Atribuindo significado ao seno e cosseno utilizando o software Cabri-Géomètre

• Autor(a) principal: Martins, Vera Lúcia de Oliveira Ferreira
• Data de Publicação: 2003
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/11234
• topic: Ciclo trigonometrico; Seno e cosseno; Ferramenta-objeto; Sequencia de ensino; Cabri-Geometre; Matematica -- Estudo e ensino; Educacao matematica; Matematica: Educacao Matematica; Trigonometric cycle; Sine and cosine; Tool-object; Teaching sequence; Cabri-Géomètre; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The objective of this work is to introduce the concepts of sine and cosine in a coordinated form, starting from right-angled triangles, passing through the trigonometric cycle and ending with the graphs of the corresponding functions, aiming to provide conditions which would enable students to attribute meaning to these concepts. To this end, a teaching sequence comprised of seven activities was devised as a means to investigate whether students of the 2nd year of Ensino Médio (High School), who had already studied trigonometry of the right-angled triangles and the trigonometric cycle, would use this knowledge, during the teaching sequence and with the help of the software Cabri-Géomètre, in the construction of graphs of the sine and cosine functions. The design and analysis of the teaching sequence is based on elements of the tool-object dialectic and the notion of the interaction between frameworks of Régine Douady. The activities were administered to a group of 16 students from a state school in the centre of the city of São Paulo during the year of 2002. In the problem-solving processes developed to solve the proposed questions and through the results obtained, the software Cabri-Géomètre demonstrated its efficiency, helping the students to associate the concepts already studied with respect to the right-angled triangle and the trigonometric cycle with the sine and cosine functions. The results also indicated that the majority of students perceived that the sine and cosine studied in the case of right-angled triangle do not differ from those studied in relation to the trigonometric cycle and, moreover, that the sine-curve and cosine-curve provide accurate portrayals of these concepts