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Konklusion: Die Koordination in komplexen operativen Systemen kann nicht der natürlichen Selektion zugeschrieben werden, sondern ist Ergebnis des Lernens +
Metapher +
Konklusion: In der Ontologie hat Selektion nicht Eliminierung zur Folge, sondern erfolglose Versuche +
Konklusion: Ein Organismus lernt, was zu zufriedenstellenden Ergebnissen führt +
Konklusion: Neue Verhaltensweisen entstehen, wie Mutationen, ohne biologischen Grund und werden von Generation zu Generation aufrecht erhalten, sofern sie die Lebensfähigkeit nicht beinträchtigen +
Infragestellung der allgemein gültigen Annahmen und Sichtweisen +
Konklusion: Um eine bestimmte Sittuation oder Veränderung der Unmwelt zu überleben, muss ein Organismus die erforderlichen Eigenschaften durch Mutation bereits vorher erworben haben. +
Erkenntnisse, die schockieren +
Irreführungen aufzeigen +
Wissen kann nicht das Ergebnis eines passiven Empfanges sein, sondern ist das Produkt einer aktiven Subjektivität. +
Ideen, die nicht beachtet werden +
Die Produkte bewusster kognitiver Aktivität haben immer einen Zweck und werden danach bewertet, wie gut sie diesen Zweck erfüllen +
Weil die Erlebniswelt genauso wie die Umwelt dem Organismen Grenzen setzt, werden im Lichte der Erfahrung Regelmäßigkeiten, Faustregeln und Theorien entweder als zuverlässig oder nicht zuverlässig eingestuft. +
Schwächen und die Möglichkeit der Missinterpretation der eigenen Theorie aufzeigen +
Die Welt, die konstruiert ist, ist eine erfahrene Welt, die keinerlei Anspruch auf "Wahrheit" im Sinne der Übereinstimmung mit einer ontologischen Welt +
"Durch "Natürliche Selektion" werden nicht die Stärksten und Fittesten selektiert, sondern die aussortiert, die den Test der Überlebensfähigkeit nicht überstehen +
Dilemma der klassischen Sichtweise +
Der Erfolg eines Schlüssels hängt nicht davon ab, ob ein Schloss gefunden wird, in das er passt, sonndern nur davon, ob er den Weg zu einem bestimmten Ziel öffnet. +
Wir können unsere Wahrnehmung nur durch den Vergleich mit anderen Wahrnehmungen prüfen, aber nie mit dem Objekt wie es sein könnte, bevor wir es wahrnehmen +
Es gibt keinen Zusammenhang zwischen den "objektiven" Welt und der Überlebensfähigkeit biologischer Strukturen und Verhaltensweisen. +
Entweder eine Art passt zu ihrer Umgebung oder sie passt nicht, d.h. sie überlebt entweder, oder sie stirbt. +
Der einzige Aspekt der "realen" Welt, der tatsächlich in den Bereich der Erfahrung eintritt, sind die Einschränkungen dieser Welt. +
Ablösen klassischer Denkweisen +
Erfahrungen und alle Objekte der Erfahrung sind unter allen Umständen das Resultat unserer Wege und Mittel des Erlebens +
So wie Umwelt dem lebenden Organismus Grenzen setzt und beseitigt, was die Grenze überschreitet, so bildet die Erfahrungswelt die Grenzen für unsere Ideen (kognitiven Strukturen) +
Gleichheit ist immer relativ +
Die Umwelt kann bestenfalls für das Aussterben verantwortlich gemacht werden, aber nie für das Überleben +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Bfg3odrse4 +
In this requirement, representation is similar to recognition. Both often work hand in hand, e.g., when one recognizes
a Volkswagen though one can see only part of its back but is nevertheless able to visualize the whole. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Bsgnvh5vo1 +
An example may help to clarify what I am trying to say. If, in someone’s account of a European journey, you read or hear the name “Paris”, you may register it as a pointer to a variety of experiential “referents” with which you hapen to have associated it—e.g., a particular point on the map of Europe, your first glimpse of the Eiffel Tower, the Mona Lisa in the Louvre— but if the account of the journey immediately moves to London, you would be unlikely to implement fully any one of them as an actual re-presentation. At any subsequent moment, however, if the context or the conversation required it, you could return to the mention of “Paris” and develop one of the associated re-presentations. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Camouqfaz8 +
Any re-presentation, be it of an experiential “thing” or of a program of actions or operations, requires some sensory material for its execution. That basic condition, I believe, is what confirmed Berkeley in his argument against the “existence” of abstracted general ideas, for it is indeed the case that every time we re-present to ourselves such a general idea, it turns into a particular one because its implementation requires the kind of material from which it was abstracted. This last condition could be reformulated by saying that there has to be some isomorphism between the present construct and what it is intended to reconstruct. Clearly, this isomorphism does not concern a “thing-in-itself” but precisely those aspects one wants to or happens to focus on. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/D3z4577hkq +
By this I mean that, as particular users of the word become more proficient, they no longer need to actually produce the associated conceptual structures as a completely implemented re-presentation, but can simply register the occurrence of the word as a kind of “pointer” to be followed if needed at a later moment. I see this as analogous to the capability of recognizing objects on the basis of a partial perceptual construction. In the context of symbolic activities, this capability is both subtle and important. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Ndkqy9lz7e +
Reflecting upon experiences is clearly not the same as having an experience. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/P55yeeak0x +
No act of mental re-presentation, which in this context of conceptual analysis means neither less nor more than the re-generation of a prior experience, would be possible if the original generation of the experience had not left some mark to guide its reconstruction. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Sktb6xjmvl +
Hence I suggest that, pace Berkeley, we are quite able to abstract general ideas from experience and that we do this by substituting a kind of place-holder or variable for some of the properties in the sensory complex we have abstracted from our experiences of particular things. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Tb4vyjiobf +
