Abstract
The aim of this research is to identify some conditions and constraints of the transposition of some didactic praxeologies in teacher training. For this purpose, an inquiry (in the sense of the anthopological theory of the didactic) on the topic of functions has been implemented during the first year of secondary school in France (15-16-year-old students) by a teacher trained within the framework of the ATD. The inquiry led by the teacher is divided into two parts: the first one aims to teach the notion of function as a relation between magnitudes and its optimisation by using graphic and algorithmic techniques; the second one focuses on the study of quadratic functions and resolution of equations. This paper presents the analysis and results related to the first part. The analysis of the inquiry unveils some didactic phenomena concerning the realisation of the technological-theoretical moment that suggest ways of developing teacher training.
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Notes
- 1.
This research is an extract of a master’s dissertation supervised by Michèle Artaud at Aix-Marseille Université, which is is available at: https://irem.univ-amu.fr/sites/irem.univ-amu.fr/files/public/alfieri_memoire_enligne.pdf.
- 2.
Such a table is elaborated by a calculator for a given function: it shows the list of the x-values and the list of the corresponding f(x). The x-values are established by the user, who chooses the distance Δ between two consecutives x-values.
- 3.
In the ATD, a system is a piece of nature that we wish to study by questioning a model that should provide us information on the system.
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Alfieri, C. (2021). Modifying Teachers’ Didactic Praxeologies in the Perspective of the Paradigm of Questioning the World: The Case of the Technological-Theoretical Moment. In: Barquero, B., Florensa, I., Nicolás, P., Ruiz-Munzón, N. (eds) Extended Abstracts Spring 2019. Trends in Mathematics(), vol 13. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-76413-5_1
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