AVENTURAS AO ENSINAR (E APRENDER) MATEMÁTICA NA TRANSIÇÃO DE PARADIGMAS: DESENHANDO PERCURSOS DE ESTUDO E PESQUISA COM (FUTUROS) PEDAGOGOS

Abstract

This thesis is the result of the development of a Study and Research Path (SRP) that sought to answer the following guiding question: How does a study and research path occur in the paradigm shift with (pre-service) teachers who teach mathematics in the early years? Ultimately, what (re)constructions are produced, or not, in the praxeological apparatus of (pre-service) teachers toward the Paradigm of Questioning the World? To provoke a paradigm, shift in teacher education, we mobilized the Anthropological Theory of Didactics (ATD) and, to complement this theoretical lens, some elements from Paulo Freire theories in Pedagogy. The thesis is interwoven with two works by Lewis Carroll, Alice in Wonderland and Alice Through the Looking Glass, which leads us to weave together the Dialectic of Art and Mathematics Education. The SRP was developed with teachers and prospective teachers of the primary grades from different regions of Brazil, with meetings held online via Google Meet between October 2021 until September 2022. The format of this thesis has a dual meaning. On the one hand, it presents itself as a map of questions and answers, a tool that allows for the presentation of the knowledge produced throughout the SRP. Consistent with this proposal, the Questions/Answers expressed on the map are connected through narrative pathways, which help weave the texts together and provide a way to ensure digital accessibility in reading the thesis map itself. On the other hand, the presentation in map format led us to consider it a multipaper text, with the potential to mobilize the reception-diffusion dialectic of knowledge, with some texts potentially being published in journals in the fields of Education and/or Mathematics Education. The results highlight the difficulty of a paradigmatic shift due to conditions and constraints arising from different levels of the didactic codetermination scale, such as demands arising from work and/or the higher education programs to which they were also subjected; teaching and learning practices culturally rooted in the paradigm of visiting works; and challenges in shifting from a retrocognitive to a procognitive attitude. Through the analyses, it was possible to identify (re)constructions in the praxeological apparatus of the (pre-service) teachers involved, as is the case with the doctoral student's own relationship with aspects arising from inclusive education, especially in the context of the specific needs of people with visual impairments. This allows us to infer that a SRP that takes into account some Chevallardian dialectics, as well as the educator-student dialectic, which is constituted through affective sensitivity in openness to dialogue, highlights the conditions and constraints for its implementation in an inclusive teaching system, in addition to provoking (re)constructions in the praxeological framework of (pre-service) teachers involved in this path.