Incentivando o uso de argumentação e provas nos cursos de licenciatura em matemática

Abstract

Research into Argumentation and Proof in mathematics teaching has seen a growing number of studies addressing different aspects of investigation. The main studies deal with different aspects related to mathematical proof, such as the role of proof in the classroom (Hanna, 2000, 1995; Aguilar Júnior e Nasser, 2012; Costa, 2008), students' and teachers' conceptions of tests (Harel e Sowder, 1998; Caldato e Nasser, 2022), and the constructions and validity of an evidence (Weber, 2008; Balacheff, 1988). These researches show the need to encourage teachers and students to see the ability to argue and prove as an object of mathematical background. This study presents research results aimed at investigating whether and how undergraduates are encouraged to argue and prove mathematical topics during their degree course. To carry out this research, a questionnaire with five questions was drawn up and applied to mathematics undergraduates from various public institutions. A total of 53 mathematics undergraduates took part on a voluntary basis, as this was a convenience sample. The results showed that the respondents themselves recognize that they are not fully capable of demonstrating mathematical results. This is proven both when they are put into practice and when they are asked to argue about the possible gains of their application in basic education. The lack of awareness of argumentation as an object of mathematical background may be due to various factors that are discussed throughout this research. In addition, a relevant point was the acceptance of informal arguments presented by basic education students and a lack of consensus on whether there is an incentive to develop the ability to argue and prove in undergraduate courses. This lack of mastery in arguing and proving shows a need to better understand the gaps present in teacher training and awareness of one's own ability. One proposal that could contribute to the training of mathematics undergraduates who are aware of the relevance of having autonomy in the ability to argue and prove is the use of the Argument Model developed by Toulmin (2006). Combining these schemes with the teaching of argumentation, it is possible to conclude that the ability to argue should not be considered innate, but rather can be developed, it means, it can be taught and learned.