaud Grobecker's claim for a Piagetian approach to learning disabilities in mathematics. Second, we share her criticism of the prevailing information-processing approach. And third, we agree that current teaching methodologies and assessment tools need significant modification. In fact, by arguing that actions and their coordination are the main source of logical-mathematical knowledge, Piaget's theory gives us grounded concepts to interpret, and workable methods to deal with, the difficulties that children may experience when learning logical and mathematical ideas (Inhelder, Sinclair, & Bovet, 1974). In contrast, by appealing to mental processes disembodied from actions and their context, the information-processing perspective often resorts to ungrounded concepts, ignores development, and bypasses the question of the meaning and relevance of knowledge, a question that Piaget and Garcia (1991) addressed in their important book Toward a Logic of Meanings.It is not of much help to hear that children's difficulties with the operations of addition, subtraction, multiplication, or division may stem from their lack of skills in receiving inputs, encoding them in representations, processing the information contained in the representations, decoding them, and generating an output. Instead, and in accordance with Piaget and Grobecker, we find it more fruitful to investigate whether such difficulties are not primarily due to the child's lack of opportunities to operate on, and interact with, her physical and social environments.

If the preceding statements summarized all the major issues in Grobecker's article, then we would have no qualms with it. Unfortunately, that is not the case, for the author also chose to cloak Piaget's theory in a physical garb that is as fashionable as it is abusive and misleading. As we shall document, the author's frequent use of terms from physics in particular, thermodynamics and non-linear, dynamic systems theory,is never justified; the intended meaning of these technical terms is never elaborated; and their relevance for the issues at hand is never demonstrated. Grobecker's article illustrates clearly three of the features identified and criticized by Sokal and Bricmont (1998) in their post-parody analyses¹:

1. "Importing concepts from the natural sciences into the humanities or social sciences without giving the slightest conceptual or empirical justification. If a biologist wanted to apply, in her research, elementary notions of mathematical topology, set theory or differential geometry, she would be asked to give some explanation. A vague analogy would not be taken very seriously by her colleagues." (pp. 4-5);

2. "Displaying a superficial erudition by shamelessly throwing around technical terms in a context where they are completely irrelevant." (p. 5);

3. "Manipulating phrases and sentences that are, in fact, meaningless. Some of these authors exhibit a veritable intoxication with words, combined with a superb indifference to their meaning" (p. 5)

To illustrate how the preceding features characterize Grobecker's article, consider how the concept of energy is used throughout her paper. Cognitive structures are conceived as open systems of energy; patterns of activity are characterized as energetic; equilibration is described as "a regulator of activity within and between individual and environmental energies" (p. 1, italics added); the individual is featured as a collection of energy systems; the physical environment and society illustrate additional energy systems. Energy is also what is exchanged within and between systems; children may extend energy into the world; energy is the stuff interactions are made of, for these interactions are depicted as "cyclical energy exchanges between the self and the social and cultural forces" (p. 8, italics added). Energy is also dynamic.

Unfortunately, however, the sense of the concept of energy is never elaborated. What in fact does it mean to say that physical environments, societies, action patterns, social interactions, cognitive systems, and equilibration, for example, are all forms of energy? Clearly we are not dealing here with the concept of energy in its everyday sense of strength, vigor, or mental alertness, because in this sense societies, institutions, and physical environments are not energy systems. But neither are we dealing with the technical sense of the concept, the sense intended when, for example, a physicist says that heat and light are forms of energy, or that energy is conserved, because in this technical sense social and cultural interactions are not energy exchanges, nor do children extend energy into the world.

Alas, our inability to understand the meaning of the concept of energy in the article extends to many other concepts which the author imported from physics: degrees of agitation of cognitive systems, dissipation of the form of cognitive structures, disturbances in the way reality is defined, processes of order and disorder that shape the form of mental activity, stability and instability of cognitive structures, transformations, forces, statics and dynamics, equilibration cycles, and the like. In each and every case, the problem is the same: On the one hand, a literal interpretation of these concepts and expressions in the contexts where they occur yields gibberish. On the other hand, a metaphorical interpretation yields the illusion that something profound and rigorous was said merely by using a homonym of a technical term.

And if any doubts remained perhaps the foregoing concepts have reasonable and clear meanings in the contexts in which they occur the following account of the source of learning disabilities would suffice to eliminate them:

"I have argued that, from a systems approach to development, the source of learning problems lies in the equilibration cycle in that the spiral of mental activity in LD [learning disabilities] is not as expansive as that of their same-aged peers as it winds itself upward and outward by the exercise of its forms . This qualitative difference in the equilibration cycle in children with LD creates a vulnerability in their system that could easily magnify and disrupt all developmental levels to follow. For example, their systems may experience an excessive degree of agitation, when structures are dissipating their forms of reorganization onto higher-order levels. As a result, cognitive systems may favor a return to their initial state rather than sustaining the tension necessary to reorganize their structures onto higher-order levels" (p. 4, italics added)

