O desenvolvimento do pensamento computacional e algébrico na formação inicial de professores de matemática: um estudo de caso com Scratch

Abstract

Nowadays, there is a significant interdependence between physical and digital spaces that tends to expand over time. This relationship has changed the way we live, think and act within our society, the school is not immune to these changes. It is necessary to discuss how to integrate digital technologies into the school routine, to prepare students to live in this society highly dependent on the cyberspace. For this integration to occur, it is necessary to pay attention to teacher training. In particular, we turn our attention to the initial training of Mathematics teachers. Given this context, this study sought to answer the following question: What aspects of Computational Thinking and Algebraic Thinking Mathematics teachers in initial training manifested by realizing activities with Scratch? For this we conducted an exploratory case study with a mixed approach. The subjects of this research were 14 academics of the fourth years, full and night periods, in the initial training of Mathematics teachers of a Higher Education institution in the state of Paraná. Empirical data were collected during a didactic sequence developed by the authors and validated by the Research Group on Educational Technologies in Mathematics (GTEM). The data collection instruments used were pre-implementation questionnaire, algorithms for constructing a square and a triangle in native language and in Scratch. Qualitative data were analyzed according to Bardin's Content Analysis, while quantitative data were analyzed using simple percentages generated from the frequencies of the categories. Based on Radford, Brennan and Resnick we outline two general aspects of the algorithms: algebraic and computational. Algebraic aspects are subdivided into objectification, symbolization and generalization, while computational aspects are subdivided into structure and debugging. These aspects were analyzed using indicators produced during this research. Among the results obtained, we highlight that: a significant portion of the subjects claimed not to know Scratch, as well as fundamental concepts of Computational and Algebraic Thinking; the algorithms with more complex structures were produced by students who had previous experience with programming or showed interest in this topic; the programming activity proposed in this research allowed us to identify three types of difficulties for subjects in relation to programming and reflect on their causes, the difficulties occurred in relation to: understanding of mathematical objects, symbolization and elaboration of algorithms; we observed that in some cases the Scratch interface and structure helped students in the elaboration of the algorithm, since these subjects were not able to elaborate the algorithm in native language. Finally, we highlight that in this study we show that it is possible to address these themes in the initial training of Mathematics teachers without carrying out long and complex programming projects, since even short projects, such as the design of a square, work with a variety of concepts and practices of those thoughts.