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|Didactics as Desing Science
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|The concept of documentational genesis (Gueudet & Trouche, 2009) is a new theoretical concept that seems to be a useful analytical tool for studying the development of mathematics teachers. The concept of documentational genesis can be considered as an analogy of the concept of instrumental genesis (Rabardel, 1995; Trouche, 2005b) into the field of mathematics teacher education. In this new approach the focus is on the activities that the teacher develops outside the classroom, but that influence his work in the classroom. In particular the focus is on the documentation work of the teacher, i.e. the interaction of a teacher with a set of elements that shape and define his work in the classroom; for example, to draw examples and exercises out from a textbook for his mathematics lesson plans, to look up his own notes of previous courses, to analyze the mathematical productions of his students, to listen to suggestions or criticisms of his fellow teachers and his students, to study a curriculum reform to be implemented in his school, etc. This set of elements with which the teacher interacts in order to carry out his documentation work is called resources. There are situations where the interaction between mathematics teachers and resources is not spontaneous. In these contexts there is a need for organizing and arranging the set of resources that the teachers interact with, in order to develop specific aspects of their professional knowledge. Here I am referring to the in-service mathematics teacher education programs. Inspired by the concept of instrumental orchestration (Trouche, 2004; Trouche, 2005a), the aim of this paper is to illustrate and to argue that at least in the field of mathematics teacher education, it make sense and is relevant to use and to develop the concept of documentational orchestration. I will highlight the necessity of studying in a joint way this concept together with the 11 concept of documentational genesis. Particularly it is shown how the instrumentalization and instrumentation processes that constitute a documentational genesis, can be taken as a basis to guide the refinement and redesign of an orchestration. The empirical evidence supporting the arguments are taken from an online educational program for mathematics teachers, that is to say, the structure and operation of the program is based on the use of the Internet and its associated tools.
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