Ensino-aprendizagem de espaços vetoriais via exploração-resolução-proposição de problemas: Uma experiência na Licenciatura em Matemática

Abstract

The current research investigates the contributions of Exploration-Solving-Posing of problems aligned to the Multiple Representations in Algebra in what concerns the teaching-learning process of the concept of Vectorial Space and other significant concepts (Addition and Multiplication by Scalar Operations, Linear Subspace, Linear Combination, Linear Dependency, Generated Subspace, Linear Transformations, and Linear Operator) on the initial teacher education of mathematics teachers. The research carries out a qualitative method (BOGDAN; BIKLEN, 1994; YIIN, 2016), in the perspective of a pedagogical research (LANKSHEAR; KNOBEL, 2008). The study has been developed in a workshop with students from distinct semesters of the Mathematics Teaching Course and also with a student from a Physics Teaching Course, both from public universities in the Brazilian state of Paraíba. The lectures in the workshop were carried out remotely (due to the pandemic situation caused by the virus Sars-Cov-2), throughout the application WhatsApp (BARBOSA; CARVALHO, 2018). Furthermore, this strategy supports the data gathering through planned activities highlighted from Friedlander and Tabach (2001), and it was developed with the teaching-learning methodology of Mathematics and Exploration-Solving-Posing of problems (ANDRADE, 1998; 2017). In order to support this method and the data gathering, the research set up and delivered to participants a questionnaire about the workshop development and its methodologies. The analysis tool of interviews considered the Discourse of the Collective Subject – DCS (LEFÉVRE; LEFÉVRE, 2005), an instrument of analysis recently developed in Brazil. The descriptions and investigation of the meetings and interviews point out, throughout the workshop, that the students were able to understand the importance of how the structural conception of Linear Algebra has to the comprehension of mathematical concepts of elementary, high, and superior education. The research highlights, on this perspective, the relevance of the mediation-refutation of the researcher carried out to the students on the Workshop, mainly on the dialogues, in which the students point out the interactions made them consider their own process of teaching-learning and about their future acting as teachers on the elementary education. Considering this context, while concerning the Vectorial Space, it is clear the advance on teachers, mainly to express the problem resolutions on the mathematical language. Concluding, the results highlighted that the Multiple Representations in Algebra and the transition between them support a teaching-learning of Vectorial Spaces with better understanding. In addition, the methodology of mathematics teaching-learning throughout Exploration-Solving-Posing of problems contributes with a conception on the teaching of Vectorial Spaces.