PROPORTIONAL THINKING: FROM THE ART OF WEAVING HAMMOCKS TO THE ART OF LEARNING MATHEMATICS AT SCHOOL
.Weaving. Social practices. Proportional thinking. Theory of Objectification.
This study specifically arose from the formulation of the following research problem: how do students immersed in a pedagogical practice that aims to engage mathematical knowledge and local social practices become aware of these knowledge and practices and reframe their perspective, understanding, and relationship with this local practice? Thus, we propose to understand the mathematical knowledge related to proportionality mobilized in the production of hammocks by a community of weavers in Jaguaruana, Ceará, and to analyze the development of proportional thinking among students from this community, engaged in a teaching and learning process that aims to foster dialogue, recognition, and appreciation of this knowledge. To achieve this objective, we used Objectification Theory and discussions related to proportional thinking as our theoretical foundation. Furthermore, we used qualitative, participatory, descriptive, interpretative, and ethnographic research methodologies to analyze data produced in two research sites in the municipality of Jaguaruana, Ceará: weaving houses and a rural school. The data were gathered through dialogued interviews with eight hammock weavers, as well as from an extension course with 15 seventh-grade elementary school students (ages 12 to 13). These interviews were analyzed using multimodal analysis. In this research, we argue that the social practices of hammock weavers in Jaguaruana, Ceará, contribute to the teaching and learning of proportional thinking, as well as to the recognition and appreciation of this knowledge, based on a didactic project grounded in the sociocultural approach of Objectification Theory. The results revealed evidence of semiotic knots and contractions in the activities of students Amanda, Denise, Glauber, Nilo, Pedro, Valéria, Vitoriano, and Wilson, when discussing issues related to proportional thinking. We also observed attitudes of recognition and appreciation for the weaving practice, when they decided to research and discuss the history of local weaving, produce a small hammock, create a social network to promote the project's activities, and participate in the community's young entrepreneurs' fair. In short, we highlight the relevance of the educational project, which integrated the mathematical quantities used in weaving and proportional thinking, leading us to rethink mathematics pedagogical practices, permeated by cultural reality and historically established mathematical knowledge.