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The Mathematics Enthusiast

Volume

18

Issue

3

Abstract

In this article, I carry out a qualitative metasynthesis of six doctoral theses that were directed by me, identifying the theoretical and methodological frameworks that support these researches, and how the articulations were made between different theories chosen. I also revisit the results achieved by the studies to highlight their relevance to the Mathematics Education area. This study, although not exhaustive, provides a vision of possible dialogs of Mathematics Education (or education) theories related to teaching and learning of mathematics and the Didactics of Mathematics. The diversity of theories and the specificities of each of them confirm the idea that a single theoretical tendency, or a single model, hardly ever explains and makes explicit all the phenomena involved in the teaching and learning processes of mathematical concepts. All the research works analyzed were used to study the epistemological, ecological, and economic dimensions, to identify the different forms of conceptions of a given mathematical object to help them in the didactic analysis of the findings. This study allowed us to identify, among other aspects, the reasons for being of the mathematical objects and the problems of their teaching. For teacher education, all mapped research, except one, has been supported in teacher education trajectories. The objective of these investigations is to familiarise teachers in initial or continuing education with these training trajectories as a didactic device that has the potential for their professional development, preparing them for an effective transition from the monumentalist paradigm to the world’s questioning paradigm. For the teachers’ training, the researchers presented didactic devices not based solely on the monumentalist paradigm, and somehow resorted to devices with PEP-FP-type structure.

First Page

385

Last Page

417

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