Sobre ensino e aprendizagem de números negativos: o que apontam as pesquisas

Abstract

This doctoral thesis is the product of research that was developed in the Postgraduate Program in Education (PPGE) in the Teaching, Knowledge, and Professional Development line of research at the Federal University of Santa Maria (UFSM), within the scope of the Group of Studies and Research in Mathematics Education (GEPEMat). The research aimed to describe and analyze elements inherent to school education revealed in Brazilian research on negative numbers of stricto sensu postgraduate programs. In order to contemplate this objective, four investigative actions were defined: To list aspects that Brazilian research involving negative numbers describes as important about the Teacher who Teaches Mathematics; to identify what Brazilian research points out about the teaching of negative numbers; to understand the constitution of the historical movement of negative numbers through what is presented in Brazilian research; and to verify what the curricular documents indicated by Brazilian research guide on the teaching process of negative numbers. The theoretical principles used were based on the Historical-Cultural Theory, which includes, among other fundamentals, that learning takes place through social interactions; and more specifically on the Activity Theory, which shows that human beings are driven to act by needs, and it is through these processes that they humanize themselves and develop their Higher Psychological Functions. In the search for elements that reveal the specific object of the investigation, the learning of negative numbers, four isolates of analysis were defined: Teacher who Teaches Mathematics; the teaching of negative numbers; the historical movement of negative numbers and curricular documents. The mobilizing actions of the research took place through a Systematic Literature Review (RSL). Professional master's, academic master's and doctorate research was sought on CAPES Portal of Theses and Dissertations Portal and on the Digital Library of Theses and Dissertations that focused on learning negative numbers. After refinements and following the RSL steps, as well as the adoption of inclusion and exclusion criteria, 59 investigations that could reveal the essence of the investigated phenomenon in its entirety were selected. Regarding the teacher who teaches mathematics, the aspects that became evident refer to their career, to the organization of teaching, and to the knowledge about content and teaching. Regarding the teaching of negative numbers, it was revealed that it arises from the teacher's main activity which is teaching, the student's activity which is learning and the modes and instruments of teaching and learning. Regarding the historical movement of negative numbers, six epistemological obstacles and the studies of different civilizations and mathematicians on these numbers stood out and bring to light the essence of their historical process. Regarding curricular documents, it was found that, in particular, negative numbers appear in the PCN and BNCC, which express curricular guidelines and issues relating to the citizen expected to be educated. Based on the analysis of the four isolates, it is argued that teacher training, the intentional organization of teaching, knowledge of the historical movement, and guidelines for curricular proposals are determinant to promoting teaching aimed at learning theoretical knowledge about negative numbers.