Disertación de Maestría
DOI
Documento
Autor
Nombre completo
Izabela Cesario Correa Ananias
Dirección Electrónica
Área de Conocimiento
Fecha de Defensa
Publicación
São Paulo, 2019
Director
Tribunal
Druck, Iole de Freitas (Presidente)
Rangel, Letícia Guimaraes
Silva, Angélica da Fontoura Garcia
Título en portugués
Transformação de frações em números: uma experiência no Ensino Fundamental
Palabras clave en portugués
Ensino Fundamental
Frações
Números decimais
Representações
Resumen en portugués
Título en inglés
The transformation of fractions into numbers: an experience in Basic Education
Palabras clave en inglés
Basic Education
Decimal numbers
Fractions
Representations
Resumen en inglés
This study concerns the issue of teaching and learning fractions in Basic Education and, more particularly, regards the students apprehension of fractions as numbers. The notion of fractions as numbers is described in Mathematics Education literature as problematic for students, since, generally, they understand the representation a/b (where a and b are natural numbers and b is different than zero) only as a double counting process in the part-whole model. Therefore, we decided to investigate the impact of some approaches that broadened the notion of fraction as part of a whole. In order to achieve that, we used as a basis research that highlights different ideas and situations to conceptualize fractions, as well as Raymond Duvals Theory of Registers of Semiotic Representation, due to the importance of approaching fractions in their diverse meanings, through different representations. We carried out an experimental study of qualitative character, inspired by the Design Experiment methodology, with 24 students in the 6th grade from a school in Goiânia. The activities were written based on the theoretical constructs analyzed in the bibliographic search, as well as based on an initial questionnaire that allowed us to identify the main difficulties that the student group had. The hypotheses considered in the design were: emphasis on activities concerning representation conversion between numerical or figural registers and graphical (number line) in both directions; and focus on the idea of fraction as the representation of a division of two natural numbers. Four activities were carried out, with several tasks in each one, along nine meetings in the context of regular Math classes. The activities varied between group and individual tasks, involving traditional resources and concrete materials, with the data collection taking place essentially through the researchers observations and oral and written records of the students productions. In the main activity, we introduced a resource to facilitate the division of segments into congruent parts, aiming to help the students depict non-decimal fractions in number lines without converting them into the decimal register and/or using inaccurate approximations. The analysis shows that, generally, there was an improvement in the students concerning the ideas presented in the activities, bringing them closer to the concept of fractions as numbers, as they demonstrated understanding aspects of equivalence and order by placing fractions in number lines and realized that these fractions corresponded to the results of divisions of two natural numbers, that is, quotients perceived as quantities.

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Fecha de Publicación
2019-06-27