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Contributo para o desenvolvimento do raciocínio proporcional : uma experiência de ensino no 6º ano
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Esta investigação teve como objetivo compreender se o trabalho com tarefas que explorem e interliguem conceitos essenciais da proporcionalidade direta, como as noções de razão, fração, razões equivalentes e diferentes representações como proporção, tabelas e gráficos, promove a compreensão da proporcionalidade direta e do significado da constante de proporcionalidade e se contribui para o desenvolvimento do raciocínio proporcional. O quadro teórico envolve aspetos fundamentais do raciocínio proporcional e a importância e conceitos-chave para o seu desenvolvimento, bem como a análise das dificuldades dos alunos. O estudo seguiu uma metodologia de Investigação Baseada em Design, com base numa experiência de ensino, desenvolvida com uma turma de 29 alunos, do 6.º ano. O trabalho na unidade de ensino decorreu no ano letivo de 2016/2017, durante os meses de dezembro e janeiro. A unidade de ensino foi constituída por uma ficha de avaliação diagnóstica, nove tarefas e um teste escrito. A análise das produções escritas dos alunos procurou identificar estratégias usadas e principais dificuldades. Atendeu à evolução dos alunos na compreensão de relações entre duas medidas de grandeza, da constante de proporcionalidade e no uso de estratégias proporcionais e na identificação da existência de proporcionalidade.
Os resultados mostram que o trabalho com razões, frações e equivalência de frações proporcionou a compreensão das relações entre as medidas de grandeza, das relações multiplicativas e o aprofundamento do sentido de invariância e covariância. Este trabalho fomentou o uso de estratégias proporcionais, escalar e funcional, mas pontualmente surgiu o uso da estratégia pré-proporcional, de composição/decomposição (building-up). De um modo geral, os alunos identificaram situações onde existia ou não existia proporcionalidade direta, recorrendo a várias estratégias. As dificuldades reportaram-se ao trabalho envolvendo a constante de proporcionalidade ou medidas de grandezas representadas por dízimas ou numerais mistos. Os alunos revelaram ter noção da existência da constante de proporcionalidade e identificaram-na com relativa facilidade, mas mostraram dificuldade na interpretação do seu significado no contexto dos problemas.
This research aimed to understand whether work with tasks which explore and interconnect essential direct proportionality concepts, such as ratio notions, fraction, equivalent and different ratio representations like proportion, charts and graphics, promote the understanding of direct proportionality and the meaning of the principle of proportionality and whether it contributes for the development of proportional reasoning. The theoretical board involves fundamental aspects of proportional reasoning and the importance of key-concepts for its development, as well as the analysis of students´ difficulties. The study followed an investigation methodology Based on Design, supported by a teaching experience, developed with a class of 29 students, from the 6th grade. The work in the teaching unit occurred in the school year of 2016/2017, during the months of December and January. The teaching unit was formed by a diagnostic evaluation form, nine tasks and a written test. The analysis of the students´ written productions aimed to identify used strategies and main difficulties. It took into consideration the students´ evolution in the comprehension of relations between two magnitude measures, direct proportionality and in the use of proportional strategies and identification of the existence of proportionality. The results show that the work with reasons, fractions and equivalence of fractions made the understanding of relations between magnitude measures, multiplicative relations and the deepening of the sense of invariance and covariance, possible. This work fomented the use of proportional strategies, both scalar and functional, but at some point the use of the pre-proportional strategy came up, as well as the composition/decomposition (building-up). Overall, students identified situations where direct proportionality existed and did not exist, making use of various strategies. The difficulties were reported to the work involving the principle of proportionality or the magnitude measures represented by tithes and mixed numerals. The students revealed that they were aware of the existence of the principle of proportionality and could easily identify it, but showed difficulty with the interpretation of its meaning in the problems context.
This research aimed to understand whether work with tasks which explore and interconnect essential direct proportionality concepts, such as ratio notions, fraction, equivalent and different ratio representations like proportion, charts and graphics, promote the understanding of direct proportionality and the meaning of the principle of proportionality and whether it contributes for the development of proportional reasoning. The theoretical board involves fundamental aspects of proportional reasoning and the importance of key-concepts for its development, as well as the analysis of students´ difficulties. The study followed an investigation methodology Based on Design, supported by a teaching experience, developed with a class of 29 students, from the 6th grade. The work in the teaching unit occurred in the school year of 2016/2017, during the months of December and January. The teaching unit was formed by a diagnostic evaluation form, nine tasks and a written test. The analysis of the students´ written productions aimed to identify used strategies and main difficulties. It took into consideration the students´ evolution in the comprehension of relations between two magnitude measures, direct proportionality and in the use of proportional strategies and identification of the existence of proportionality. The results show that the work with reasons, fractions and equivalence of fractions made the understanding of relations between magnitude measures, multiplicative relations and the deepening of the sense of invariance and covariance, possible. This work fomented the use of proportional strategies, both scalar and functional, but at some point the use of the pre-proportional strategy came up, as well as the composition/decomposition (building-up). Overall, students identified situations where direct proportionality existed and did not exist, making use of various strategies. The difficulties were reported to the work involving the principle of proportionality or the magnitude measures represented by tithes and mixed numerals. The students revealed that they were aware of the existence of the principle of proportionality and could easily identify it, but showed difficulty with the interpretation of its meaning in the problems context.
Descrição
Dissertação de mestrado, Educação (Área de especialização de Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2017
Palavras-chave
Razão Estratégia Dificuldades Teses de mestrado - 2017