As representações semióticas de multiplicação: um instrumento de mediação pedagógica

Abstract

The Teaching of Mathematics in the early years of schooling is the context in which our research is inserted. The general objective is to analyze the teaching of multiplication aiming to demonstrate the place / role attributed to semiotic representations in the process of teaching and learning, relating them to the concept of pedagogical mediation. In this context, we advocate the thesis that semiotic representations of multiplication are instruments of mediation in the process of teaching and learning that content. To defend it, we discussed the concepts of teaching, learning and pedagogical mediation, supported on cultural-history theory, with contributions by Vygotsky and Leontiev, the concept of semiotic representation registers by Raymond Duval, and we also draw on authors in Mathematics Education who have been researching the teaching of the subject, particularly, multiplication. The methodology for data collection was based on qualitative research, which follows the investigation of complex social phenomena that require further description and discussion. The chosen methodological approach was a discussion group with teachers of early years (Rubio and Varas, 1999), by means of a course we outlined on Teaching Multiplication of Natural Numbers which served at the same time as the locus of field research and a space for academic qualification for the 08 (eight) participating teachers, which also featured as an intervention. During this process the teachers classes were visited and information collected about students' understanding of multiplication. Content analysis was the procedure used for organizing, systematizing and analyzing data, and thematic analysis constituted a means of identifying 'units of meaning'. The data were systematized in two main areas: multiplication, its teaching and students' understanding; semiotic representations used in the teaching of multiplication and produced by the children. The results showed that the teaching of multiplication is still centered on the idea of adding equal portions, with strong appeal to the use of concrete material; mental calculation, through fundamental facts, is a neglected strategy. On students' understanding, we observed difficulties in all explored meanings of the operation, including those most commonly used by teachers; besides, in problems of reverse and combinatorial multiplication this was most evident. Considering all the classes, we demonstrate the variety of semiotic representations of multiplication in teaching, as well as tables and graphs. Regarding students records, we identified the lack of a systematic pedagogical work, involving the clarification, treatment and conversion, since the children s difficulties in these tasks were significant. We conclude that the semiotic representations of multiplication can become pedagogical mediation tools as long as the teachers work focuses on this purpose, so as to encourage discussion and reflection in the classroom on the different semiotic records and strategies for problem solving