CONCEPTUAL FIELDS 2
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FIELD THEORY OF CONCEPT 2
Gérard Vergnaud 2
SUMMARY CONCEPTUAL FIELDS
1. A conceptual field as a set of situations that require an addition, a subtraction, multiplication or division or a combination of these operations, the role of situations is possible to generate a classification that is based on the analysis of cognitive tasks and procedures that can be brought into play in each of them.
a) The concept of situation is here the meaning of the teaching situation but rather the task,
b) The idea is that any complex situation can be analyzed as a combination of tasks that it is important to know the nature and difficulty of their own.
c) The difficulty of a task is neither the sum nor the product of the difficulty of the different subtasks,
d) The failure of a subtask involves global failure.
2. The theory of conceptual fields favors models attribute a central role to the very concepts.
a. the form of statements and the number of elements involved relevant factors of complexity, but their role is subordinate.
3. The theory of conceptual fields appears more like a psychology of concepts, even though the term "structure" to intervene in the appointment of the conceptual field itself considered: additive structures, multiplicative structures.
4. The conceptual field of the structure is both the set of situations whose treatment involves one or more additions or subtractions, and the set of concepts and theorems to analyze these situations and tasks.
SITUATIONS
• The concept of situation concerns the cognitive processes and the subject's responses are a function of the situations to which they are confronted.
will retain two main ideas:
1) the variety: there are a variety of situations as a conceptual field, and the situation variables are a means of generating systematically all the possible classes;
2) the history: the knowledge of the students are shaped by the situations encountered and mastered progressively especially for the first situations which can give meaning to the concepts and procedures that they want to teach.
• In normal situations of life, relevant data are embedded in a set of little or no relevant information, not always be expressed clearly the issues that may arise.
a) so that the treatment of these conditions involve both the identification of issues and operations must be done to answer them.
b) This invites analysis, but not easy after-life situations to establish a systematic classification.
• In principle, therefore, any situation can be reduced to a combination of data base relationships of known and unknown, which correspond to as many issues as possible.
• The classification of the basic relationships and the kinds of problems that can be generated from them is an indispensable scientific work.
• No work is without a systematic classification.
• This classification allows also open the field of possibilities, and overcome the very limited picture of the everyday situations of life.
signifier and signified
• These are the situations which give meaning to concepts, but the meaning is not in the same situations. It is also not in the words and symbols.
a. However, it is said that a symbolic representation that a word or a sentence has meaning, or multiple meanings, or no sense to such and such individuals are said also that the situation makes sense or does not.
• The meaning is a relation of subject to the conditions and significant.
a. More precisely, are the patterns evoked in the individual subject or a situation which constitutes a significant sense of this situation or this significant for this subject.
• a given situation or a particular symbolism in an individual does not recall all the schemes available.
• When we say that such a word has this sense, it actually forwards to a subset of schemas, thus operating a restriction on the set of possible schemes.
o However the question of the role of signifiers in thought, and the nature of the schemes that organize the treatment of signifiers, in their understanding and their production.
or linguistic activity clearly favors the completion of the task and the resolution of problems encountered, without which it would intervene
• The activity fosters the discovery language relevant relations, the temporal organization of action and control.
• It thus comes to the representational function of language, but this role is threefold:
• representation of the relevant elements of the situation;
• representation of action ,
• representation of the relationships between action and situation.
The language is different orders of things, and linguistic activity has several functions.
• The express language activity also other important aspects such as the involvement of the subject in the task or trial issued, their feelings, their estimate of the plausibility of a hypothesis or conclusion, or even the relationship these elements together.
CONCLUSIONS:
I. The theory of conceptual fields is based on a principle of pragmatic development knowledge.
II. You can not theorize about learning mathematics English or science or only from the symbolism, not only from situations. It is necessary to consider the meaning of situations and symbols.
III. The key is to consider the subject's action in situation, and the organization of their behavior.
a. Hence the importance attached to the concept of schema.
IV. The scheme is recognized in a dynamic and functional whole, the scheme does not therefore requires less analysis.
a. If you organize the subject's behavior involves rules of engagement and anticipations. But this is not possible but that is integral scheme implicit or explicit representation of reality analyzable in terms of objects, en-act categories (properties and relations) and theorems-in-action.
b. These operational invariants organized the search for relevant information by the problem to solve or purpose to be achieved, and direct inferences.
V. The subject's cognitive functioning in a situation depends on the state of their knowledge, implicit or explicit.
a. It is therefore necessary to give great attention to cognitive development, their continuity, their breakups, the steps required, to the relative complexity of the kinds of problems, procedures, symbolic representations, the analysis of major errors and major discoveries.
VI. A concept takes its meaning in a single class of situations, and a situation is not dealt with the help of a single concept.
VII. Additive structures and multiplicative structures are currently the two main examples of conceptual fields studied in some detail, but science offers many different examples.
VIII. The homomorphism between reality and representation not to be sought first at the level of symbolism, but the level of operational invariants contained in the schedules. This is where lies the main base of the conceptualization of reality.
IX. Schemes organize the subject's behavior for a class of given situations, but organized both his action and the activity of symbolic representation, especially language, which accompanies this action.
X. The treatment of a new situation is accompanied by linguistic and symbolic activity. This activity is eventually internalized; it is increasingly important and manifests as the situation is newer and less automated processing, the very new problem solving is impossible without language, especially when the resolution requires new conceptualizations and the transformation of certain elements in objects of thought clearly identified
XI. In connection with these two functions, there is another function of language:
a. aid to thought and
b. the organization of action.
XII. This function supports itself on the basis of representation, but what it represents then are both elements of the situation considered, action, and their relationships.
XIII. The language and symbols play a role in both the conceptualization and action.
a. Without schemes and situations, would be rendered meaningless. BIBLIOGRAPHY
Brousseau, G. (1986) fondements et des méthodes mathématiques the didactique. Recherches
in didactique des Mathématiques
, 7 / 2, pp. 33-115.
Douady, R. (1986) Framesets and tool-object dialectic. Research Didactics
Mathematics, 7 / 2, pp. 5-31.
PIAGET, J. (1967). Biology and Knowledge, Paris, Gallimard (especially Chapter V on
epistemology basic levels of behavior).
Vernaud G. (1981) The child, mathematics and reality, Bern, Peter Lang.
Vygotski (1986) Language and Thought. Paris, Editions Sociales Messidor.
Traducción: Juan D. Godino
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FIELD THEORY OF CONCEPTUAL
Gérard Vergnaud 1 SUMMARY PART
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