O processo de apropriação do conceito de multiplicação à luz da teoria histórico-cultural

Abstract

This study focused on the learning of the concept of multiplication through Learning-Triggering Situations (LTS). In order to address the research question “How does the appropriation of the concept of multiplication by fourth-grade elementary school students occur through the implementation of LTS?”, the study aimed to identify and analyze the procedures and strategies used by students to solve multiplication-related problems proposed in the LTS, as well as to examine what students’ actions reveal about the appropriation of the concept of multiplication as they engage in these situations, grounded theoretically in Activity Theory. This is a qualitative study with a descriptive and interpretive approach. Based on an everyday emergent situation, four LTS were designed encompassing the following conceptual nexuses of multiplication: repeated addition, proportionality, combination, and rectangular arrangement. These situations sought to promote student actions aimed at solving problem situations which, through this process, could foster conceptual formulations and reformulations, syntheses, and other actions generated by learning motives established by the students during interactions. Seven fourth-grade students from a full-time municipal elementary school located in the interior of the state of São Paulo participated in the study. The LTS were implemented during after-school hours, in the afternoon period, as part of a mathematics workshop, and were carried out over four meetings, each lasting approximately three class hours, totaling about twelve class hours. Data collection instruments included field notes with the researcher’s observations, audio and video recordings, and student-produced materials, such as response sheets related to the actions performed. For data analysis, episodes were constructed that highlighted the process of appropriation of the concept of multiplication by the participants. The findings revealed that the participants employed different strategies and demonstrated varying levels of understanding of the concept of multiplication; thus, many students are still in the developmental phase of theoretical thinking. Thus, it can be concluded that further learning activities with students are necessary in order to support their gradual transition from empirical thinking to theoretical thinking. As part of the outcomes of this study, an e-book was developed for teachers working in the early years of elementary education, focusing on the learning of the concept of multiplication through Guiding Teaching Activity and Learning-Triggering Situations.