By Fabrice Vandebrouck (auth.), Fabrice Vandebrouck (eds.)

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**Extra resources for Mathematics Classrooms: Students’ Activities and Teachers’ Practices**

**Sample text**

Integrated within a conceptual structure of the work situation, these concepts relate to indicators (observables) and ways of acting (Vidal-Gomel & Rogalski, 2007). ). A number of versions of this concept can be found in the literature: zone of near development, zone of proximal development, or even zone of potential development. I have chosen to use “proximal” to refer to this zone. Our focus, coming from didactics, is actually on the development of knowledge and particularly the process of conceptualization, rather than on general logical processes.

We hypothesize that this activity may contribute to constructing the desired availability. We first distinguish simple and isolated tasks (SIT), or immediate applications of a piece of knowledge without adaptation or combination. A single piece of knowledge is used, potentially with simple replacement of general inputs by the given information in the context of the exercise. 36 WHY AND HOW TO UNDERSTAND WHAT IS AT STAKE IN A MATHEMATICS CLASS Different levels of knowledge use When tasks are simple and isolated (SIT), we speak of student work at the technical level.

We also do not consider extreme cases of students who do not participate at all in the class activities, whether because they refuse or because they do not understand the transformation expected for knowledge activities. These last students act in ways that are too different from the ways intended. By contrast, some of the studies presented introduce the concepts of action logic (success logic) or learning logic, according to the possible ways to include students in their own learning. The double regulation system from chapter 1 is only used in certain studies, most notably those that explicitly concern individual subjects.