Abstração reflexionante com uso de material dourado mediada pela engenharia didática

Abstract

This work aims to evaluate the use of golden material with a focus on reflective abstraction, applying Didactic Engineering in teaching Mathematics to students in the 5th year of Elementary School. The research was carried out in a school in the State Public Education Network, located in the South Zone of Manaus. The investigation starts from the question of which didactic sequences aimed at teaching mathematics that propose the use of golden material, have the potential to develop reflective abstraction? And can they be supported in an intentional pedagogical environment guided by the Theory of Didactic Situations? Great was the journey that culminated in the child as a citizen with a subjective right to education and who needs logical-mathematical instruments, especially in the 21st century ('bombardment' of diverse multimedia content), to develop intentional cognitive structures, capable of leading them to the intelligence of filtering and appropriating this content, throughout its historical process of physical and social maturation. In this sense, the approach taken is qualitative with a dialectical method. As for its nature, it is considered applied research, and the objectives are classified as descriptive research. The procedures are guided by Didactic Engineering. Regarding the results, it was evident that the Northern Region of Brazil does not use golden material as an instrument to develop reflective abstraction and does not make Piaget's works of this concept available in its public libraries; It was also identified that the use of golden material has been more focused on Special Education. Regarding the analysis of the textbooks used, it was observed that they present a gap regarding the subject related to the object of this investigation. In the Preliminary Analysis of Learning Difficulties and Obstacles, according to the students' opinion, in relation to the subject used in research on the Decimal Number System for practical life, they are divided: whether they recognize that they have difficulty in learning or simply state that they do not have difficulty in learning the content. In the a posteriori analyses, in didactic sequence 01, the reflective abstraction of reflection was found at a frequency of five within a universe of eight students evaluated; as well as in didactic sequence 02, the frequency of five occurrences of reflective abstractions against four occurrences of empirical abstractions, and, finally, in didactic sequence 03, eight occurrences of reflective abstractions of reflection in a universe of nine evaluated students, ratifying that the use of golden material It has the potential to promote in students, with the mediation of Didactic Engineering, the development of their critical sense regarding the choice of other cultural goods offered to them in a multimedia environment because it promotes the exercise of reflection and reflection. Therefore, the use of golden material with a focus on the development of reflective abstraction is possible in an intentional pedagogical context and can be a teacher's strategy in public schools for student appropriation of mathematical cultural goods. Future research, in this sense, would provide several consequences to be mapped and deepened.