O treino da aplicação de regras do cálculo diferencial e integral para estudantes de ciências biológicas : um enfoque na filosofia de Wittgenstein

Abstract

This research aimed to investigate how students of the IFMA Biological Sciences course interpret and apply rules in the learning of differential and integral calculus. For this, we divided the research into four parts. The first one deals with the research delineation, in which we describe the research problem, the objectives and the methodology. From a bibliographic study we show the significance of the problem for the area of mathematics education. In the second part, we present the theoretical foundation that contributed to the construction of the analysis categories, data analysis and interpretation of the research results. To this end, we seek subsidies in the Philosophical Investigations of Ludwig Wittgenstein, regarding the issue of language and the perception of aspects in mathematical objects, in order to show that subjective at interpretations about these objects are often investigated to the detriment of language. This part comprises four sections: in the first, we present the conception of language Wittgensteinian; in the second, we deal with the application of rules; in the third, we highlight the Wittgensteinian perspective on the expressions seeing and seeing-as; finally, we present the wittgensteinian understanding with regard to the term training. In the third part, we present the result of what we call Diagnostic Assessment, which was applied to students enrolled in the discipline of Calculation of the course of Biological Sciences. Finally, in the fourth part, we perform the analysis of the data produced by students in learning situations. The purpose was to analyze the students footsteps regarding the aspects of seeing the algebraic expression that defines a function as an expression that is prepared for the application of mathematical rules in the calculation of limits. The analyzes showed us that the training of the application of rules, through the technique of making and redoing the use of rules in the most diverse possible situations, through assisted exercises, in the sense of clarify the residues left by the language formalization process and to dissolve conceptual confusions , contributes significantly to student learning. Therefore, we conclude that training is the way to insert students in the language game of differential and integral calculus. Through training, they build their conditions of sense that allow them to make use of certain terms and apply certain rules during the realization of the mathematical activity.