The Idoine or Suitable MWS as an Essential Transitional Stage Between Personal and Reference Mathematical Work

In the context of teaching and learning processes and for a given institution, the personal mathematical work undertaken by students is quite different from the reference mathematical work. This is evident when a new field of study is planned, but it is also true for a field which has already been taught. The notion of idoneity, as a recursive adaptation process, is a strong idea that makes it possible to gradually bring these two forms of mathematical work closer together, or at least to better understand their divergence. The purpose of this chapter is to present how idoine or suitable Mathematical Working Spaces emerge. In this way, it is possible to look at the interactions between teachers and students, adaptation to specific contents and to given mathematical domains. This adaptation involves the choice and design of predetermined tasks enabling both the progress of conveying knowledge by teachers and the progression of the students toward the expected work to be monitored.KeywordsSuitable MWSActual and potential MWSMathematical task designMathematical work and co-workingBlockages and confinement in MWS