Análise de uma seqüência didática para a aprendizagem do conceito de função afim

Abstract

The purpose of this research was to investigate the effect of the use of a sequence of activities related to the concept of the affine function in an authentic context of problem solution with students in the first year of secondary school. The sequence was composed of two groups of activities, designed to emphasize the understanding of the notion of variation among linear magnitudes, emphasizing the relationship between how these can represent the affine function in natural language, graphically, algebraically, and on a table. The literature researched indicates that the study of situations which introduce the concept of function by means of magnitudes which vary, one depending on the other, help to build the concept of the affine function. The design and application of the didactic sequence was based on Guy Brousseau’s (1892) Theory of Didactical Situations in Mathematics. According to him the phenomena controlling the teaching-learning process involves three poles: the teacher, the student, and the knowledge. Learning about a mathematical object is directly linked to the student’s involvement in the search for a solution to a problem by means of a teaching situation elaborated by the teacher. This sequence was used with a group for first year secondary students in a public school in the city of Recife, Pernambuco (Brazil). The results obtained led us to the conclusion that there was an improvement in the students’ concepts related to the affine function, aided by the understanding of the relationship between the dependent and independent variables and by the connections between the different ways of representing the function.