Notice how the articulation of the various concepts provides the illusion of an explanation when none was effectively offered. In what sense does mental activity expand along a spiral? The trajectory of an oscillating pendulum plotted in a velocity-position phase space defines a spiral, for the pendulum continuously loses velocity due to friction and approaches an equilibrium point in which it is motionless. But how one goes from the pendulum, or any other similar system, to mental activity and its spiraling upward and outward, we confess we do not know. In the same vein, in what sense is a cognitive system vulnerable and agitated, or dissipates its form of reorganization? When water is heated, the degree of agitation of its molecules (their mean kinetic energy) increases; when the heat source is removed, the water dissipates its energy and cools down. But how one goes from boiling water, or similar systems, to agitated cognitive structures, we confess we do not know. It also eludes us the sense in which developmental levels are magnified, or cognitive structures elect to move to one state rather than another. Having failed to understand the main elements of the account, inevitably we also failed to grasp their connections: How or why does a difference in the spiraling activity of the mind create a vulnerability in the child's cognitive system? And how or why does the agitation of the child's cognitive system favor a return to an initial state?

Consider another example: "The coordinations of actions schemes, as a biological process, are fueled by the self-regulated activity of anticipating possibilities to solve meaningful problems and altering those actions as they are acted upon and evaluated" (pp. 2-3) Again, the sense in which the anticipation of possible solutions is a self-regulated activity, or how the anticipation fuels the coordination of action schemes, remains a mystery. Furthermore, when it is stated that these coordinations are biological processes, one naturally wants to ask 'Biological? As opposed to what?' Despite the density of the prose, in the end the reader remains as ignorant about how actions change, or about how children learn to coordinate their actions, as he was at the start.

Not only do the foregoing concepts, expressions, and accounts lack reasonable and clear meanings, but they also lack relevance. For no greater understanding of a child's interactions was obtained by conceiving of society as an energy system, of human development by conceiving cognitive change in terms of agitated structures dissipating energy, and of mathematical learning and its disabilities by conceiving of the child's behavior as an extension of energy into the world. The account is irrelevant for two interrelated reasons. First, it never went beyond loose analogies with thermodynamics and non-linear systems theory, analogies more akin to poetry than science. And second, the issues pertaining to learning disabilities offered no resistance to their assimilation by concepts of physics; and without resistance there can be no accommodation to the demands of reality.

Equally distressing is the fact that Grobecker's article espouses some aspects of what elsewhere we have called the standard interpretation of Piaget's theory (Lourenco & Machado, 1996; see also Chapman, 1988)². In particular, it conceives of cognitive structures as reified, functional entities in the child's mind, entities that somehow explain the child's behavior. To wit, the difference between LD and non-LD children in solving logical-mathematical problems is due to the fact that "the cognitive systems of these [LD] children are less complex, preventing them from acting on and transforming material forms using higher-order structures" (p. 4). This view is part and parcel of the more general (and fashionable) tendency to conceive of the mind as an internal causal process, as an internal mechanism perhaps with filters, operators, and switches, or with energy systems, psychic tensions and strengths, substructures with more or less rigid boundaries, insides and outsides, and so on that somehow controls the person's behavior.

The alternative to the standard interpretation of Piaget's theory starts with a simple consideration: To solve a problem is not to be guided by cognitive logical structures, or "structures of mental activity," as one may be guided by a signpost, a verbal command, or a recipe. Rather, it is to act and operate in particular ways upon the questions and materials at hand. According to this interpretation, cognitive structures are descriptive concepts or tools used to classify what children do when they solve logical, mathematical, or other types of problems. As Piaget put it, "genetic psychology takes mental processes in their construction and the [developmental] stages [and structures-of the-whole] are preliminary tools to analyze those processes; they are not ends in themselves" (Piaget in Osterrieth et al., 56, p. 14; see also Carpendale, Chapman, & McBride, 1996, and Lourenco & Machado, 1996). In the muddled language of causation, cognitive structures are formal, not efficient causes; they describe the properties (e.g., reversibility, equilibrium) of certain modes of acting and thinking, but they have no existence independent of these very modes of acting and thinking (see Chapman, 1988; Lourenco & Machado, 1996). At the risk of simplifying considerably, one could say that cognitive structures are to certain acts and patterns of thinking as a friendly smile is to the face, mouth, and lips.

Grobecker's article also illustrates the problems that occur when the two conceptions of cognitive structures are intermixed. When the author presented the results about the development of logical-mathematical structures, she used the structures to classify and describe the different ways of solving the fish task evidenced by LD and non-LD children. However, in her theoretical considerations throughout the paper, Grobecker speaks of structures of mental activity as "psychological forces that generate the means used to solve problems." (p. 2, italics added). That is to say, children with and without learning disabilities solve the fish task differently because they have different structures of mental activity. The problem, though, is that the existence of these structures and systems was inferred from the fact that more non-LD students "achieve [the descriptive level] of multiplicative structures" (p. 8). Lest the reasoning be patently circular, one cannot explain by invoking that which one used to describe.

