This article presents the results of an evaluative research on the impacts of collaborative research in the evolution of the practices of researchers and associated teachers. It was a question of understanding how the collaborative approach was useful and relevant to the participants, how it enabled them to better take ownership of their role as an associate teacher, and how to transform their practices.

In this theoretical contribution, we interpret the notion of professional development in the light of concepts coming from cognitive development. This brings us to consider teacher training as not only having to allow the elaboration of skills, but also as having to encourage the development of new cognitive structures. We explore the theoretical concepts in relation with certain processes revealed by the reflexive texts of the students. Finally, we propose ways that could foster certain dimensions of global professional development in (...) learners, among which self-regulated learning, the focus on certain concerns and taking into account certain types of information. (shrink)

We study function fields over p-adically closed fields in the first-order language of fields. Using ideas of Duret [D], we show that the field of constants is definable, and that the genus is an elementary property.

We study first-order properties of the quotient rings C(V)/P by a prime ideal P, where C(V) is the ring of p-adic valued continuous definable functions on some affine p-adic variety V. We show that they are integrally closed Henselian local rings, with a p-adically closed residue field and field of fractions, and they are not valuation rings in general but always satisfy ∀ x, y(x|y 2 ∨ y|x 2 ).

We consider valued fields with a distinguished isometry or contractive derivation as valued modules over the Ore ring of difference operators. Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.