As concepções e as crenças do professor sobre a multiplicação e a divisão para ensinar crianças de anos iniciais

Abstract

The objective of this research was to identify possible relationships between the conceptions and the beliefs of the teacher about multiplication and division with their teaching practice in the initial years. In the dissertation, we have as a research question: "How do the conceptions and beliefs of teachers reach the process of teaching the multiplicative field with regard to multiplication and division?" To that end, our research locus was at the Darcy Vargas Municipal School, belonging to the public network of the municipality of Duque de Caxias, whose subjects involved are 4 teachers of the initial series, regents of 3rd, 4th and 5th years of elementary school. We have as theoretical foundations the studies of Gerard Vergnaud (1983, 1988, 1990, 1991, 1998, 2009, 2011, 2012) in order to develop the ideas brought by Conceptual Field Theory, besides counting on the contribution of Magina et al (2009) Depth, specifically, in the classifications of the Conceptual Field of Multiplicative Structures. We also have, in the study of the beliefs and conception of teachers who teach mathematics, with Chacón (2003), Ponte (2016), Callejo & Vila (2006). The research has a qualitative approach in the case study modality. The methodology consisted of a field diary, which made it possible to record classes by identifying subjects' attitudes and behaviors; Semistructured interview, bringing the statements of the teachers complementing what was observable; Diagnostic test on the multiplicative field teachers would apply to their class and questions asked about them by them. As a result, we point out that the beliefs and conceptions brought by the subjects restrict the concept of multiplication and division by not delving deeper into what Vergnaud states as a multiplicative conceptual field.