With regard to the need for an acting agent, a program is similar to a map. If someone draws a simple map to show you how to get to his house, he essentially indicates a potential path from a place you are presumed to know to the unknown location. The drawing of the path is a graphic representation of the turns that have to be made to accomplish that itinerary, but it does not and could not show what it is to move and what it is to turn right or left. Any user of the map, must supply the motion and the changes of direction with the focus of visual attention while reading the map. Only if one manages to abstract this sequence of motions from the reading activity, can one transform it into physical movement through the mapped region. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Tm9j7422k1 +
If someone, having just eaten an apple, takes a bite out of a second one, and is asked which of the two tasted sweeter, we should not be surprised that the person could give an answer. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Vop5onvlls +
Hence I suggest that, pace Berkeley, we are quite able to abstract general ideas from experience and that we do this by substituting a kind of place-holder or variable for some of the properties in the sensory complex we have abstracted from our experiences of particular things. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Wpt5k6ohg9 +
I hope to make this clear with the help of an example. A child growing up in a region where apples are red would neessarily and quite correctly associate the idea of redness with the name “apple”. A distant relative arriving from another part of the country, bringing a basket of yellow apples, would cause a major perturbation for the child, who might want to insist that yellow things should not be called “apples”. However, the social pressure of the family’s usage of the word will soon force the child to accept the fact that the things people call “apple” come in different colors. The child might then be told that apples can also be green, which would enable the child to recognize such a particular green thing as an apple the first time it is brought to the house. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Y3m0svglur +
In my terms this means, symbols can be associated with operations and, once the operations have become quite familiar, the symbols can be used to point to them without the need to produce an actual re-presentation of carrying them out. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Zibsapwn7j +
In other words, one can be quite aware of what one is cognitively operating on, without being aware of the operations one is carrying out. +
Annotationen:Abstraction, Re-Presentation, and Reflection: An Interpretation of Experience and of Piaget’s Approach/Zvvv0kffkv +
Hence, from his perspective, there is no linear progression without end, but simply development of method and concepts in one discipline leading to novel conceptualization and coordination in another. The recent impact of the physics of molecules and particles on the conceptual framework of biology would seem a good example. +
In order to survive a particular situation or change in the environment, an organism must have the required characteristics before the situation or change in the environment occurs that makes these characteristics necessary. In other words, surviving organisms are adapted before the event and it would make no sense whatever to say that they did or could change because of the event. There simply is no causal connection between the selecting event or environmental pressure and the properties the surviving organisms have acquired at a prior time through mutation or some other accident. +
From an evolutionary point of view, it would be far more consistent to say that, like mutations, novel behaviors may arise for no biological reason at all and may be perpetuated from generation to generation, provided they do not diminish the organisms’ biological viability below a critical point. +
Let me cite one example that is particularly well-documented and well-known: the Japanese macaque Imo on Koshima Islet that started washing her sweet potatoes (Kawai, 1965). Within 10 years the entire population, with the exception of a few old males who were too conservative, practiced potato washing. There was no time for a mutation or some other genetic accident to increase or decrease anyone’s viability. Nor, indeed, is there any evidence that potato washing has increased anyone’s genetic fitness. But as the new activity quickly created exceptional familiarity with water, it led to yet another novel behavior: swimming. Since all this has taken place in a country where earthquakes and tectonic disasters are not at all impossible, it might be tempting to conjecture that if Koshima Islet should one day sink into the sea, the swimming skill might yet become the crucial feature that allows these macaques to reach a safe shore while the macaques in other sinking regions perish. Subsequent generations of sociobiologists could then use the swimming macaques as a textbook example for “evolutionary explanation.” But such a scenario in which swimming might become an important asset toward the survival of macaques or macaque genes has not yet happened. Yet the washing of food and swimming have become part of the behavioral repertoire of a macaque population without the benefit of an evolutionary explanation. +
If something has been found to work, it is likely to work again. +
Hence one may also introduce the concept of reinforcement which, in phylogeny, would remain vacuous, since the only thing that could count as reinforcement on that level (i.e., survival) is not contingent upon the organism’s modification of its behavior but upon its past and therefore immutable history of genetic variation. +
In other words, the basic operational elements were there, but their coordination into complex operational systems cannot be ascribed to natural selection, since it is demonstrably the result of learning in a very peculiar and highly sophisticated environment. +
