O desenvolvimento do pensamento teórico acerca do conceito de função em situações desencadeadoras de aprendizagem

Abstract

This study, assuming historical-dialectical materialism as the theoretical-methodological framework that guides understanding and analysis, investigates the organization of teaching for the development of theoretical thinking. It is supported by the constructs of Cultural-Historical Theory, Activity Theory, and Developmental Teaching Theory. The organization of teaching is materialized through the Teaching Orienting Activity, in which learning triggering situations are implemented by means of a virtual story, inspired by the logical-historical genesis of the function concept, with the aim of simulating contexts in which this concept becomes necessary. The general objective consists of analyzing the development of theoretical thinking regarding the function concept based on the significations produced by students in learning triggering situations. As specific objectives, it seeks to analyze the role of mediation elements present in the organization of teaching in the production of these significations, as well as to understand how these significations constitute the movement of theoretical thinking about the function concept. The research is guided by the following question: how do the significations produced by students in learning triggering situations allow for the understanding of the development of theoretical thinking about the function concept? The research adopts a qualitative approach, developed within the workplace of the teacher-researcher, involving 24 first-year high school students from a state school in Minas Gerais, Brazil. The data collection instruments included student records, audiovisual recordings, and field diaries. Data analysis involved the transcription and organization of records, followed by the grouping of indicators and preindicators into cores of signification. This process explored internal relations (intra-cores) and interactions (inter-cores), considering the significations regarding the function concept. The results were organized into three cores: the first addresses the emergence of relations of dependence and causality; the second deals with the constitution of the variable concept and its field of variation; and the third covers generalization and synthesis expressed in multiple representations. In the analyzed cores, an articulation between quantitative and qualitative aspects of the phenomenon under study is observed, as well as significations expressed in different forms of representation, which indicate approximations to the nexuses of interdependence, fluency, movement, and variation. These significations reflect the ways in which students engaged with the function concept and suggest that the articulation between conceptual genesis and the Teaching Orienting Activity contributed to the creation of a distinct classroom dynamic, aligned with the proposed teaching organization. Such significations configured collective constructions that sought to express the essence of the function concept, creating conditions that distance themselves from traditional practices. It is observed, however, that the students remain in a conceptual formation process in transition, marked by empirical and partially developed traits. In this sense, the investigative path culminated in the educational product “Function Concept: A Journey of Changes and Possibilities,” a teaching unit that materializes this proposal for reorganizing teaching toward the development of theoretical thinking, aiming for conceptual appropriation by the students.