Consistent with the idea that cognitive structures are descriptive tools and not explanatory constructs, note that when Piaget referred to factors of development he did not mention structures of mental activity, as the standard interpretation would suggest, but maturation, physical experience, social factors, and equilibration. And when he spoke about the process of equilibration he referred to the actions and operations performed by the subject to assimilate or understand what appears to be relatively disturbing or new.

In summary, Grobecker's article falls prey to three common fallacies, which for lack of standard terms we name the fallacy of the alchemist, the fallacy of Moliere's doctor, and the fallacy of the missing hippopotamus. The appeal to complex concepts from physics reminds us of the medieval alchemist who resorted to obscure terms and entities whenever he ignored the basic principles of chemistry. The circular use of the concept of cognitive structures reminds us of the doctor who explained the sleeping effects of opium by its soporiferous virtues. And the description of cognitive development in terms of energy systems, spirals of mental activity winding upward and outward, agitated and dissipating mental structures, and the like, reminds us of an example provided by Wittgenstein when he discussed logical and philosophical issues with Bertrand Russell: "Suppose I state 'there is an hippopotamus in this room at this minute, but no one can see it, no one can hear it, no one can smell it, no one can touch it'; have I now with all these added provisos said anything meaningful at al?" Drury, 1973, p. 6).

Grobecker's paper proposes a Piagetian, constructivist approach to the area of mathematics disabilities, a proposal we enthusiastically endorse. But if there is something unique to Piaget's approach to development, it is precisely the idea that everything of psychological significance is rooted in action. As a consequence, thinking and cognition are always grounded, which is not the case in many information-processing theories of cognitive development. To her credit, Grobecker does appeal to the role of actions and their coordination in mathematics disabilities, but this central aspect of Piaget's theory is completely overshadowed by a constant appeal to irrelevant terms and expressions, ungrounded mental processes, and loose analogies and metaphors. Ironically, sundry homonyms of technical terms have the unwanted effect of bringing Grobecker's approach in line with the information-processing approach it purports to replace. Unless, that is, we find out in the days ahead that the article was also a parody in the spirit of Sokal's. At least that would be a happy ending.

Betsey Grobecker
Auburn University

I appreciate the time Lourenço and Machado have taken to comment on my proposed model regarding the origin of children's difficulties in constructing logico-mathematical knowledge. Such comments are necessary to determine the validity of the model I proposed and possible adaptations of it. Unfortunately, I found the criticisms of the authors to lack a more careful study of the facts presented as well as the theoretical premise that served as a basis for my arguments. As a result, my words were depicted to be without grounding and to "have the unwanted effect of bringing [my] approach in line with the information-processing approach it purports to replace."

For example, the authors stated that my proposal that children with learning disabilities (LD) have less complex cognitive systems that prevent them from acting on and transforming material forms using higher-order structures is "to conceive of the mind as an internal causal process, as an internal mechanism that somehow controls the person's behavior." Citing the work of Chapman (1988) and Lourenço & Manchado (1996), they argued that cognitive structures "are formal, not efficient causes; they describe the properties (e.g., reversibility, equilibration) of certain modes of acting and thinking, but they have no existence independent of these very modes of acting and thinking." They further argued that my reasoning was circular because I used structures (i.e., composite unit structures) to classify and describe the different ways of solving the fish task as evidenced by LD and non-LD children and then stated that the reason that the children did poorly was due to the fact that they have different structures of mental activity. Thus, there is a problem in that "the existence of these structures and systems was inferred from the fact that more non-LD students" abstracted less coordinated composite unit structures from the objects acted upon.

A related criticism was the authors' contention that, "everything of psychological significance is rooted in action. As a consequence, thinking and cognition are always grounded" According to the authors, this aspect of Piaget's theory was overshadowed by a "constant appeal to irrelevant terms and expressions, ungrounded mental processes, and loose analogies and metaphors" due to my choice "to cloak Piaget's theory in a physical garb that is as fashionable as it is abusive and misleading."

To address these criticisms, I believe there is a need to first clarify what cognitive functions consist of and their relationship to children's actions on objects in relation to Piaget's "open system" theory of cognitive evolution. I will then use this premise to elaborate on the proposed model of learning differences relative to Piaget's thinking.¹ Finally, I will conclude with a synopsis of the legitimacy of the criticisms set forth.

Piaget and the New Science of Life²

Evolution of Cognitive Forms and Structures of Mental Activity

Although thinking and cognition are grounded in action, beyond the reflective abstractions from the general coordinations of actions, logico-mathematical structures evolve "from nervous coordinations, and so on back to the most widely generalized of the organizing functions in life" (Piaget, 1971, p. 342).

