The age of six to eight years old conceptual tools generally marks a decisive turning point in the development; children so far have been satisfied on the internalization of those activities, or conceptualized, the reversible conversion of qualifications obtained demonstration of the status of some of these conversions changing the variables, and let the other variables remain unchanged. Moreover, this basic innovation must be seen as progress in the coordination of access to the results of demonstration of the basic characteristics is that they can be formed as closed system or fundamentally different from the previous stage it can be and must not regard it as an absolute beginning. but only after a more or less continuously as the conversion result. the absolute beginning of the development process is never see, new things, as we have been able to prove it, is the gradual coordination of differentiation or the result of progressive, or is this the result of both. Thus, the behavior of one stage of each before it phase separation of the basic difference between the behavior must be viewed as a transition to the limit, and the unique characteristics of each stage is we need to be determined. We mentioned that an example of this situation is to have one after another from some physical activities to those activities in the thinking of the simultaneous appearance of the transition, we think that this marks the symbolic features began to appear. In the current knowledge on the demonstration of the case, we encountered a similar time course: predictable and fused into a single review activities mm which is the basis of demonstration of reversibility.
here serialization provides a particularly clear example. When asked by the order of ten children, root length difference is very small (that is needed pairwise comparison) stick, the first demonstration of the first stage of the level of the children will be divided into one to one on the stick (a short and a long, etc.), or divided into groups of three (a roots short, a medium and a long, etc.), but they can not be coordinated into a single sequence. The second level of the subjects can be arranged in correct sequence, but to go through trial and error and correction error. On the other hand, we are talking stage, the subjects were often in a stepwise, first find the shortest stick, and then from the left, find the shortest stick, has been to do so. is clearly, there is such an assumption: any element has been put out under both longer than the various elements, such as E> D, C, B, A, while shorter than not laid out the various elements, such as E H and so on. Thus, at this stage to introduce the innovation is the simultaneous use of Error-free system that replaces the way to deal with relationships. the first level of this individual being tested is the only approach towards a single direction (When he asked about another possible direction, would be puzzled. but from now on next, his approach is taking into account the two directions (because the E element is seen as looking for both E> D , is E Therefore, generally speaking mm This applies to both categories are equally applicable to a number of serialization mm in front of this level of simple limit characteristic is: not after the fact, not after the event had actually been made to correct, but to correct the error in advance, by the positive demonstration of the interaction of speech and the inverse operation, or in other words, as we have just have seen, is a combination of predictable and review the results, or, more precisely, he said, is a possible review their predictable results. In this regard, demonstration of forms in control theory is sometimes termed To before being tested through empirical trial and error and do the serialization; in the classification (A It is clear that the transmission of classified or relationship (if AlB and BlC, the AlC) is associated with a closed system: as long as the closed system formed by trial and error, is the series the way, the first establish some relationship, and then coordinate a whole, then, there is a causal relationship can not be the kind of transitivity, transitivity can only be through the A for the demonstration of conservation the formation of the structure provided the best indicator that the structure with the transmission and closed both of which are closely linked. It links with the transitive is evident; as a person because of A = B and B = C and that A = C, this is because there are some features from A to C to maintain a constant; the other hand, if A = B and the recognition test B = C is inevitable that these two conservation, he would with the same argument to infer A = C. Children at this stage is often used to describe the three main arguments for conservation, all that a self-closed structure of the combination of unique, self-closed structure is such a structure, it internal conversion is neither beyond the limits of the system, and internal conversion to occur, do not require any external element to appear. In explaining the most common form of conservation arguments, subjects only said, with a collection or object A state change from state B, it remains the same number as we discuss here is no longer unique to the previous level of quality of identity. (The reason is simple, the quality of the identity or conservation is not the equivalent requirements.) So, a that the identity of the involved operator is +0, and this operator only makes sense within a system. In the second type of argument that conservation, from A to B conservation reasons, it is able to A B state back to the state (generated by the reversible inversion). This is another demonstration of the problem within the system, the previous level, children sometimes may actually be re-admitted back to B state A state, however, This does not necessarily have a true conservative. In the third category argument, subjects said, because although the longer the object, but narrow, so the number has not changed (or, in this collection although the spread account for more space, but the distance between them was not so secret). subjects sometimes said that two variations of a compensation another (generated by the reciprocal relationship between the reversibility). On these occasions, which more clearly, children and themselves from a closed system to be thinking a whole. He does not conduct measurements to estimate the changes, he just. priori way to a pure interpretation of the role of changes in compensation judge, this implies the invariance of the whole system this initial assumption.
