Marianna Bosch i Casabò

Mathematical modelling as a tool for the connection of school mathematics

We start introducing some aspects of the theoretical framework: the Anthropological Theory of Didactics (ATD). Then, we consider on the research domain commonly known as “modelling and applications” and briefly describe its evolution using the ATD as an analytical tool. We propose a reformulation of the modelling processes from the point of view of the ATD, which is useful to identify new educational phenomena and to propose and tackle new research problems. Finally, we focus on the problem of the connection of school mathematics. The reformulation of the modelling processes emerges as a didactic tool to tackle this research problem. We work on the problem of the articulation of the study of functional relationships in Secondary Education and present a teaching proposal designed to reduce the disconnection in the study of functional relationships in Spanish Secondary Education.

La formación matemático-didáctica del maestro de Educación Infantil: el caso de "como enseñar a contar"

The aim of this paper is to design a training program to be implemented amongst secondyear Teacher Training students at the Complutense University of Madrid. The purpose of this training program is to respond to the question: «How can kindergarten pupils be taught to count?» In order to tackle this question, a more basic question of an epistemological nature has to be considered and closely examined, i.e. «What constitutes counting in Kindergarten teaching?» The methodology used is based on the axiom that all training, and in particular kindergarten teachers’ pedagogical mathematical training, should be based on the dialectic between the raising of topics in professional work and the construction of responses or response elements to these topics. This methodology, with an essentially qualitative character, has been based on the construction of an environment in order to describe the training component’s central questions to which Kindergarten teacher training must respond. The most important results of this investigation are the following: 1) the designed and tested training program allows topics related to «doing mathematics» to be integrated with those that refer to «teaching and learning mathematics». This result is a very important one since it demonstrates that mathematics teacher training programmes are able to integrate these two, previously separate dimensions; and 2) the methodology used for designing the training process has revealed two main issues. On the one hand, the central role of Didactics of Mathematics in teacher training programmes and, on the other, the theoretical and practical advantages of connecting the proposals and results obtained in two distinct, although very close, pedagogical theories: The Theory of Didactic Situations and the Anthropological Theory of the Didactic.