[T]o suppose that the ultimate origin of the coordinations underlying logico-mathematical structures is to be found at the very center of the most highly generalized functioning of the living organization is itself a solution of a kind, insofar as it concerns the harmony between these coordinations or structures and the outer environment. The living organization is an "open system" Thus, the living organization is the organization of an exchange system, and the term "organization" simply designates the internal aspect of a system which is in a state of perpetual adaption. So to attribute logic and mathematics to the general coordinations of the subject's actions is not an idealistic overestimation of the part played by the subject; it is a recognition of the fact that, while the fecundity of the subject's thought processes depends on the internal resources of the organism, the efficacy of those processes depends on the fact that the organism is not independent of the environment but can only live, act, or think in interaction with it. (Piaget, 1971, p. 345)

This "open system" that Piaget referred to is based upon the premises of the new science of life. Specifically, Piaget's work on self-organizing chemical and biological structures is comparable to Prigogine's work on the molecular structures of biological cells because they both drew upon the theoretical biologists such as Waddington (1957, 1975) Doll1986, 1993). Piaget and Garcia (1989) also emphasized the similarities between Prigogine's work on "dissipative structures"³ and Piaget's work on cognitive equilibria by drawing five analogies between them: (a) Piaget conceived of cognitive structures as embodying dynamic equilibria that include interchanges with the outside; (b) these interchanges stabilize the structures through regulation; (c) equilibrium, in both cases, is characterized by a form of "self-regulation"; (d) the states, which have passed through a series of unstable states, are only understood on the basis of their past history; and (e) system stability is a function of its complexity.

Cognitive structures therefore consist of specialized organs of autoregulation (i.e, equilibration cycle) that control the exchanges underlying all behavior. These structures serve as the instruments to learning while at the same time, evolve as a result of the dynamic relationship that exists between organisms and things. (Piaget, 1971, 1985). As open systems of activity, these structures are not derived solely from the actions of the subjects on the objects, but also from the objects themselves, since physical experimentation gradually brings about modifications in the them (Piaget, 1971).

The knowledge of environment and of objects which is so admirably attained by the human mind is only so attained by virtue of an extension of the organization's structures into the universe as a whole. To say that physical knowledge is an assimilation of the real world into logico-mathematical structures amounts, in fact, to affirming ... that the organization belonging to a subject or to any living creature is a condition of exchanges with environment and cognitive exchanges just as much as it is a condition of material and energy exchanges. (pp. 338-339)

The quality of the energy exchanges within and between systems is dynamic and evolving, which makes energetic activity progressive in nature. In other words, the course of evolution consists in the construction of wider structures that embrace the former while at the same time introducing new elements into its make-up. New structures, therefore, widen the scope of former structures (Piaget, 1971) while forming the shape of a conical helix (or spiral) as it evolves (Gallagher & Reid, 1983; Piaget, 1985).

The organism chooses its material and energy aliments and sooner or later must undertake an active search for them (Piaget, 1971). Thus, cognitive development is "an active process leading to selection into the environment" (Gallagher, Reid, & Daubert, 1996, p. 4).

Equilibration is the regulator of activity between the mental structuring activity of cognitive forms and environmental energies. It consists of the biological processes of assimilation and accommodation whose function is to regulate the activity of an individual's total system. Consistent with all systems of energy, individual systems of cognitive energy act to conserve themselves while transforming and enriching their cognitive structures. Each higher-order structure is more stable and complex than what it evolved from, and is not reducible to its previous state. These structures consist of three forms of equilibration or mutual conservation between the system as a whole and its subsystems: (a) assimilation of action schemes and accommodation of action schemes to objects resulting in external disequilibria; (b) interactions between subsystems of the total system, which occur gradually and at different rates causing internal disequilibria; and (c) interactions between subsystems and the total system, which encompasses the subsystems (i.e., simultaneous differentiation of parts and their integration with the whole). The last form of equilibration differs from the second because it combines operations of subsystems into higher-order operations. As such, the interactions occur along dimensions that are hierarchical rather than horizontal (Piaget, 1985).

When persons are experiencing equilibration, their cognitive structures "have yielded and continue to yield to expected results, without bringing to the surface conceptual conflicts or contradictions" (von Glasersfeld, 1989, p. 126). However, as with all forms of matter, this state of affairs is not conducive to expansion of systems if it continues for a sustained period of time because energy patterns become increasingly more habitual, thus decreasing the flexibility in the system for change. If too inflexible, a person's mental activity will be rigid, thus ignoring the perturbation. Rather, disequilibration, or a disturbance that creates a tension by its variability and flux, is the most significant factor for propelling the equilibration cycle to reorganize its structures. It is a force that creates an obstacle to the assimilation of stimuli. At the same time, we create a need to resolve this conflict by accommodating our activity in meaningful problem-solving situations (Piaget, 1985; von Glasersfeld, 1989, 1990).

The type of perturbation aroused in us and the manner in which we respond to perturbations is dependent on the degree of coordination and integration in mental structuring activity inherent in each individual (i.e., the complexity of subsystems and the total system). Further, the ability to respond to perturbations is an evolving, generative process because new types of conflict are created each time a perturbation is resolved. In other words, by solving a problem through self-regulated reflective activity, for example, the conclusion it generates creates more complex energy systems, which in turn create new conflicts. More complex energy structures will continue to emerge from the spontaneous and self-generative interactions within and between energy systems as long as there is intelligent activity occurring in the organism (i.e., disturbance and mental action extended outward to overcome it).

