Resolução de problemas convencionais e não convencionais : uma análise das estratégias utilizadas por estudantes com prognóstico e diagnóstico de discalculia

Abstract

This research aims to analyze the way children and adolescents with a diagnosis or prognosis of dyscalculia solve both conventional and non-conventional mathematical problems. Theoretically, it is based on Consenza and Guerra (2011), Relvas (2010) and Bear (2006) with respect to the functioning of the brain; Kosc (1974), Hasse et al. (2012), Relvas(2010), Ciasca (2008), Gil (2007) and Santos (2017) defining Developmental Discalculia; Lara (2011), Stancanelli (2001), Villa and Callejo (2006), Onuchic (2014), Polya (2006), Dante (1991), Brito (2006) and Smole and Diniz (2001) on problem solving. Five students participated in the research, one of whom has a report of dyscalculia and was attending high school and four had the prognosis of this disorder, three students attending elementary school and one higher education. For data collection, four instruments were used: the Transcoding Test (MOURA et al., 2013); the Arithmetic Test (SEABRA;MONTIEL;CAPOVILLA 2013); the School Performance Test (STEIN, 1994); and the Pilot Test, involving unconventional problems. The research was conducted in two steps. In the first, there was the application of standardized tests to students and the observation of the strategies used to solve the proposed questions and mathematical problems. In the second, the analysis of the results obtained in the application of the tests was made, as well as the comparison between the resolutions of algorithms, conventional and unconventional problems. This is a qualitative research, with the purpose of monitoring and verifying the students' performance in the proposed tests, describing their performances individually, in order to compose the corpus of this research. In order to explain the results obtained, tables and graphs were prepared containing the variations of the performance of each student in the proposed tests. The information collected was analyzed through a Discursive Textual Analysis, according to Moraes and Galiazzi (2011). From the analysis of the strategies used by students to solve conventional problems, the main category emerged the use of algorithms; while solving unconventional problems, the use of mental calculus was highlighted. This shows that students are subject to solve problems with the application of an algorithm, but when unconventional problems are proposed, strategies are diversified, giving predominance to mental calculation, with use in some cases of pictorial representation. Therefore, even a student with a diagnosis or prognosis of a learning disability in mathematics, in particular Developmental Dyscalculia, may be able to solve mathematical problems, whether conventional or unconventional, through strategies other than those expected by some teachers, in particular, the use of algorithms.