Desenvolvimento da habilidade de resolver problemas do campo conceitual das estruturas aditivas: proposta de intervenção em um espaço não formal de ensino

Abstract

This research aims at identifying in which ways the activities developed in a non-formal teaching space may contribute to the development of the problem-solving ability in the additive conceptual field by a group of students. Approaching mathematical teaching, the Conceptual Field Theory, the problem solving and the non-formal teaching spaces, the study presented in this dissertation has its theoretical basis grounded in authors such as NACARATO et. al. (2011), MAGINA et. al. (2008), NUNES et. al. (2009), VERGNAUD (2014), MOREIRA (2002), POLYA (1995), POZO (1998), VAN DE WALLE (2009), JACOBUCCI (2008), GOHN (2006), among others. Performed in a non-formal teaching space in the city of Porto Alegre in the state of Rio Grande do Sul (RS) with a group of students who, in a formal teaching space, were regularly enrolled in the 3rd year of Primary School, the research had eight students and one teacher participating. As data-collection instruments, a list of problems was used, in which there were problems relative to the conceptual field of additive structures – and which were reviewed individually after the solving of this list -, a list of operations related to addition and subtraction algorithms and observations of all meetings that took place. The research, defined as a case-study type and using the method of Content Analysis, had its instruments analysed from a qualitative approach and took as its basis three categories a priori, as it follows: Solving problems from concrete material handling, Solving problems through drawing and Solving problems arithmetically. From the results found, it was concluded that the activities developed in a non-formal teaching space contribute to the development of the problem-solving ability in the additive conceptual field, once they make the student think, establish resolution strategies, solve the problem using the strategies created and review what was solved in order to understand what was proposed, thus arousing new knowledge. Finally, it was concluded that the students presented considerable progress in their mathematical abilities and showed development of their discerning abilities as to what was being studied, since their learning was noticeable, as well as their appropriation of mathematical concepts related to the arithmetic operations of addition and subtraction.