A compreensão de expressões algébricas sob a perspectiva da filosofia de Wittgenstein

Abstract

This research aimed to investigate the students’ difficulties when it comes to developing mathematical rules in the classroom context, which the main emphasis were on discussions about language, based on Wittgenstein's philosophy of language, highlighting the importance of the language, mathematics and knowledge. Its main objective was to investigate the difficulties related to the learning of school algebra, especially in algebraic expressions. For this, it presented a discussion about following rules, see-how, natural/mathematical language translation, working on meanings and some math fundamentals which are mainly approached by the Austrian philosopher in his work Philosophical Investigations.As methodology, this research was developed with 24 elementary school students from the State Network in the city of Castanhal – PA. We attended the classes of algebraic expressions in order to motice some difficulties related to language and some difficulties by the students because of that language. In order to collect the data, we applied a questionnaire containing four questions and the resolution of exercises distributed in five annexes that provided us a perception of the confusions during their resolution. From the answers and observations, we mainly notice students do not master the techniques required to follow the mathematical rules fundamental to the correct development of remarkable products and factoring. The contents of algebra are usually considered obstacles to learning, since they involve other ways of dealing and operating with the mathematical objects involved. From this result, we emphasize the importance of the teacher's performance, since the students cannot discover the mathematical rules, but they need to be shown and explained.