The extended theoretical framework of Mathematical Working Space: comparison with the Anthropological Theory of the Didactic and use in physics or chemistry
Résumé
The theoretical framework of the Extended Mathematical Working Space (Extended MWS) allows to analyse the tasks implemented during a few steps of a physics or chemistry modelling cycle. The analysis of the work is also carried out with the anthropological theory of the didactic (ATD) to compare the two theoretical frameworks in the a priori analysis of the tasks to be performed by the students. Then, only the extended MWS model will be used for post-analysis. A sequence of teaching special relativity using a diagrammatic approach in the final year of high school in France (grade 12) is first studied. The Minkowski diagram is used with the GeoGebra dynamic geometry software. The work on the chronological inversion of events in two reference frames is done with students during problem solving in a relativistic context. The analysis using the extended MWS theoretical framework makes it possible to highlight the learning advantages of this diagrammatic approach during a complete didactic engineering. The theoretical framework of the extended MWS is also used in a teaching sequence dealing with the chemistry of solutions in secondary education, which includes an experimental part. The construction of graphs allows both to work on the notion of stoichiometry with GeoGebra and to deduce the mass concentration of a pharmaceutical product. The methodological framework used is also didactic engineering. We will see that it is possible to propose new strategies when using GeoGebra with another semiotic representation register to work on problem solving.