Indícios de objetivação dos nexos conceituais da álgebra por professores dos anos iniciais do ensino fundamental em um curso online

Abstract

This professional doctoral research carried out in the Postgraduate Program in Scientific, Educational and Technological Training (PPGFCET) of the Federal Technological University of Paraná (UTFPR) has as its central question “how do teachers of the Early Years of Elementary School present signs of objectivation of the conceptual nexus of algebra during an online continuing education course?”. It was guided by the general objective of “analyzing signs of objectivation of the conceptual nexus of algebra by teachers teaching in the Early Years of Elementary School in a continuing education course organized in a Virtual Learning Environment”. The subjects involved in the research were teachers working in the Early Years of Primary School who teach Mathematics. To collect the data, a continuing education course was developed with synchronous tasks carried out between May and June 2021 using the Google Meet videoconferencing platform and asynchronous tasks using UTFPR Moodle Virtual Learning Environment. To organize the data, three steps of transcription were followed: firstly, all the passages of the recordings were transcribed, secondly, the segments with possible signs of objectification that met the intentionality of the research were selected and, finally, the images were inserted, as well as the chain of dialogues carried out by the participants, highlighting gestures and intonations. In order to understand the data, the theoretical and methodological foundations of Radford Objectivation Theory (2006; 2015; 2017) were adopted, seeking to recognize the conceptual nexuses of algebra systematized by Sousa (2004) and Panossian (2008, 2014): fluency and movement, quantities, control of quantities in the sensitive concrete, interdependence, language, variation, field of variation and generalization. The data showed that the method of conducting the course remotely had limitations due to the lack of technological resources, the short duration of the continuing education course and the timid participation of the teachers, despite them being encouraged to interact and having opportunities for actions in subgroups. The understanding of algebra presented by the teachers is close to a possible generalized arithmetic based on singular cases without recognizing the quantities involved and their variations. The influence of the National Common Curriculum Base (BNCC) was also noticeable, as teachers’ latent understanding considering the recognition of patterns and regularities in recursive and repetitive sequences of numbers or objects. The analysis of the data also pointed to evidence of the objectivation of the conceptual nexuses of algebra, especially by participant Joana, who sought to give new meaning to the process of organizing the teaching that had already been developed in her pedagogical praxis. She introduced ordered procedures to lead students to establish relationships between quantities, highlighting the conceptual nexus, with the aim of overcoming merely quantifiable questions that can be solved by counting and patterns of recursive or repetitive terms, making it possible to lead students to develop algebraic thinking, overcoming the arithmetic aspects of counting. Based on the continuing education course and the data collected, the Educational Product (PE) was created as an integral part of the research. The PE is a Didactic Material called “Teaching Algebra in the Early Years of Elementary School: a proposal for continuing teachers’ training” which is an e-book with a theoretical foundation, reports, videos, podcasts and bibliographical indications that guided the development of continuing education. It is hoped that this research will contribute to the scientific community as material to support thedevelopment of continuing education courses for teachers who teach mathematics in the Early Years of Primary School, considering algebra and its teaching.