Introduzindo o conceito de derivada a partir da ideia de variação

Abstract

This research aimed to develop, implement and analyze a didactic sequence that enabled the construction of the concept derived from the notion of change. Results obtained by researchers as Igliori and Silva (1996), Dall'Anese (2000), D'Avloglio (2002), Rezende (2003) and Lehmann (2011) show that this way of introducing the derivative can contribute to the improvement of learning this important mathematical concept. Fieldwork was conducted in a public institution offering higher level courses and didactic sequence was applied to a class that began its studies of Differential and Integral Calculus. We chose to search our own class room, and so, according to Lankshear and Knobel (2008), this research is characterized as a pedagogical research. Principles of Engineering Didactic established by Artigue (1996) and the research of Silva and Igliori (ibid.), Dall'Anese (ibid.) and D'Avloglio (ibid.) in subsidies provided for the method of preparation, application and analysis of didactic sequence. The theory of concept image and concept definition established by Tall and Vinner (1981) and the reflections of Grattan-Guinness (1997) and Reis (2001) on intuition and rigor in teaching calculus, contributed to the preparation and analysis of didactic sequence. The results of this research indicate that essentially most students managed properly conceptualize the derivative as a measure of variation, including some of their meanings, such as: instantaneous velocity, instantaneous rate of change and the slope of the tangent line to the graph of a function.