Epistemology thus becomes the study of how the mind operates, of the ways and means it employs to construct a relatively regular world out of the flow of its experience. +
Two eggs may be considered the same because of their shape, size, or color, or because they come from the same hen; but there will be a pungent difference between them if one was laid yesterday and the other six weeks ago. A fieldmouse and an elephant are different in many ways, but they will be considered the same whenever we want to distinguish mammals from other animals. Finally, all eggs, all animals, and indeed all objects that I have ever seen or imagined, are the same in that one respect that I have isolated them as bounded, unitary objects in the total field of my experience. +
A similar, often cited example, is the movie film which, depending on the conditions of perception, we see as a sequence of individually different images or as one continuously moving image. Irrespective of any “real” horse that may or may not have trotted somewhere at some time and been filmed while doing so, when the film is presented to us, we ourselves must construct the motion by constituting a continuous change of one horse from the succession of images. +
Just a the environment places constraints on the living organism (biological structures) and eliminates all variants that in some way transgress the limits within which they are possible or “viable,” so the experiential world, be it that of everyday life or of the laboratory, constitutes the testing ground for our ideas (cognitive structures). +
The only aspect of that “real” world that actually enters into the realm of experience, are its constraints; +
The question is unanswerable, because no matter what we do, we can check our perceptions only by means of other perceptions, but never with the apple as it might be before we perceive it. +
Sameness, however, as we have seen, is always relative: Objects, and experiences in general, are the “same” with respect to the properties or components that have been checked in a comparison. Hence, an experience that consists, for instance, of the elements a, b, and c, can be considered the same as an experience consisting of a, b, c, and x, as long as x is not taken into account. +
because the success of a key does not depend on finding a lock into which it might fit, but solely on whether or not it opens the way to the particular goal we want to reach. +
In other words, experience as well as all objects of experience are under all circumstances the result of our ways and means of experiencing, and are necessarily structured and determined by space and time and the other categories derived from these +
“natural selection” does not in any positive sense select the fittest, the sturdiest, the best, or the truest, but it functions negatively, in that it simply lets go under whatever does not pass the test. +
No one uses these conceptual possibilities more skillfully than the professional magician. During a performance he may, for instance, request a spectator’s ring, toss another ring across the room to his assistant, and then let the stunned spectator find his ring in his own coat pocket. The magic consists in directing the spectators’ perception in such a way that they unwittingly construct an individual identity between the first experience of the ring and the experience of the thrown object. Once that has been done, it would, indeed, require magic to transfer the ring from the assistant to the spectator’s pocket. Another case is that of the red ribbon which the magician cuts into little pieces and then – literally with a flick of his hand – produces once more as one whole piece. +
Hence, the environment can, at best, be held responsible for extinction, but never for survival. +
either a species fits its environment (including the other species), or it does not; i.e., it either survives, or it dies out. +
A key fits if it opens the lock. The fit describes a capacity of the key, not of the lock. Thanks to professional burglars, we know only too well that there are many keys that are shaped quite differently from ours but nevertheless unlock our doors. The metaphor is crude, but it serves quite well to bring into relief the difference I want to explicate. +
Quite generally, that means that the world which we experience is, and must be as it is, because we have put it together that way. +
The products of conscious cognitive activity, therefore, always have a purpose and are, at least originally, assessed according to how well they serve that purpose. +
The passage I quoted also indicates that there is more than one level of adaptation. On the sensorimotor level of perception and bodily action, it is avoidance of physical perturbation and the possibility of survival that matter. On the level of thought we are concerned with concepts, their connections, with theories and explanations. All these are only indirectly linked to the practice of living. On this higher level, viability is determined by the attainment of goals and the elimination of conceptual contradictions. +
The pattern of learning, however, is the same as in Piaget’s scheme theory, and once we impute to an organism the capability of reflecting upon its experiences, we can say that the principle of induction arises in its own thinking. +
Without the conception of change there would be no use for the notion of causation. +
All my decisions to carry out specific actions are based on the expectation that they will bring about a change towards the desired goal. +
Let us look at the example more closely. I am thirsty, and there is a glass of water in front of me on the table. From past experience I have learned (by induction and abstraction) that water is a means to quench my thirst. This is the ‘voluntary purpose’ I have chosen at the moment. In other words, I am anticipating that water will do again what it did in the past. But to achieve my purpose, I have to drink the water. There, again, I am relying on past experience, in the sense that I carry out the ‘specific movements’ which I expect (anticipate) to bring the glass to my lips. It is these movements that are controlled and guided by negative feedback.
