DESENVOLVIMENTO DO PENSAMENTO ALGÉBRICO EM ESTUDANTES DOS ANOS FINAIS DO ENSINO FUNDAMENTAL: UMA PESQUISA BASEADA EM DESIGN - Melo, Charles Bruno da Silva (2023)
This is a research that aimed to analyze the development of algebraic thinking in students of the Final Years of Elementary School from the theoretical-methodological assumptions of Research Based on Design. It was used the stages proposed by Reeves (2000): educational problem description, description of an artifact development from a guiding theory, pedagogical intervention description and design principles description, to conduct the research. The collaborators group was composed of six professionals, besides the researcher. From the classroom everyday life, reports and reflexions from teachers and SAEB data analysis, the identified education problem have been linked to how to promote the algebraic thinking development in Final Years classes in the city of Cerro Branco. The theoretical grounding was established through a literature review, that implied on the necessity to build our description to the algebraic thinking , on changes in the process of teaching and learning the algebraic concepts and in the search for possibilities to minimize the difficulties and develop this way of thinking. Having the conceptions of Lins (1992); Radford (2011); Blanton and Kaput (2005); Kieran (2004); Kieran, Pang and Schifter (2016); Fiorentini, Miorim and Miguel (1993) and Fiorentini, Fernandes and Cristovão (2006), our algebraic thinking description had been defined as the meaning construction to the mathematical objects and the algebraic symbolical language, from the capability to establish relations/comparisons, shape, generalize and represent/operate with the unknown. To structure the pedagogical artifact, the researcher selected and adjusted fourteen questions that focused the BNCC abilities development allied to the capability of think algebraically. The questions were refined and discussed by the group, analyzing the difficulties and strategies used in the resolution, the possibility of application in 8° and 9° grade Elementary School classes and contributions to improve the feasibility in classroom, providing a structured didactic sequence. The pedagogical intervention was realized in 2022, in two municipal public schools with 8° and 9° grade classes, featuring two applications. The data collected were descriptive, extracted through participant observation, field journal and document analysis. The group looked forward to evaluate the didactical sequence contributions to promote the algebraic thinking in a way to refine it, beyond the aspects related to application in classroom. Both in the first as in the second intervention, in questions were mobilized, even as a partial way, at least one ability of algebraic thought. Relating the application records and the SAEB data, both show the same failures in the development of abilities related to the algebraic thinking. It is necessary to expand the approaches in the process of building templates and in the connections between the algebraic and geometric representations. The principles of design were: the necessity to embrace a description of algebraic thinking; the constructed didactic sequence promoted the development of this way of thinking, besides being a diagnostic tool; even with a educational context opposed to the ideal and with learning gaps, it was possible to affirm and verify manifestations of this way of thinking and that is necessary for the teaching job to be facing the mediation, incentives and a collective planning in the search to the algebraic thinking development. The PBD proved to be effective to promote the algebraic thinking, once it made possible a collective planning, guided by discussions and exchanges, promoting professional development, beyond the construction of a didactic sequence, which can be also used as a tool to help the teaching and learning process.