Thus, the evolutionary process has its origin not in the gene, but in a nonhereditary somatic variation that results from interactions with environmental pressures. The resultant disequilibrium between the imposed pressures of the environment and the hereditary program creates a need in the organism to adapt to the disturbance. If the boundaries of the organism's system have enough flexibility to enable the system to create a far-from-equilibration state, a change in the phenocopy of the organism will most likely result. Through a process of regulation, this altered activity in the system will descend to the level of the genome. Thus, as a result of exogenous influences on the organism, transformed endogenous constructions are manifested in the organism's structures of organization on each lower level that it penetrates. In effect, the endogenous constructions are a result of exogenous influences on the organism and the way the organism adapts to those influences (Chapman, 1988; Gallagher & Reid, 1983; Gallagher et al., 1996; Piaget, 1971, 1980).

The disequilibration will sensitize the genes which respond with a genetic variation. This response is self-regulated and incorporated selectively into the organismal framework (both internal and external) until equilibration is achieved. The new variation converges with the previously nonhereditary modification as it addresses the specific need provoked by environmental pressure and answered by the self-regulation of the organism. (Gallagher et al., 1996, p. 7)

The notion of evolution as "change in the constitution and distribution of developmental systems" (p. 17) puts to rest the nature/nurture controversy of the "Central Dogma" regarding developmental evolution (Oyama, 1989). Specifically, nature and nurture can no longer be viewed as alternative sources of form and causal power. Instead, "nature is defined as the product of the process of the developmental interactions we call nurture" (p. 5, italics not added). According to Oyama, the nature of the organism is its form and function, which depends on its developmental context as profoundly as it depends on the genome. Thus, transgenerational stability and change are at the heart of the evolutionary process. "Stability of species characteristics is due to stability of developmental systems ... in which developmental systems are hierarchically organized. (Oyama, 1989, p. 24, italics not added)

Products of Self-regulation

Piaget (1987a) referred to the products of this ongoing cyclic activity as falling into the realms of possibility and/or necessity. The possible results "from the accommodative activity seeking actualization" (p. 6). In recognizing a different possibility (a new actualization), there is simultaneously a disturbance, or a new gap to be filled. To attend to this disturbance, openings in children's biological systems are created extend energy into the world. However, what children perceive and reflect on as possible is dependent on the stability and flexibility of their action schemes and the amount of resistance offered by reality as constructed at any given point in time.

Necessity, which involves comprehension of the reasons for success and failure of our actions (i.e., a judgment and synthesis of actions), is the source of closure of a system of operations in the technical sense⁴ (Piaget, 1987b). Necessity is inferential in nature because it seeks to integrate and coordinate past knowings with the current understandings, thereby helping to stabilize the system. The greater the degree of enriched, problem-seeking behavior (i.e., ability to adaptively accommodate to the environment), the greater the number of schemes or subsystems of the total system.

Possibility and necessity are interdependent processes that have their origin in the increasing number of assimilatory schemata, which are coordinated and lead to the inferential capacity of necessity (i.e., closure of operational structures). Piaget (1980) referred to the "norm of accommodation" as consisting of the number of interactions and coordinations that the organism's system has been able to enter into with other schemes. In other words, the stability and flexibility of the child's dynamic system determines the strength of its integrative capacity upon which disequilibration and the generation of new possibilities depend. Reality, which is independent of the child, becomes increasingly more objective⁶ as possibility and necessity become increasingly more integrated and coordinated. Through this developmental process, the strength of the integrative capacities of the system evolves.

To enhance the progress of intellectual growth, it is important to maximize disequilibration (Piaget, 1980). This process involves reaching beyond the initial state of the child's structures so that the compensation made by the child does not entail simply a return to its former starting point. Rather, the compensation made by the child goes beyond current understandings in the direction of the best possible equilibrium that is most compatible with the situation. However, if we push children too far beyond their current structures of knowing, "learning" is disengaged from their mental reflections, which are driven by the need to resolve conflicts. The end result is the acquisition of specific knowing to a specific context that cannot be generalized (Dewey, 1933, 1934/1980; Duckworth, 1996; Piaget, 1973), and, thus, serves little adaptive purpose.

Social Forces in Self/Societal Growth

Piaget (1981, 1995a,b,c) believed that knowledge construction is a result of interpersonal experiences with objects and people that requires co-construction and cooperation with others.

[S]ocial life transforms the very nature of the individual, making him pass from an autistic state to one involving personality. In speaking of cooperation, therefore, we understand a process that creates new realities and not a mere exchange between fully developed individuals ... there are neither individuals as such nor society as such. There are just inter-individual relations. (Piaget, 1995, p. 210).

Affective forces are necessary to cognitive growth because they serve as the "energizing force" for the evolution of cognitive structures as disequilibration between assimilation and accommodations arises (1981). Specifically, interest is a force necessary for seeking new ways of understanding when previous adaptive behaviors no longer provide adequate explanations for our actions. As a result, schemes seek aliment from the environment, although negative feedback from our actions can diminish arousal and thus, intellectual growth. Dewey (1934/1980) further argued that the continuation and expansion of life always involves "an overcoming of factors of opposition and conflict; [such that] there is a transformation of them into differentiated aspects of a higher powered and more significant life. Equilibration, which sustains this process thus comes "out of, and because of, tension" (p. 14).