When I reflect upon this sequence of decisions and actions, it becomes clear that the notion of causality plays an important role in the event. +
The use of a cause-effect link in order to bring about a change is based on the belief that, since the cause has produced its effect in the past, it will produce it in the future. +
Even in Aristotle’s day, bright people had noticed that those who regularly took some physical exercise such as walking, had a better chance of staying healthy. They had observed this often enough to consider it a reliable rule. Given that they had Olympic games and were interested in the performances of athletes, they probably also had some plausible theory of why exercise made one feel better. Consequently, they were confident in believing that going for walks was an efficient cause that had the effect of maintaining and even improving your health. People who felt that their physical fitness was deteriorating could, therefore, reasonably decide to use walking as a tool to bring about a beneficial change in their condition. +
Anyway, the more sophisticated view of the reflex enabled Piaget to take the tripartite pattern of perceived situation, action, and result as the basis for what he called ‘Action Scheme’. It provided a powerful model for a form of practical learning on the sensorimotor level that was the same, in principle, for animals and humans.
Studies of animal behavior had shown that even the most primitive organisms tend to move towards situations that in the past provided agreeable experiences rather than towards those that proved unpleasant or painful. +
To believe that the future affects the present is no doubt a superstition, but to declare that purpose and goal-directed action must be discarded because they are teleological notions is no better. It shows an abysmal ignorance of the difference between empirical and metaphysical teleology. +
If you consider that in the context of the Darwinian theory of evolution, “to be adapted” means to survive by avoiding constraints, it becomes clear that, for Piaget, “to know” does not involve acquiring a picture of the world around us. Instead, it concerns the discovery of paths of action and of thought that are open to us, paths that are viable in the face of experience. +
Hence, when we intend to stimulate and enhance a student’s learning, we cannot afford to forget that knowledge does not exist outside a person’s mind. +
Knowledge, then, could be treated, not as a more or less accurate representation of external things, situations, and events, but rather as a mapping of actions and conceptual operations that had proven viable in the knowing subject’s experience. +
At best one may observe that in a given number of situations their constructs seem to function in the same way, i.e. they seem compatible. +
If two people share a room, there is one room and both live in it. If they share a bowl of cherries, none of the cherries is eaten by both persons. +
Hence, no matter how one looks at it, an analysis of meanings always leads to individual experience and the social process of accommodating the links between words and chunks of that experience until the individual deems they are compatible with the usage and the linguistic and behavioral responses of others. +
Hence, when Piaget speaks of interaction, this does not imply an organism that interacts with objects as they “really” are, but rather a cognitive subject that is dealing with previously constructed perceptual and conceptual structures. +
That is to say, no matter how hard investigators try to adapt their analyses to the “foreign” ways of children, the model they build up will always be a model constructed out of concepts that are necessarily the investigators’. Because children’s ways of thinking are never directly accessible, the investigators’ model can never be compared to a child’s thought in order to determine whether there is or is not a perfect match. The most one can hope for is that the model fits whatever observations one has made and, more importantly, that it remains viable in the face of new observations. +
In other words, they must come to share some basic ideas on the process of education and the teaching of mathematics in particular. +
if one wants to generate understanding, the reasons why a student operates in a certain way are far more indicative of the student’s stage of conceptual development than whether or not these operations lead to a result that the teacher finds acceptable. Only when teachers have some notion of the conceptual structures with which students operate, can they try to intervene in ways that might lead students to change something in these conceptual structures. +
therefore, they need first of all a plausible model of the conceptual structures with which students are operating at the time. +
In order to formulate even the most tentative model of cognitive change, educational scientists must witness the growth of mathematical knowledge in particular children and clarify and substantiate their interpretations by means of deliberate interventions. Conceptual analysis alone is simply not sufficient as a source of insight in model building. It is only on the basis of models of particular children, that a more general model can eventually be abstracted – and the models of particular children are a natural bridge between educational scientists and the teachers. +
