action, what is usually called the “instruction” (the initial guidelines of the task pupils have to achieve) is only one of the tools that influence the process of devolution in a learning situation, a somewhat excessive power to act is granted to those instructions, as if the teacher could entirely constrain the action of the students. However, any human action, even if it results from a prescription, is always the object of an interpretation that transforms the prescription, an interpretation that, even if it actually causes the reality to deviate from the prescribed, is the mark of the subject’s investment in the situation (Clot 1999). Moreover, in the school context, especially in elementary school, the implementation of teaching situations involves objects, and, in particular, material objects, objects of the world that “evoke the uses and affects that [the pupil] already knows” (Laparra and Margolinas 2016, p. 176). The teacher’s efforts to create a situation in which the student encounters situational knowledge that is appropriate to institutional knowledge can be nullified by the students’ previous uses (academic or otherwise) of objects that the teacher has, sometimes by chance, used (e.g. see, in particular, Chapters 1 and 2).
The student’s role in the devolution process
“The student is well aware that the problem [situation] was chosen to help him/her acquire new knowledge” (Brousseau 1998, p. 59); however, the student does not know the teacher’s project, and, especially in elementary school, does not always know how to clearly identify the school subject concerned (Reuter 2007). Moreover, the student cannot know in advance the knowledge in question, which is one of the paradoxes of devolution:
The teacher has a social obligation to teach everything necessary about knowledge. The student – especially when he or she is failing – asks him or her to do so. So the more the teacher gives in to these requests and reveals what he or she wants, the more precisely he or she tells the student what he or she needs to do, the more likely the student is to lose his or her chances of obtaining and objectively observing the learning that he or she is actually trying to achieve (Brousseau 2003, p. 9).
One of student’s first roles in the devolution process is therefore to accept trusting the teacher, who is responsible for the situations he or she asks the student to invest.
The student is confronted with a milieu that he explores according to his previous situational knowledge. This interaction with the environment mobilizes or provokes the construction of situational knowledge whose nature depends on the actual situation. The student’s point of view is the opposite of the teacher’s: he or she must arrive at the institutional knowledge the teacher started with to create his or her teaching project, by constructing situational knowledge in a situation. However, numerous works (see, for example, Margolinas 2004; Coulange 2012; Clivaz 2014) show that very often the situations set up by the teacher lead some students:
– to invest a situation not foreseen and/or not observed and/or not favored by the teacher;
– to encounter useful but unrecognized situational knowledge that is not appropriate to the target knowledge;
– to find themselves in a gap with the knowledge encountered through institutionalization.
I insist on the fact that such situations are not “pathological” and it is undoubtedly their recognition and regulation rather than their avoidance that must be the object of our attention. Indeed, the student gives the teacher a part of his or her activity to see, which the teacher observes and interprets, based on his or her knowledge (Vignon 2014). The student thus informs the teacher, more or less voluntarily, about his or her own interpretation of the situation in place, which can help the teacher (Mercier 1998), when possible, to redirect the devolution of the programmed situation or at least to imagine a new future situation.
However, the clues which, for an external observer who is a tutor of mathematics, can be interpreted as the investment, by a student, of a situation installed by the teacher without the latter’s knowledge, or can be interpreted by the teacher as proof of inattention or of the academic or disciplinary difficulty of the same student, independent of the situation.
One of the student’s difficulties is that the situational knowledge that he or she actually encounters in a situation, the knowledge that he or she has managed to develop a little and that he or she would like the teacher to recognize and explain, is not always the knowledge that is institutionalized.
Open conclusion on the processes of devolution and institutionalization
Wondering about the devolution process thus leads to questioning the institutionalization process. These processes, when understood as a movement between institutional knowledge and situational knowledge (devolution: from institutional knowledge to situational knowledge; institutionalization: from situational knowledge to institutional knowledge) appear to be interdependent. The teacher, at the moment when he or she conceives a project of teaching, is led to install situations that summon situational knowledge (process of devolution); this situational knowledge, which is invested by the student, will be progressively transformed (formulated, validated, formalized, memorized, etc.) into knowledge in the institution of the class and finally be brought together with knowledge from other institutions (process of institutionalization).
This description might suggest that these are processes that flow smoothly, but this is generally not the case:
– The situations put in place more or less deliberately by the teacher and invested by students may not call upon a situational knowledge that is appropriate to the knowledge to be taught, in which case it causes a rupture for these students, in their expectation of legitimization of the situational knowledge they have invested during the situation.
– The situational knowledge used by students in situations, especially when they do not correspond to what the teacher has anticipated, may be ignored by the teacher who may believe that the student is not engaging any situational awareness (that he or she is inattentive, that he or she has not understood the instruction, etc.).
If these phenomena occurred only rarely and if they almost never involved the same students, it would have little effect. However, there seems to be a recurrence of phenomena that I have called “didactic bifurcations” (Margolinas 2005), which often involve students participating in the devolution process by investing in unforeseen situations (Margolinas and Thomazet 2004; Margolinas and Laparra 2008).
This observation leads us to reconsider knowledge. Indeed, there are many institutions and they all produce knowledge, but some is not recognized as such, in particular knowledge that strongly engages bodies in the co-presence of other bodies: the knowledge of orality (Laparra and Margolinas 2016). The didactic transposition (Chevallard 1985) studies and describes the transformations necessary for this knowledge to be considered, in another institution (the school institution), as knowledge to be taught, which is historically and socially constituted as “school disciplines”. The didactics of the disciplines were historically constituted with reference to the disciplines of secondary education, which was undoubtedly an initial necessity in order to affirm the specific character of the study of the transmission of each field of knowledge. However, knowledge, which is at the heart of the didactics of each “discipline”, is thus defined externally to the didactics, which is not a satisfactory solution at the epistemological level.
Concretely, by working for 15 years with a French language tutor (Marceline Laparra, CREM, University of Metz), several phenomena have come to light that lead to questioning of these disciplinary boundaries. In particular, we have shown (Margolinas 2010; Laparra and Margolinas 2016) that the enumeration, pointed out by Brousseau (1984) and characterized by Briand (1999), provides leads for the analysis of recurrent difficulties of students in a large number of school situations, particularly in French language classes. The fact that enumeration appears only marginally in official texts (in France, only once, in the 2015 Cycle 1 curriculum, in relation to numbers) and that it is associated only with counting, prevents teachers from conceiving a link between the differences they observe in student procedures