Ideias/significados da multiplicação e divisão: O processo de aprendizagem via resolução, exploração e proposição de problemas por alunos do 5º ano do Ensino Fundamental

Abstract

This paper presents the results of a Master research carried out in the context of Mathematics’ 5 grade class of the Elementary school. Its objectives are: investigating the potential and the process of teaching and learning through solving, exploring and proposing problems with ideas / meanings and properties of multiplication and division by students in a 5 grade class of the Elementary school; identifying the students’ understandings and conceptions about solving problems with ideas/meanings and properties of multiplication and division. Is also aims to describe and analyze the process of teaching and learning of solving, exploring and proposing problems with ideas/meanings of multiplication and division by students of the 5 year of Elementary school. Furthermore, at the end of the survey it proposes to list ways which can contribute didactically and methodologically with the teaching and learning of problem solving with ideas/meanings and properties of multiplication and division. Our research is qualitative in the teaching mode. The research took place in a public school in Campina Grande-PB, in a 5 grade class with 33 students. We performed the survey/data collection of this research in fifteen meetings (31 lessons taught) in the 5th grade, working the resolution, exploration and proposition of problems with many ideas/meanings of multiplication and division. The notes of the researcher on the development of the meetings, the students’ records of the problems’ resolution and the dialogues, which came up during class, formed a material for reflection and analysis to our investigation. Over the meetings we observed a better understanding of the problems’ statements and the more relevant choices/applications of operations/processes for resolutions and the creation of strategies by the students. The exploration of the problems occurred in various moments of this research, in short and continuous times. The proposition problems by the students was a complex activity at the beginning of the investigation, but after some experiments we noticed a greater resourcefulness to elaborate problems. Among the many possibilities that can be developed by students in the teaching- learning process of solving, exploring and proposing problems with ideas/meanings of multiplication and division, we highlight a few: autonomy; creativity; reflection; interpretation; creating different strategies; acquiring new forms of knowledge and improving the old ones. We also emphasize the ability of solving different kinds of problems, the idea that we can solve the same problem with more than one operation, the power to propose problems and perform questions. We conclude that solving problems is a process: sometimes it is complex and it stimulates the learning of Mathematics contents and concepts, contributing to the development, educational and social instruction of the student/citizen.