Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2023.tde-05012024-153908
Document
Author
Full name
Fernando Siqueira Vieira Lima
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2023
Supervisor
Committee
Souza, Vera Helena Giusti de (President)
Oliveira, Maria Cristina Araujo de
Title in Portuguese
Concepções de área e de perímetro de alunos dos anos finais do Ensino Fundamental
Keywords in Portuguese
Área
Definição de Conceito
Didática
Ensino
Imagem de Conceito
Matemática
Perímetro
Abstract in Portuguese
Title in English
Area and perimeter conceptions by Elementary School students
Keywords in English
Area
Definition of Concept
Didactics
Image Concept
Mathematics
Perimeter
Teaching
Abstract in English
In this work, we present conclusions obtained in a research for Professional Master's Degree in Mathematics Teaching at IMEUSP, which aimed to investigate conceptions related to area and perimeter of flat figures ideas from some Brazilian Elementary School - Final Years students. Researches related to teaching and learning of these geometric concepts show that students have misconceptions related to these ideas, such as confusing greatness with its measurement or thinking that if the area of a flat figure increases, then the perimeter also increases. The theoretical basis was sought in the ideas of evoked Concept Definition and Concept Image as given by David Tall and Vinner and on Geometry paradigms defined by Bernard Parsysz aiming to answer two research questions Individual evoked Concept Images of students in final years of Elementary School regarding the area and perimeter of flat figures show conceptions numerical, geometric, and of magnitude?, Do students in final years of Elementary School show they articulate a geometry of observation and a geometry of demonstration?. Based on theoretical foundation and research questions, a set of 45 activities was elaborated and, due to pandemic, were used, individually and remotely, with three 7th and 9th grade students, in a reflective interview format. These interviews were audio recorded and transcribed and, together with collected protocols, served as basis for the analyzes carried out. It can be observed that the three participants showed difficulty in understanding a closed curve as a one-dimensional object, which does not include the region limited by it, recognizing regions of the plane that have ¨holes¨ and working with comparisons between curves and surfaces without using a unit of measurement. We concluded that the individual images presented do not contemplate conceptions as magnitude. The participants encountered difficulties in articulating an geometry of observation and a geometry of demonstration, especially in making comparisons without the use of any graduated instruments. The final product of this Dissertation is the set of activities used, which were revisited and reformulated at the end of the research, as a suggestion for a different approach to the subject, in Basic Education Mathematics classes.