Thus, emotions and knowledge, desire and object work together and "have their common origin in the biological evolution of human sociability and in the individual development of each child " (Furth, 1987, p. 172). Due to the interdependent relationship of human beings to each other and to the whole of society, society is a product of the lives that gave it form and structure (Bohm & Peat, 1987; Piaget, 1981, 1995a,b,c). In turn, individuals are shaped by the society they evolve (Piaget, 1981). Therefore, laws, customs, and limitations of society do not operate as external forces that are "alien" to the people that they act upon, but are expressions of the very nature of the people who created them (i.e., the embodiment of the mind's being) (Bohm & Peat, 1987).⁵

The New Science of Life and Learning Differences

Evolution of Cognitive Forms and Structures of Mental Activity

Thelen (1989,1990) argued that there is a need to rethink linear, unidimensional models of development which are so dominant in the study of learning differences. According to Thelen, there would be great benefit from studying human differences from the perspective of "open systems" of dynamic energy (i.e., systems composed of heterogeneous subelements that change over time.) To do so, consideration has to be given to interactions within and between individual energy systems and their interaction with all other energy systems (e.g., the physical environment, society, etc.) that exist in time and space.

Unfortunately, the field of learning differences is grounded in the information- processing paradigm of learning. Therefore, we resist the idea that the evolution of cognitive structures is a self-regulated, biological process that is active and which leads to selection into the environment (Gallagher et al., 1996; Piaget, 1971, 1980). As a result, both external (e.g., explicitly taught metacognitive strategies) and internal (e.g., modular systems) organizing powers of learning activity have been reified. Prigogine and Stengers (1984) referred to the work of Bergson (1911), who noted that the tendency of science to reify an internal organizing power to direct activity is the result of an inability to comprehend evolutive organization without some kind of preexisting goal. But there are no exact, predictable paths to forms of energy because they comprise chaotic oneness (i.e., dynamic interrelated layers of organized activity that evolve through perturbations) (Prigogine & Stengers, 1984).

As meaning is constructed by the inherent biological drive to seek increasingly more coordinated, ordered relationships in the world acted upon, order and structure to mental energy evolve. When knowledge is removed from its patterns and structures of ordered activity, it is removed from its source of meaning. It is only through the process of ordering elements in relationship to each other and to the whole (i.e., creating form and structure as the world is acted upon) that symbols come to have meaning (Dewey, 1934/1980; Piaget, 1977; Sinclair, 1990). When this activity has as its source imaginative intuitions, symbols acquire a deeper, esthetic value as they evolve (Dewey, 1934/1980).

The perspective of positivism has left children's vital, organizing activity largely unattended, enabling us to construct beliefs that are reductionist and that have been validated by equally reductionist tools. As a result, we have falsely come to accept as "truth" the notion that a diagnosed "deficit" exists as an isolated phenomenon independent of average IQ as measured on psychometric testing and affective activity. Because this assumed truth is so deeply ingrained in our psyches, we resist reseachers' calls to reconsider the validity of the IQ test (Furth, 1973; Gould, 1981; Inhelder, 1966; Siegel, 1988,1989; Stanovich, 1991) and to acknowledge the multitude of complex forces that are interdependent in the learning process (Heshusius, 1989; Poplin, 1984, 1988; Reid & Stone, 1991; Stone & Reid, 1994).

The new science of life does not support the notion of a hereditary cognitive ability that remains stable throughout life and that can be captured adequately on standardized measures. Rather, life itself is a dynamic system in which the essence of evolution is transgenerational stability and change (Oyama, 1989). In fact, cognitive scientists such as Spearman and Thurstone, who appealed to biology to help advance their claims that cognition can be captured in standardized testing, failed to confirm a concrete tie between any neurological object and a factor axis (Gould, 1981). In other words, these tests fail to reflect the inherent biological and psychological activity that organizes the world through anticipated⁷ perception which is self-regulating when directed by an adaptive purpose for generating and extending mental structuring activity into the world. By making the mind immaterial (i.e., isolated from the energetic, rhythmic activity inherent in the relationship of doing and undergoing) "the body ceases to be living and becomes a dead lump" (Dewey, 1934/1980, p. 264).

Learning activity is a multilayered transformative process that cannot be reduced to additive and incremental steps (Heshusius, 1989). In fact, had we not chosen a reductionist path in defining learning problems, where the complex dynamics of cognitive, social, and emotional forces have been separated both in testing and in instruction, perhaps there would be no such thing as a specific learning disability. If we want to capture the complex nature of learning problems, it is necessary to attend to two main areas that have been virtually ignored in our field: (a) the quality of children's self-generated biological activity (i.e., mental reflections) when engaged in learning activities that allow for the investigation of means-ends consequences as thinking is formulated; and (b) the intentions and purposes in children's behaviors. (See Meltzer & Reid, 1994, for a discussion of alternative assessment techniques and Reid, Robinson, & Bunsen, 1995, for a description of narrative research.)

