Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica
Abstract
This research was started because of concerns regarding the teaching and learning
of Counting Problems in Elementary School. With the intent of contributing to the
construction of basic Combinatorial concepts, we elaborated exploratory-investigative
tasks and we tried through these tasks, to analyze the answers that were made by
students of an 8th grade of Elementary School, in order to answer the following
investigative question: what learning occurs with the mobilization of registers of
semiotic representation theory to do counting in a scenario of exploratory-
investigative tasks in an 8th grade of Elementary School? The theoretical and
methodological reference is constituted by the registers of semiotic representation
theory propounded by Duval; by the theory of Mathematical Investigations, Ponte et
al. Besides that the research also had the collaboration of Pessoa and Borba. We
present a brief historical retrospective on the subject, besides a previous analysis of
other works in the area and official documents aimed at teaching and learning of
Mathematics subject regarding to contents of Counting Problems in Elementary
School. The research was developed with a group of 25 students of the 8th grade
Elementary School in a public school in São Paulo state, in the year 2016. The data
collection was done through field notes (logbook), and from the records written by the
students during the development of the sequence of tasks. Through this
investigation, we could verify that the study of Counting Problems through
exploratory-investigative tasks allows the articulation of different registers of semiotic
representation, leading to a better understanding of this topic.