Expectativas neurocognitivas da atenção em uma sequência de ensino para a habilitação do raciocínio axiomático durante a aprendizagem da demonstração da lei dos senos

Abstract

The studies on trigonometry stimulate discussions which foment numerous researches in the area of Mathematics Education and, through them, the hypothesis of the existence of obstacles in the process of construction of the demonstration of the law of the sines was raised. Thus, this research presents the results of an investigation that aimed to analyze the attentional neurocognitive expectations available during the process of construction of the axiomatic reasoning used in the demonstration of the law of the sines. The methodological conduction of the research was organized through learning protocols based on the pillars of classical didactic engineering (preliminary analyzes, conceptions and a priori analysis, experimentation, a posteriori analysis and validation), with Artigue (1988) as a prominent name. Following the phases of this methodology, a historical, epistemological and habitual teaching analysis was developed in order to understand the context and obstacles related to knowledge about the mathematical object under analysis. The theoretical framework was based on the knowledge about the history of mathematics, specifically the law of sines, through the (re) visitation in Eves (2004), Euclides (2009) and Boyer (2012); in partnership with the knowledge of cognitive neuroscience, especially in the studies of Posner and Petersen (1990, 2012), Kandel et al. (1991), Lent (2002), Gazzaniga et al. (2006), Sternberg (2010), Cosenza and Guerra (2011) and Posner (2012), with emphasis on the process of capturing, conducting, coding and consolidating information. Regarding the levels of demonstration in mathematics teaching, it was supported in Balacheff (1984) and De Villiers (2001, 2002). The investigation was implemented through the application of a didactic sequence for students of the degree course in mathematics in the first semester of 2018, of the Universidade Federal de Sergipe, which was intermediated by the use of the mobile trigonometric cycle and learning protocols. In the view of the investigations, application and analysis of the didactic sequence, it was concluded that when working on the law of Sines, the use of contextualization and the mobile trigonometric cycle, it is possible to identify the student's interest in the studied content, sharpening their attentional system through visual-tactile, which triggers greater attention and focus when working on the demonstration of the law of the sines.