O conceito de função: da operacionalização da definição à aprendizagem significativa

Abstract

To understand a Mathematical concept is necessary to know how to articulate its representations. In the case of the function concept, to achieve the articulation, students need a landmark inside the Abstract Terminology. Something leading their interpretations about functional relationship and connect in a coherent whole all the abstract terms that orbit the concept. We believe the landmark must be the definition of function. Not any definition, but one we can use consciously as a connecting link between other representations, this process is called Operationalization of the definition of mathematical function. In this work, we intend to know if a learning environment guided in the searching for operationalization of the definition of function can favor the meaningful learning of this concept. Firstly, we did a survey of a general theoretical framework about the tradition of teaching of function concept. The historical-epistemological development of the function concept, the multiple representations and learning disabilities of this concept, as well as the acquisition process of concepts by students were the focus of the bibliographic search, which aimed to identify some aspects enabler of the operationalization. Later, three didactic sequences based in the variable raised in the preliminary analyses, elaborate and analyzed under the conjectures of the Didactic Engineering, research methodology used, were applied to twenty junior high school students of a public school in Manaus-AM. The observation outcome accomplished during the didactic sequences, the writing production of the students and the argument of two exams (one applied before the activities and another after them) suggests the evolution of using of the definition: an inert definition, abandoned of any reasoning soon after been enunciated, to an operational definition, used as a guiding source of the functional thinking. In conclude that an operational definition can be considerated the primary element of the Meaningful learning process of the function concept.