This is considerable progress, in terms of its logic, it marks the beginning of the specific demonstration of phase. to have two levels of a the dividing line between the limit (as we have said) the transition is complex, actually consists of three aspects linked to each other. The first is to make high-level structure generated from the low-level structure of the reflexive abstraction. For example, : As a serialization order of the basis, from the experience on a pair of two, three order of such a group and already appears in the local construction of the sequence of the evolved; demonstration of the unique combination of classification Images of collections from the previous demonstration of the concept and formation of the local portfolio is based evolved, and so on. The second is coordination, this coordination is towards the system as a whole, and thus tend to spread by the order of these or local joint, and so link up to produce a closed system. The third aspect is unique to this coordination process of self-regulation. It's connected to the system in terms of both positive and negative balance. In other words, the balance is the limiting process to obtain the outstanding features of these systems also has a unique, new features different from the previous reasons, in particular the demonstration of reversible causes.
these different aspects, you can go from children under the relationship between class and order of the concept of integrated integral analysis of the process out again. a number of values or a collection, not to mention the collection of a count, is classified with those who can or can just a collection of serialized On the contrary, the head of a feature is its quality of individual items taken out so that all of the individual have become equivalent. So they are still able to form a class of overlapping line up: (I) <(I + I) <(I + I + l) I- > Ihh in that order (space or time position, or a few numbers in order) the resulting difference, although it is a sequence can be replaced, that no matter what one of the order, the order remains the same . Therefore, the performance of the classified demonstration of the number and sequence of demonstration of the fusion, that once on the classification and sequence as the basis of demonstration of the quality difference between each other abstract necessary when it immediately became a comprehensive. Thus, the construction appears to be an integer with the demonstration of both structure formation take place simultaneously. (see to this new development shows that the construction of all demonstration of the three main areas: a reflexive abstraction, it generated a classification of relations and order relations; a new co-ordination, which combined these two relations as a whole {[ ,],[each child as a whole in whole or in conservation. However, this does not mean that the number of sequences integrated in the classification and the completion of the structure has occurred after, because the level from the previous demonstration of no later appeared that the image of the total number of conserved number; the number of classification can promote the formation of the formation, the promotion of equal extent, and sometimes greater than the number classified as the promotion of the formation. Therefore, the structure appears to be from the initial start, we can classify the existence of relationships and reflexive relationship between the abstract in order to serve multiple purposes, and in the class, and several relations between the three basic structure of the relationship between variable collateral.
demonstration of spatial (and the nineteenth volume) is in front of the demonstration of the formation of parallel closely together, but is no longer classified as discrete objects, as the similarities and differences in quality as a basis, but on the basis of proximity and separation. On the whole do not longer be a collection of discrete items, but a complete and continuous object, its parts are in accordance with the principle of proximity or linked together, including in, or separated. Therefore, the separation or displacement of the primary location and transport speech, the same classification or serialization is a demonstration of the primary structure of the same; if we remember, the first demonstration of the initial level, the space between the object and the former logical collection of relatively undifferentiated condition (see by order of the image of the collection space, or method or arrangement according to the ranks of the length to estimate the number of image), above this point is especially clear. nearly seven to eight years old, these two structures are clearly differentiation, we then will be able to continuity and those who do not similarity or difference of (different levels equivalent) operation based on a logical address into a mathematical demonstration of, and the continuity and proximity to those generated from the operation speech as a start, and the object together or to be serialized, and so on, while the second type is the object of a separate continuity. In between these two types of demonstration of transitive relations is not, as Socrates nose, although a part of his own, but not the same as Socrates is a man of Athens, Greeks or Europeans, and so on.