We can judge the underlying quality of reflective abstractions by the specific nature of adaptive behaviors generated when children are engaged in meaningful learning activities (Reid & Stone, 1991; Stone & Reid, 1994). In tasks that allowed for the observation of children's self-generated mental reflections of their activity, children with LD were quite capable of engaging in problem solving behaviors (e.g., Grobecker, 1997; Swanson, 1993; Wansart, 1990). Specifically, they invented means to solve problems and evaluated their actions to create different means. However, the doubts they encountered and investigated differed from those of their same-aged peers with no learning differences (NLD) in that children with LD used actions characteristic of younger children to solve problems. These findings are consistent with Reid's (1991) observations that children with LD generally display "rudimentary, exploratory behaviors" (p. 257) or procedures in which they attend to the physical features of objects while engaging their thinking through trial and error and immediate observables of actions on objects.

From the perspective of a system's approach to development, I am arguing that the above observations of children with LD strongly suggest significant differences in their structures of mental activity (as compared to those of their same-aged peers with NLD), which direct what is abstracted in interaction with their world. Recall that Piaget (1987 a, b) argued that the type of perturbation aroused in us and the possibilities considered to accommodate to this conflict is dependent on the degree of coordination and integration in mental structuring activity. It follows that if children with LD experience disequilibrations in their thinking, which typify their younger-aged peers, then their spiral of mental structuring activity is not as expansive as that of their same-aged peers as it winds itself upward and outward through exercise of its form. Thus, the cognitive systems of these children are less complex, preventing them from acting on, and thus, transforming, material forms using age-related higher-ordered relationships. (See Grobecker, 1996, for an explanation of how less complex cognitive systems affect the reading/language and mathematics processes.)

Recall also that the nature of the equilibration cycle is evolving and generative and can be understood only on the basis of its part history. Thus, as children with LD actively search for means to solve problems while evaluating the consequences of the means chosen, they will continue to enrich their forms and structures of mental activity. In turn, openness to more complex possibilities is created as forms and structures of mental structuring activity are expanded through the opposing processes of dissipation and reorganization. However, because I am suggesting that their mental activity is not as expansive as that of their same-aged peers, their cognitive systems limit the number of interactions entering into the system that can be coordinated with other schemes. As a result of these biological dynamics of the system, the quality of their mental reflections in interaction with the environment will vary in degree of complexity throughout their life-span. The degree of disorganization and disintegration in mental structuring activity that affects children's ability to engage in reflective abstraction when asked to infer meaning to problems presented varies along a continuum (Grobecker, 1996).

Tensions necessary to create and sustain the disturbance for change in structures of mental activity can also be suppressed due to environmental forces encountered when energy is extended into the world. Children's vital activity is charged with emotion and the tension it calls out to give it form in reality creates the activity of reflection (Dewey, 1934/1980). Significant stressors (e.g., frustration, discouragement, derogatory criticism) encountered when constructing meaning create a lack of desire to extend one's energy into the world, resulting in qualitatively different thought structures (Piaget, 1972; Thelen, 1989, 1990). Specifically, the child's system creates a need to set up rigid boundaries in its structures to keep negative influences out. In turn, openness to perturbations is decreased. Without perturbations, no tensions are created to stimulate a need to solve problems and to evaluate one's actions on objects. And without meaningful problems to be resolved, there is minimal exercise of cognitive activity which enables the expansion and growth between subsystems and the system as a whole. As such, even if the problem did not originate in children's mental structuring activity and/or if the problems were subtle, environmental stressors have the power to significantly alter the course of development.

Thus, the factors that influence increasingly more adaptive responses to the environment are both exogenous and endogenous to the child. Individual differences are created within the developmental process itself, which is stochastic in its dynamics. However, a delicate balance between change and stability is and not a reciprocally engaged, related force that leads to the transformation of its own neuro-activity as well as the material forms that this activity acts upon.

If children are given learning experiences that are appropriate for their levels of understanding and that contain a relevant purpose for seeking solutions, then strategies (i.e., means to solve problems) are a vital outcome of the learning process. Further, the means to solve a problem and the material acted upon will be continually adapted as both are transformed into more complex orders of activity as their forces act upon each other. The teacher does not assume a passive role in these learning dynamics. Rather, he or she critically attends to children's learning activity and challenges their constructions through questioning and guidance or reinforces constructions evolving within a level. Thus, although directed instruction is provided, the direction is generated from children's logical orders and interests for the purpose of extending and transforming or stabilizing their mental constructions. The nature of the instruction is thus dialectical rather than deterministic because it seeks to help children overcome discrepancies and expand their knowledge structurations at each succeeding level that schemes reorganize themselves onto.

Societal Forces

As discussed, societal forces and relations with others in society have much power in shaping who we become. Behavior itself is extremely complex because it encompasses desires, aims, interests, and modes of response, which we can come to understand only when these personality characteristics become an expansion of our own being. Through such an expansion, the impressions of another are built into our own structure; a process that is highly complex and that evolves over time (Dewey, 1933).