In adopting the new, cognitive paradigm, then, it becomes imperative that both teachers and researchers acquire some theoretical notions of how this “making sense” can be conceptualized. +
Working with children is in many ways like working with foreigners with whom one has only fragments of a language in common. +
A model, then, “simulates reality”; it is a conceptual construct that is treated as though it gave an accurate picture of the real world, but has the actual function of making experimental results and other experiential elements compatible with the general assumptions that are inherent in the research program’s core. +
Just as the interpretation of a piece of language is always guided by the individual interpreter’s experience and expectations, so the interpretation of what one observes is always governed by some theory one has in mind and a goal one has chosen. +
Teachers, therefore, need an at least partially generalized theory and a model of the learner that is general enough to serve as a basis for the establishment of more than one individual model. Ideally, then, the teachers’ models of individual students will be instantiations of the educational scientists’ more general model of mathematics learning; and conversely, the individual models the teachers construct for individual students will be a continuous testing ground for the theoretical assumptions the scientists have incorporated in the more general model. +
When I visually distinguish a hand from the writing pad and the table on which it lies, I carry out exactly the same kinds of operations as when I distinguish the coffee cup from the table on which it stands, or the picture from the wall on which it hangs, or the cardinal outside my window from the branch on which it happens to be perched and from the rest of the landscape. +
In other words, if there are several kinds of disturbance and, consequently, several kinds of error signals, the system has to discover which of the activities in its behavioral repertoire is most likely to correct a particular error signal. On the simplest level this can be achieved only through inductive inference. +
It allows us to proceed much as a bricklayer, who can devote all his energy and attention to the creation of a wall or an arch, without ever stopping to ask where the bricks he is using came from or how they were made. And just as the characteristics of the bricks (e.g., shape and size) make it impossible for the bricklayer to build certain structures, so the ready-made conceptual building blocks impose constraints on any future construction. +
To refer once more to the feedback model, one might say that assimilation, insofar as it adjusts sensory signals, reduces the generation of error signals. Accommodation, on the other hand, occurs only when there is a discrepancy or disturbance for which the organism does not yet have an established remedy. +
There seems to be no way around the assumption that, as far as the organism is concerned, an “object” must be a construct, actively abstracted from a number of experiences by holding on to a somewhat flexible constellation of characteristics and allowing each of them to vary within a certain range. +
Hence this use of an invariant scheme is by no means a manifestation of the concept of object permanence, because its invariance arises from and consists in the repetition of an activity and does not yet involve the invariance of an independent object. +
Now, if the invariant can be used on the representational level, without an activity, it becomes like a program or a subroutine that is invariant in that it is stored somewhere in a memory from which it can be retrieved. It is this change of status that gives rise to the concepts of permanence and of identity, a further step in the construction of permanent objects. +
For many five-year-olds, for instance, the sun today and the sun yesterday are not yet one and the same individual (Piaget, 1971, p. 87). +
Suppose a very young child applies the word dog to every four-legged creature he sees. He may have abstracted a limited set of attributes and created a large category, but his abstraction will now show up in his vocabulary. Parents will not provide him with a conventional name for his category, e.g., quadruped, but instead will require him to narrow his use of dog to its proper range...
The child who spontaneously hits on the category four-legged animals will be required to give it up in favor of dogs, cats, horses, cows, and the like ... The schoolboy who learns the word quadruped has abstracted from differentiated and named subor- dinates. The child he was abstracted through a failure to differentiate. Abstraction after differentiation may be the mature process, and abstraction from a failure to differentiate the primitive. +
Here I shall confine myself to pointing out that the kind of knowledge our simple organism acquires by installing connections between error signals and activities is, indeed, a form of construction, and since it deals exclusively with the proximal data of the organism’s own subjective experience, one would be justified in calling it wholly subjective. +
In other words, we can come to know only what we consider to be in some sense separate from our knowing selves. By questioning something, by the very act of asking what it is, we have already set our self, the questioner, apart. +