If we turn attention to the construction of the measure, then this mathematical demonstration of the logic and the with minor in time later than the emergence of a few, the fact is: not by the elements of the unit elements of the discontinuity of the implied, but something must be separated from the continuous construction to be successful, and must also imagine that Segmentation can be transferred to other parts of the object to. In this way, as a separate and measure the displacement of the order of the emergence of an integrated, people can have the emergence of some forms of behavior to pursue this difficult step by step development of the stage. This integrated concept with the construct of the relationship of a comprehensive classification and order of nature is closely similar. just the end of this new integrated, the number of directly applied to space through the continuous unity of the above, measurement was only simplified But the children still are the first to go through the necessary process logic (of course, in addition to his existing unit is not the case when).
Let us now as a symbol of this specific demonstration of many of the first stage to a level of achievement related to the achievement and causality up. As the level before the demonstration of causality is psychological first morphological normalization factor to the activity pattern of the object, then the activity pattern of spread that can objectively be shown the same function, to seven to eight year-old stage, in a sense, put the demonstration of the existence but also due to the case of the object, so that the object up to operator status, its activities can now be rational in a way much together. Therefore, The problem is where to pass campaign, demonstration of the transfer of as an intermediary to involve a move the last generation. because in the middle of this line had a slight displacement of the object, and push each other, but yet he imagine a . In dealing with the balance between the two weights, the child will be considered compensation and equal to, thus bringing the number of addition and subtraction are both attributed to a combination of the object. In short, people can say that this is about cause and effect demonstration of the relationship between the beginning; does not mean that the demonstration of previously described is formed completely independently, but in reality it only after due. On the contrary, children make a causal interpretation, is often performed during the operation of integrated at the same time, which in turn consolidated due to the object. It also occurs as a result of both reflexive demonstration of the abstract form of a result of relying on simple and abstract with the experience drawn from the physical to the material mm of this material can facilitate (or hinder) the logical structure and spatial structure of the formation of mm between the two is the interaction of all the different achieved.
last talked about this leads us to the limits inherent in this level to, or lead to a general unique to the specific demonstration of the limits to go. and eleven to twelve-year-old reached, the form of demonstration of what we call demonstration of these characteristics mm it is possible to carry out by assuming that reasoning, and requested that the forms of association and authenticity of the content open to mm, respectively, very different from that stage, Now these activities (or causality in the object to be counted as midnight was attributed to the object of those activities) were given a demonstration of the structure, that is, they can be a combination of transmission and irreversible manner up. This being the case, it is easy to understand, some of the object is more or less easy for such a structure, while others object is not the case; it means to say, with the contents of the form had not yet separated, with some of the specific demonstration of will apply to different content, just in time have different. Thus, the weight, the amount of conservation, seriation, etc., or even the same amount of transitivity, are only approximately nine to ten time to master, and seven to eight years old can not. In the seven-year-old can only grasp simple content. The reason is that weight is a force, the weight dynamics of the causal relationship between this kind of demonstration of the structure of a hindrance. However, when the demonstration of the structural indeed occur, the use of children in the seven to eight years old when he used the conservation of serialization or transfer of some of the ways and the same with some of the arguments of the. < br> Another concrete demonstration of the basic structure of the composition of the limitations is that they are carried out step by step, rather than any kind of combination of principle. This is the example is the classification. If A, B, C, etc. are some of the classes overlap interaction, A ', B', C 'is more than their fill, then the following equation can be established are:
(1) A + A '= B; B + B' = C; so
(2) B-A '= A; CB = B'; so
(3) A +0 = A
(4) A + A = A, resulting A + B = B; so
(5) (A + A ') + B' = A + (A '+ B')
that: (A + A)-AnA + (AA)
as: AA = 0, and A +0 = A in this case, such as A + F 'so that the composition of a non-neighbor does not have a simple class, The result is: (C-E'-D'-C'-B'-A '). Moreover, this is a situation clusters zoological classification, where other methods combined. Although the numbers seem to be integrated to avoid these limitations mm because the integers zero, negative numbers together to form a group, rather than a One of the features is: Even if only a few of the comprehensive the characteristics of the various stages can be used broadly to describe the number of 1-7,8-15,16-30 so. beyond these limits mm beyond the limits of the progress is very slow to still contain only a few mm are classified in terms of or serialized, as long as these two characteristics of the integrated still in a state not to have been completed will be the case (
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