Consciously or unconsciously, we may carry negative attitudes that are communicated to children who cannot learn in traditional classrooms and create resistance to learning (Erickson, 1984; McDermott, 1977). This negative attitude toward children whom we have chosen to identify as "disabled" is most likely a factor contributing to their loss of self-esteem accompanied by social problems that have been documented by researchers (e.g., Swanson & Malone, 1992). The implications of this poor self-esteem on the learning process have been discussed.

Because the individual and the social "jointly determine the movement of a system of which they are a part" (Bidell, 1988, p. 342), change will not come by blaming the schools, teachers, or children in isolation from each other. Rather, intervention to the social problems experienced by children with LD must start by examining the problem jointly. In other words, is only by understanding how all forces "interpenetrate" the learning situation (i.e., society, culture, teacher, and student) that problems can be better defined and rectified (Erickson, 1984).

Conclusion

Due to this cyclic nature of exchange of organizing activity between self and others, the quality of composite unit structures abstracted while acting on objects mirrors the quality of the structures of organizing activity that guide and constrain these reflections while, at the same time, transforming their form. I thereby stand by my contention that if LD children abstract composite unit structures that lack a degree of coordination (as compared to same-aged peers) then there are qualitative differences in their equilibration cycles (i.e., mental structures of organizing activity) that regulate actions on objects. Further, emotional forces such as lack of confidence and fear of failure could close the child's system down such that he or she is unwilling to experience the psychic⁸ tension that is inherent to the process of knowledge transformation.

This premise does not, in any way, separate actions from modes of acting and thinking. In fact, it reinforces the interdependency between children's reflective abstractions from the general coordinations of actions (described by the level achieved in the fish task) and the organizing functions of life from which such coordinations are regulated and evolve. Further, this premise implies an open, dynamic system that transforms behavior rather than an internal mechanism that controls behavior.

I believe that I presented evidence that my model to explain learning differences does have grounding in viable concepts. With regard to my "fashionable" and "abusive" use of terminology to explain these concepts, this terminology was clearly drawn from the third phase of Piaget's work. I am perplexed as to why the authors did not discuss this aspect of Piaget's work in order to specify why my writing was "gibberish." In fact, as I see it, much of there criticism is specific to Piaget's use of these terms and related concepts. Are they saying that Piaget was incorrect in how he used notions related to the new science of life, which I believe is well grounded in scientific explanation, or are they suggesting that I have misrepresented his thinking in this area? Had the authors checked a reference provided where I explained the vocabulary and concepts in greater detail (Grobecker, 1998), perhaps their criticisms would have been better tempered in reason.

I do not believe that the potential of my model can be fairly judged without reference to this third aspect of Piaget's work. If the authors continue to believe that my model is without validity, then they must either specify how Piaget inappropriately used the terminology and concepts related to the new science of life or how I distorted elements of Piaget's work to account for differences in the evolution of logico-mathematical structures with respect to the open system perspective of cognitive evolution.

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Footnotes

1. Parts of this article were taken from a previously published manuscript (Grobecker, 1998).

2. James Gleick (1987) referred to recent discoveries regarding the nature of matter as a "new science" and Rubert Sheldrake (1981) wrote a book entitled "A New Science of Life." The foundation for this new science emerged in the early to mid-1900s with the discoveries of relativity theory (i.e., the illusion of absolute space and time) and quantum theory (i.e., the illusion of a controlled measurement process). Most recently chaos theory, which emerged in the mid 1970s, has broken the illusion of deterministic predictability (Gleick, 1987).

3. A "dissipative structure" is a dynamic state of matter that has originated from a structure that is far-from-equlibrium (i.e., a dissipative state) and reflects the interaction of that system with its surroundings (Prigogine & Stengers, 1984).

4. To formulate inferences, children's structures must be closed (i.e., reversible) so that the elements under consideration can be related adequately to each other and to the whole simultaneously. However, children's cognitive structures remain open to energy exchanges with other subsystems and the environment. In fact, the evolution of operational structures involves a tension between the opening (synthesis) and closure (differentiation) of energetic patters of activity (Piaget, 1980, 1985).

5. See Grobecker (1998) for an extended discussion of the similarities and differences between the thinking of Piaget and Bohm regarding thought and society.

6. Piaget's (1987b) "objective reality is decentered from the self and, therefore, able to be understood using a perspective that is logically organized. In contrast, subjective reality is pre-logical thought (i.e., not reversible). Piaget's description of objectivity differs from the Cartesian-Newtonian view (in degree) because the subject's actions and operations include reality in a network of possibilities and necessary relations. As such, reality has the potential to become correspondingly richer (i.e., perceived in terms of more complex patterns of organization) where every real event appears as one actualization among others that is possible within a system of logical-mathematical transformations. Piaget (1981) further emphasized the necessary psychological force of interest for cognitive activity to evolve.

7. Anticipation refers to the application and generalization of schemes and is explained by the process of transfer or inference based on previous information. As part of a constructive mechanism, it functions only on the condition that it is autoregulatory (Piaget, 1971).

8. Psyche refers to the mind functioning in relation to thought, feeling, and behavior and consciously or unconsciously adapting the body to the social and physical environment.

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