THEORY OF CONCEPTUAL FIELDS (Part One)
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FIELD THEORY OF CONCEPTUAL
Gérard Vergnaud 1
Part 1. It is a psychological theory of concept or rather, the conceptualization of reality, to locate and study the affiliations and ruptures between knowledge from the viewpoint of conceptual content.
2.
also allows a. analyze the relationship between concepts while explicit knowledge,
b. operative invariants implicit in the subject's behavior in specific situations. Such as:
i. explicit theory
ii. relations between signifier and signified
3. The theory conceptual fields defined by its characteristics as a cognitive theory, because:
a. It aims to provide a coherent framework and some basic principles for the study of development and learning of complex skills.
b. provides a framework for learning.
c. is of interest to the teaching courtly.
4. The theory of conceptual fields is not specific to mathematics, but has been primarily developed to account for progressive conceptualization processes of additive structures, multiplicative number-space relations, and algebra.
CONCEPTS
FEATURES:
1. A concept can not be reduced to its definition, at least if you're interested in learning and teaching.
2. A concept has to make sense to the child. Because it is:
• It is a pragmatic process.
a. Pragmatics refers to the handling of problems can be both theoretical and practical.
b. Without prejudice to any analysis of the role of language and symbolism in the conceptualization, this paper is very important.
• It is essential for psychology and didactics.
3. If driving a concept is to properly consider the extent of the adaptive function of knowledge, should be given a central place to the forms it takes in the action of the subject.
4. Rational knowledge is operative or not such knowledge, because it can differentiate:
a) Classes of situations for which the subject has in his repertoire, at one point in their development and under certain circumstances, the skills required for relatively immediate treatment of the situation;
b) The types of situations for which the subject does not have all the necessary skills, which will require time for reflection and exploration, doubts, aborted attempts, and eventually leads him to success, or failure.
5. The concept of schema
• We call the invariant organization of behavior for a class of given situations. Because:
i. In the schemes is where to investigate the knowledge-in-act of the subject, ie the cognitive elements that allow the subject's action to be operative.
ii. The competitions are also held by organizers of behavior patterns.
iii. The student's cognitive functioning involves progressively operations are automated and conscious decisions that allow to take into account variables particular to the situation in solving school problems or practical life.
iv. The reliability of the scheme for the subject rests ultimately on the knowledge you have, express or implied, of the relationships between the characteristics of the problem and how to solve them based on their theoretical knowledge - practical.
v.
Automation is clearly one of the most visible manifestation of the invariance of the organization of action to solve problems. Because in addition, participates in solving these problems a series of conscious decisions may also be the subject of an organization invariant for a class of given situations.
vi. Explain the rules by which we reach the solution of problems is difficult and almost impossible for children and sometimes even in adults, although capable of performing the series of operations of various kinds for the achievement of its purposes . But there's always a lot of it is implicit in the schemes used for their solution.
• The schema concept is easily applied to the first category of situations for which the individual has the skills necessary to achieve its purposes,
• The second category considers the observation of students in problem-solving situation, the analysis of their doubts and mistakes, shows the behaviors are equally open situation structured by the schemes.
o These are taken from the vast repertoire of schemes available, and especially those related to the kinds of situations that seem to have a resemblance to the situation currently addressed.
or diagrams are only outlined, and attempts are interrupted before it was completed, several schemes can be evoked on, and even simultaneously in a new situation for the subject (or considered by him as new).
• An outline can also be applied by an individual to a class too large: thus put in a situation of failure and the subject must restrict the scope, and break the scheme in different elements that can be reassembled differently for different subclasses of situations, possibly by attachment of additional cognitive elements.
• In the scheme, all the action dynamic Organising the subject for a class of specific situations, is therefore a fundamental concept in cognitive psychology and didactics.
easily recognized • If a scheme consists of rules of action and anticipation as it generates a series of actions to achieve some goal, not always recognized is also composed in an essential way of operational invariants (concepts-in-action and knowledge-in-action) and inferences.
• A universal scheme is always a place that is associated with a class, and also that this class is not in general finite.
The operationalization of a concept must be experienced through a variety of situations, and the investigator must analyze a variety of behaviors and patterns to understand what it is, from a cognitive point of view, this or that concept
a) Each of these concepts involves several properties in effect, the relevance of which varies according to the situations to be treated.
b) Some may understand very quickly, others much later in the course of learning.
c) A psychological approach and teaching concept formation leads to consider a concept as a whole invariant used in stock.
d) The pragmatic definition of a concept set, therefore, at stake is the set of situations that constitute the reference for their different properties, and all the schemes put into play by the subjects in these situations.
In any case, the operative action, not everything in the conceptualization of reality. Because
a) not debate the truth or falsity of a statement fully implicit, and does not identify the aspects of reality to which attention must be paid without the help of words, statements, symbols and signs.
b) The use of explicit signifiers is indispensable for conceptualization.
This is what leads to the conclusion that a concept is a triplet of three sets:
C (S, I, G)
i. S: set of situations that give meaning to the concept (reference)
ii. I: set of invariants on which rests the operability of the schemes (the meaning)
iii. G: the set of linguistic forms and non-linguistic can symbolically represent the concept, properties, situations and procedures for treatment (significant).
• Study the development and operation of a concept, in the course of learning or during use, it is necessary to consider these three planes at once.
• No general bijection between signifier and signified, or between invariants and situations. Therefore can not reduce the significance or signifiers, or situations.
Red
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FIELD THEORY OF CONCEPTUAL
Gérard Vergnaud 1
ABSTRACT first part. THANKS FOR PARTICIPATING
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