Conhecimentos sobre ensino de geometria em práticas componente curricular em um curso de licenciatura matemática

Abstract

This study aims to identify the limits and possibilities of the curricular components in Teaching Practice (TP), evidenced in the development of the necessary knowledge to the teacher who teaches Mathematics, more precisely in the area of geometry, considering a group of teachers in initial formation, attached to the Degree in Mathematics course at the Federal Institute of Education, Science and Technology of Farroupilha – Santa Rosa Campus – RS. In order to do so, Mishra and Koehler (2006) are adopted as theoretical references, who describe the technological and pedagogical knowledge of the content and its importance in teacher formation. We also adopt the ideas of Ball and his collaborators (2005, 2007, 2008) who present the knowledge of the teacher who teaches Mathematics categorized in: a) content knowledge: common and specialized; b) knowledge horizon; c) pedagogical knowledge of content, of the student and of teaching; d) knowledge of content and curriculum. As regards learning in geometry, we consider Duval’s perspective for the records of semiotic representation (2003, 2011, 2012) to identify the apprehensions mobilized by teachers in initial training. In data production, we analyzed some materials elaborated during the TP III component, in 2017, as well as protocols of a didactic sequence developed in the first semester of 2018 in the TP V component, with activities about the area of a circle, which involved manipulative and digital didactic resources. The research is of a qualitative nature (LÜDKE and ANDRÉ, 1986) and in order to produce the results, Bardin’s principles of content analysis (2016) were used, which is organized in chronological poles: pre-analysis; material exploitation; and the treatment of results, inference and interpretation. Among the results, there is evidence of common and specialized knowledge of the content in every TP III material of all groups. While in the materials from TP III it was not possible to identify knowledge of the content and curriculum as well as knowledge horizon, it was verified, in the didactic sequence, evidence of these two knowledges. Concerning apprehensions, in both material analysis and didactic sequence, perceptive apprehension is the most mobilized by teachers in initial training. In contrast, discursive apprehension has rarely been identified.