Sequência Fedathi no ensino da Teoria de Grupos Algébricos: uma análise da mediação docente sob o olhar da Teoria APOS (Action, Process, Object, Schema) de Ed. Dubinsky

Abstract

Abstract Algebra is a highly relevant subfield of Mathematics, present in undergraduate programs in Mathematics (both teaching and bachelor's degrees), Physics, Computer Science, and Engineering. However, it is common for this area to be poorly received by students, who often face significant challenges in both teaching and learning, making the teaching process particularly demanding when addressing such content. In light of this scenario, this research aimed to analyze how teaching practices based on the Fedathi Sequence can support the development of the mental structures of action, process, object, and schema, according to the assumptions of the APOS Theory (Action, Process, Object, Schema), during the learning of the algebraic group concept in the Mathematics Teaching degree program at IFCE – Cedro Campus. Methodologically, the research was classified as qualitative in its approach, applied in nature, exploratory in terms of its objectives, and as action research regarding its procedures. The theoretical framework was based on studies of the Fedathi Sequence and the APOS Theory. The research was conducted at the Federal Institute of Education, Science and Technology of Ceará (IFCE) – Cedro Campus, involving seven students from the seventh semester of the Mathematics Teaching program, enrolled in the course Algebraic Structures during the 2022.2 academic term. Didactic situations based on the Fedathi Sequence were proposed to promote the development of the students’ mental structures while studying the algebraic group structure. The results showed that applying the Fedathi Sequence had a significant impact on the participants’ learning, fostering the development of the mental structures of action, process, object, and schema, in line with the APOS Theory. The teaching practice supported by this methodology encouraged students to engage cognitive mechanisms such as interiorization, coordination, encapsulation, reversibility, and generalization, facilitating the construction of algebraic concepts as they progressed through the abstraction levels proposed by the APOS Theory. We therefore conclude that the thesis is legitimate and subject to validation: that teaching practices based on the Fedathi Sequence support the development, by Mathematics teaching students, of the mental structures of action, process, object, and schema from the APOS Theory during the learning of algebraic group content.