Isometrias: análise de documentos curriculares e uma proposta de situações de aprendizagem para o ensino médio




The aim of this research was to investigate the insertion of isometries in the mathematics curriculum, both from an official perspective and in terms of questions related to practice. To this end, it was divided into two parts. The first part considered the characteristics of isometries emphasised in official teaching instruments, such as the National Curriculum Parameters (PCN) and mathematics textbooks. In the PCN, a rupture was identified between the levels of Middle School and High School. In the Middle School parametesr, isometric transformations figure highly, while at the High School level they are not explicity included at all. In relation to the Middle School textbooks analised, isometries were not incorporated in a uniform manner: one collection did not consider the topic, while in the other they were comprehensively covered for all Middle School grades. To analise the activities presented in this second collection, a classification system based on four level of complexity of the conceptual field of Symmetry (Vergnaud, 1997) was developed. This enabled the description of a gradual progression in the appropriation of concepts associated with symmetry. In the High School textbooks, no continuation of this progression was found, as it was difficult to locate activities belonging to the conceptual field of symmetry in either of the collections analised. In the second part of the study, a set of situations was designed for High School students. The results indicated that although the students, all of whom studied at night, had never studied symmetry before, they appropriated with success the idea of axial symmetry as a property of a figure and experienced symmetry as a relationship between two distinct figures. There were also signs that they could have considered symmetry as an object with its own properties


situações-problema conceptual field matematica matematica -- estudo e ensino campo conceitual simetria symmetry ensino médio educacao matematica documentos curriculares curriculum documents high school

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