Estruturas multiplicativas: concepções de alunos de ensino fundamental - Rasi, Gislaine Carvalho (2009)
This research comprehends the multiplicative structures and its objective is to investigate the conceptions the seventh grade students put in motion when they establish ternary relations and the relational calculus. We especially search to verify how these students deal with the multiplicative relations which involve notions of transformation and binary composition, and how they make use of the properties of multiplication. Our theoretical approach is based upon Vergnaud s contributions (1991, 1996) presented in the Conceptual Fields Theory and in the Multiplicative Conceptual Field, mainly on the notions of relation and relational calculus which allowed the elaboration of activities and the results analysis. As for the methodology adopted, we chose the case study, which allowed a better comprehension of the relations established by students during the resolution of multiplicative problems, and thus contributing to the achievement of our objective. With instruments of data collection, we made observations during the activities accomplishment, in two study groups and we collected the children s written record of these activities resolution. We verified, in the data analysis, that students have a certain difficulty in composing two transformations and a concentration in the establishment of ternary relations which involve the transformation notion. These observations demonstrated the importance of improving the work with multiplicative structures in a way to promote a good variety of situations and relations regarding the Multiplicative Conceptual Field, especially the ternary relations, as a law of binary composition with its properties