The manipulative in conversions between representations of rational numbers and its implications in the phenomena of variability of non-congruence and the non-reversibility

Abstract

This text is a cut of a research developed in Graduate Program in Mathematical and Technological Education, Federal University of Pernambuco  (EDUMATEC-UFPE), whose objective was to investigate, in light of Raymond Duval Theory of Registers of Semiotic

Representations, limits and possibilities in the use of manipulative in conversions between representations of rational numbers. A pilot experiment with four such materials integrated the methodological path and resulted in the choice of the Adapted Golden Bead Material for further analysis and the conclusion of the work. In this section, the focus will be on discussion of the implications of using this manipulative and the coding rule associated with it in the exercises of conversions between representations of rational numbers with regard to the phenomena of variability of non-congruence and the non-reversibility. The results of the research showed that the mediation of the Adapted Golden Bead Material reduced the difficulties caused by the change in direction and by the variation of congruence/non-congruence in the proposed conversions. The results also demonstrated that the application of the coding rule associated with the manipulable in the resolutive path can be applied to these conversions no matter what direction they are in.