Student as a producer of knowledge- Teacher as an intellectual worker- Teacher as a producer of knowledge- Dialogue between teachers and researchers- Didactic research aiming modifying the conception
Since we work in Mathematics Education we have in our horizon the idea that an education with sense in the present society must offer the students the possibility of having access to basic forms of thinking and producing knowledge. From our perspective this supposes the idea of student like a producer of knowledge in the classroom. The conception of the teacher work with which historically the school was organized must then be reviewed. What would this modification be? What questions would raise to the research in Mathematics Education the necessity to redefine the work of the teacher? Besides the necessary actions of the public policies, what type of research would contribute to think of conditions so as new tasks of the teacher could be settled in the practices? Tasks that seem to be unavoidable if we wish the students conquer a position of intellectual autonomy as part and result of their experience of learning.
Firstly we will try to describe the teacher work as we imagine it today, taking into account that the research should contribute to produce modifications, questions and oppositions to this description. Secondly, we will outline lines of work that are opened from the raised description.
What basic modifications of the teacher work would be considered? On one hand, the teacher should have an anticipation of the reasons by which he/she would expect the students to have a producing position in his/her didactic project. This anticipation modifies the historical conception of planning, usually conceived as an organizational task of distribution of activities in the time. The planning from a production perspective includes the acknowledgement that there are didactic conditions that favor or not to deal with certain ideas in the class. It is a provisory anticipation because the effective route will be modified based on the strategies, discussions and ideas that the students are putting into practice.
On the other hand, it is expected that in a class opened to production emerges an amount of strategies and problems by the students that the teacher will have to interpret in order to interact with them. That is the way to make the work of the students constitutive of the knowledge that emerges in the classroom. The reflection a posteriori on the productions of the students and the interchanges in the class becomes then an indispensable practice. This analysis involves mathematical and didactic dimensions.
The two previous tasks - anticipation of the project and later analysis- modifies the role of the teacher inside the class. It is not about adding to the task "of giving a class" the one of planning and the one of making a later analysis. Building a bond of intellectual interchange with the students involves a way of working in the classroom different from the one that historically established. This last aspect is perhaps the one that has been worked the most in the didactic research and that is why we will not develop it in this conference.