Argumentos e metáforas conceituais para a taxa de variação

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

The aim of this investigation was to identify and to analyze arguments and metaphors used by a group of students of a masters degree course in Mathematical Education for the rate of change, to understand how they learn this topic. The option of working with those subjects relapsed in the fact that they are all teachers of Mathematics and they have already seen Calculus in their graduation. To those subjects, tasks were offered in a learning scenery where the dialogue was privileged among teacher, students and technology. The vision adopted regarding the technology was of a prothesis, in the sense that it makes it possible for the student to do things different from the way that he would do without it. With the intention of working with different texts, sometimes we offered tasks that the students interacted with the computer, sometimes we offered a task which the prosthesis was a small canal made from a PVC tube, tennis ball, ping-pong ball, chronometer and tape measure. The classes that the students worked in those tasks were filmed using a VHS camera. Notes of some speeches and interventions of the students and the teacher written on a notebook helped to enrich the collection of data. The analysis was based on Embodied Cognition Theory and on the Model of the Argumentative Strategy. We conclude that the process of understanding medium rate of change and instantaneous rate of change is not only the case of just a passage from one to another analytical formula or from a graph to a formula. There is a difference among the cognitive mechanisms to understand the graph and the analytic formula, which contributes to the students difficulty with that topic. It is not just the formal definition that is responsible for that difficulty. We observed that with the aid of the computer science technology, it was possible to create an environment where the fictive motion, intrinsic of the language, became a factive movement. That is, when secants straight lines coincided with a tangent straight line for successive approaches, and when the tangent straight line to the curve in a point could move, at the same time the values of the slope of those straight lines could be seen in the screen

ASSUNTO(S)

derivatives matematica -- estudo e ensino movimento fictivo fictive motion conceptual metaphor estratégia argumentativa derivada argumentative strategy taxa de variação embodied cognition matematica metáfora conceitual rate of change cognição corporificada

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