O raciocínio proporcional e o uso do excel: Um olhar para a gênese instrumental

Abstract

The present study aims to investigate the instrumental genesis of a pair of 9th grade students considering Excel in situations that involve proportional reasoning. As theoretical support, we use Instrumentation Theory, especially in the writings of Pierre Rabardel (1995a) to investigate subjects in activities mediated by instruments. As the latter has a psychological aspect in the form of the student’s schemes, the Theory of Conceptual Fields, developed by Gérard Vergnaud (1996, 2009) provides us with the necessary inputs for your understanding. The methodological procedures adopt the nature of intervention research (SPINILLO; LAUTERT, 2008), in an approach of a quantitative-qualitative investigation (BOGDAN, BIKLEN, 1994). The research was divided into four stages: Diagnostic Evaluation, obtaining student’s prior knowledge through questionnaires; the Introductory Activity, being an introductory step for students with the tools of the Excel spreadsheet; Intervention Activities involved four mathematical objects (Sharing, Variable, Covariance and Invariance) referring to proportional reasoning and chosen from an analysis of educational documents (BNCC, 2017; NCTM, 2000; ME, 2007); and a Final Assessment with a semi-structured interview with the students. The stages were experienced by 02 9th grade students from a state public school located in the Agreste of the state of Paraíba. The data were analyzed considering the Data Organization Scheme by the double, that guided us in describing the process of the genesis of the instrument. This scheme was chosen by comparing the Diagnostic Assessment and the Final Assessment, and a study was presented on its components (anticipations of the goal; rules of action; control, inferences and operative invariants). We are based on the S.A.I model (RABARDEL, 1995a), interpret instrumentation processes (S-I) and (O-S); instrumentalization [S– (I) -O], (I-O) e (S-O); and (I-S) and (O-I) relations. The discussion of genesis occurred during the four intervention activities, and for that, we present at the end of the analysis a synthesis elaborating the instrumental route of the pair, for a better understanding of the components of the scheme under analysis and the moments in the research. The conclusions reveal the certainty in the potential of Excel for the development of the students' proportional reasoning from the expectations of the adaptation and mobilization of the usage schemes. There was an evolution of students in the use of Excel regarding the Organization and Data Layout scheme. Students get the reasons, rates and proportions of problem situations, using formulas and comparisons in Excel; analyze the joint variation of variables and quantities; respond to activities both quantitatively, with the results showing the conditional formatting they performed between the tables, qualitatively giving meaning to knowledge objects. The perspectives are the continuity of research in understanding students' schemes, as to other mathematical objects related to proportional reasoning, analyzing the genesis, according to the new instruments to be instituted. The study of instrumental genesis contributed to the investigation of Excel in the treatment of the concepts of Sharing, Variable, Covariance and Invariance from the experienced process.