Os registros de representação semiótica mobilizados no estudo de sistemas lineares no ensino médio

Abstract

This research aimed to investigate the study of linear systems through the coordination of semiotic representations in a high in São Sepé-RS during the school year 2014. Therefore, we adopted as data collection instruments textbook Novo Olhar Matemática, volume 2 (SOUZA, 2010), the records of Mathematics students notebooks in each of the six high school classes of the school, and the protocols of three activities sequences developed together with one hundred and twenty-six students that make up these classes. Thus, we took as methodological framework the guidelines of qualitative research in the form of case study (LÜDKE; ANDRÉ, 1986) followed the principles of content analysis (BARDIN, 2011). As a result of the textbook analysis, we highlight that 16.97% of the questions posed by the book involved exclusively algebraic register treatment and 3.57% in natural language register. Conversion was present in 79.46% of the activities and explored a wider range of registers: starting, four; intermediate, eight; and finishing, six, with 92.13% of the conversion activities mobilized the algebraic record at some point, 27.91%, the natural language record, and only 9.17%, the graphic record. The analysis of the student s notebooks revealed that the two teachers favored the algebraic record both in activities requiring treatment as in conversion. Among the other representational systems taken by the two teachers as starting records, we identified the algebraic record in symbolic representation and natural language by Profα and the algebraic record in symbolic representation and algebraic register in matrix representation by Profβ. Concerning graphic record, except for just one class, it was awarded timidly in some of the proposed activities to all other classes, but it was restricted to the 2x2 system. Through the activities sequences, we noted that, in performing treatment in algebraic register, the students felt more secure and confident than in activities that required treatment in another representational system. Conversions involving graphic record also enabled us to see that many students did not identify the relevant visual variables that related algebraic and graphic register; and they showed not to have clarity on the representation of an ordered pair in the two-dimensional plane while writing it in algebraic register in the symbolic representation; and they had no clarity on the concept of proportionality and, consequently, of linear combination when analyzing the coefficients of the unknowns and independent terms through the algebraic register in the tabular representation. Furthermore, from arguments in natural language register we confirmed that students did not identify the relevant visual variables and also lacked clarity regarding the nomenclature to be adopted to refer to objects that comprise the graphic register. Thys, we aim that our work has contributed to more people having a view of how the study of linear systems occurs and how the mobilization of different representational systems promotes the identification of aspects inherent to this mathematical object.