Ideias base do conceito de função mobilizadas por estudantes do ensino fundamental e ensino médio

According to curricular documents, the concept of function must be studied in the 8th and 9th years of Elementary School, and deepened in High School. However, since the initial years it is possible to introduce base - variable, correspondence, dependence, regularity and generalization - of this concept so that during the course of the school process this concept can be developed by students. Thus, we carry out this research with the objective of analyzing the basic ideas about function mobilized by students of the 9th grade and 3rd year of secondary education, by solving mathematical tasks on related function. Data collection took place through structured interviews, which were recorded in audio, and had previously developed mathematical tasks for the students to solve. The analyzes show that students partially mobilize the basis ideas of function, but that the greatest difficulties occur in relation to the notion of generalization. In addition, students expressed difficulties in recognizing a function in graphical representations and natural language.