What is a didactical situation in mathematics?
A didactical situation in mathematics is a project organized so as to cause one or some students to appropriate some piece of mathematical reference knowledge. (The organizer and the student may be individuals, a population, institutions, and so on.)
Where did the theory of didactical situations come from?
The Theory of Didactical Situations (named TDS in this volume) began to develop in the 1960s in France, initiated by Guy Brousseau who has led its development since that time.
Why do we need a 'didactical variety' of concepts?
He stated the necessity to consider a “didactical variety” of concepts: the study of (didactical) situations must in the end allow the derivation or modification of the necessary concepts currently imported from other scientific fields (Brousseau, 1997, p. 24)
Is didactics of mathematics a basic research?
Considering the definition of “basic research” by the International Council for Science, didactics of mathematics is considered by Brousseau and Artigue as a basic research:
Didactic Engineering
The first principle (see above) is very important for didactic engineering: to every piece of mathematical institutional knowledge there corresponds a collection of situations which can be resolved using this knowledge as situational knowledge. In Brousseau’s perspective, didactic engineering lays in the correspondence between a sequenceof situatio
from Institutional to Situational Knowledge in Didactic Engineering
In this text I will develop an example about cardinality. The teaching of early number knowledge involves lots of aspects: memorization of oral number sequence, relationships between successive numbers, etc. We will focus here on discrete quantity, that is one of the aspects related to the general concept of cardinality. From a large mathematics pe
Action Situation
The first and the more general schema of situation is the ‘action situation’. The studentFootnote 2 interacts with a milieu and a stake that have no intention toward this student (Fig. 1). This figure introduces non only an action and a decision of the student but also an anticipation. In fact if the student has a constant and direct access to both
Validation Situation
There is thus another situation that represent another step toward mathematical knowledge. The messages are now objects of study in the validation situation, they are considered as “statements”, the question changed the focus from the result of and action informed by a formulation to the discussion of the formulated messages. For example, in the ca
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