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Resolução de problemas de proporcionalidade direta no 2.º ciclo do ensino básico
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Advisor(s)
Abstract(s)
O presente estudo reflete a componente de investigação da unidade curricular de Prática
de Ensino Supervisionada, constituinte do curso de mestrado em Ensino do 1.º Ciclo do
Ensino Básico e de Matemática e Ciências Naturais no 2.º Ciclo do Ensino Básico.
Decorreu durante o ano letivo 2016/2017, numa escola básica do 2.º e 3.º ciclos da
cidade de Faro, com alunos do 5.º ano de escolaridade. O principal objetivo deste estudo
consistiu em averiguar quais as estratégias utilizadas por alunos, a frequentar o referido
ano de escolaridade, na resolução de problemas de proporcionalidade direta, sem uma
abordagem prévia a este domínio da matemática, em duas aulas organizadas seguindo
uma abordagem de ensino exploratório. Pretendeu ainda verificar qual ou quais as
estratégias de resolução que predominavam nas produções matemáticas dos alunos.
É um estudo qualitativo e interpretativo que decorreu em contexto escolar, em que as
resoluções dos alunos foram interpretadas tendo em consideração as principais
estratégias apresentadas no quadro teórico em estudos homólogos. Os principais
resultados revelaram que os alunos envolvidos no estudo apresentavam competências de
resolver tarefas matemáticas simples de comparação e de valor omisso que envolviam a
proporcionalidade direta, sendo as estratégias predominantes razão unitária, fator de
mudança e algoritmo do produto cruzado, das quais se destaca, pela frequência de
utilização, a estratégia razão unitária.
Constatou-se também que os alunos conceberam duas estratégias diferentes das
encontradas na literatura, apoiando-se em conhecimentos básicos como a adição e em
conteúdos explorados no seu nível de escolaridade, no que respeita ao cálculo de
percentagens, revelando a sua capacidade em mobilizar conhecimentos prévios perante
novas situações. Os resultados revelaram também as principais dificuldades
demonstradas pelos alunos, em que o conhecimento acerca do algoritmo do produto
cruzado surge como sendo um fator que condiciona fortemente a criatividade dos alunos
quanto à conceção de estratégias alternativas a este algoritmo.
The present study reflects the research component of the curricular unit of Supervised Teaching Practice, integrated in the Masters course in Teaching of the 1st Cycle of Basic Education and of Mathematics and Natural Sciences in the 2nd Cycle of Basic Education. It took place during the 2016/2017 school year, in a basic school of the 2nd and 3rd cycles of the city of Faro, with students of the 5th year of schooling. The main objective of this study was to investigate the strategies used by students, to attend the referred year of schooling, to solve problems of direct proportionality, without a prior approach to this domain of mathematics, in two sessions organized according to an exploratory teaching approach. It also sought to verify which solving strategies or strategies predominated in students' mathematical productions. It is a qualitative and interpretative study that took place in a school context, in which the students' resolutions were interpreted taking into account the main strategies presented in the theoretical framework in homologous studies. The main results revealed that the students involved in the study had the ability to solve simple mathematical tasks of comparison and of omission value that involved direct proportionality, being the predominant strategies unitary reason, factor of change and algorithm of the cross product, by frequency of use, the unit ratio strategy. It was also found that the students conceived two strategies different from those found in the literature, relying on basic knowledge such as the addition and content explored in their level of education, regarding the calculation of percentages, revealing their ability to mobilize knowledge prior to new situations. The results also revealed the main difficulties demonstrated by the students, where knowledge about the cross-product algorithm emerges as a factor that strongly influences students' creativity regarding the design of alternative strategies to this algorithm
The present study reflects the research component of the curricular unit of Supervised Teaching Practice, integrated in the Masters course in Teaching of the 1st Cycle of Basic Education and of Mathematics and Natural Sciences in the 2nd Cycle of Basic Education. It took place during the 2016/2017 school year, in a basic school of the 2nd and 3rd cycles of the city of Faro, with students of the 5th year of schooling. The main objective of this study was to investigate the strategies used by students, to attend the referred year of schooling, to solve problems of direct proportionality, without a prior approach to this domain of mathematics, in two sessions organized according to an exploratory teaching approach. It also sought to verify which solving strategies or strategies predominated in students' mathematical productions. It is a qualitative and interpretative study that took place in a school context, in which the students' resolutions were interpreted taking into account the main strategies presented in the theoretical framework in homologous studies. The main results revealed that the students involved in the study had the ability to solve simple mathematical tasks of comparison and of omission value that involved direct proportionality, being the predominant strategies unitary reason, factor of change and algorithm of the cross product, by frequency of use, the unit ratio strategy. It was also found that the students conceived two strategies different from those found in the literature, relying on basic knowledge such as the addition and content explored in their level of education, regarding the calculation of percentages, revealing their ability to mobilize knowledge prior to new situations. The results also revealed the main difficulties demonstrated by the students, where knowledge about the cross-product algorithm emerges as a factor that strongly influences students' creativity regarding the design of alternative strategies to this algorithm
Description
Keywords
Proporcionalidade direta Tarefas Matemáticas Ensino Exploratório Resolução de problemas Estratégias matemáticas