O conceito de função nas pesquisas dos Encontros Nacionais de Educação Matemática (1987-2013) - Vasconcelos, Lívia de Oliveira (2015)
This study aimed to investigate which reveal the research published in the eleven editions of the Encontro Nacional de Educação Matemática (ENEM) occurred in the period between 1987 until 2013 in relation to the concept of function. For this, it required a deepening of the concept of function from the works of Karlson (1961) and Caraça (1984), investigating aspects of its development in perspective called by Sousa (2004) as logical and historical. The process of scientific formalization of this concept was explored in works by Boyer (1974); Keys and Carvalho (2004); Souza Júnior (2007); Karlson (1961) and Zuffi (2001). Such studies have shown the need to understand how this concept was taken from the scientific field to the classrooms, leading us to investigate how did the disciplining process of this concept and how it has been proposed in some national curriculum documents. Such theoretical way were necessary to support the analysis of ENEM the articles selected for this research. The ENEM´s papers centered on the concept of function were subjected to content analysis procedures from the perspective of Bardin (2011). The selection of papers considered relevant for this research was given by two methods: the six annals of first issues, we did a full reading of the Annals, identifying those centered on the concept of function; from the seventh edition, the Annals were made available online in text format, which allowed us to do a search by key words: role, functions and algebra consulting title, keywords, abstract and body text. Such a search located 78 papers of scientific communication that were read in the search for converging themes. In the process we identified themes that were organized into four units of analysis: The importance of the function concept; Conceptual understanding; obstacles of Teaching and Learning; and methodologies that contribute to nderstanding the concept of function. The analysis showed the importance the concept of function is related to their social role, their articulating potential of mathematics content and their usefulness for other sciences. The authors point out that the main meanings necessary to understand the concept of function is the notion of respect, dependency, variables, movement / transformation, domain, codomain and image. The analysis also allowed us list the main factors that sometimes hinder the learning concept of function, such that: the reduction of the concept of function one / some of its meanings, the overly formal approach and misunderstanding on the part of the teacher in relative to this concept. According to the analysis, more efficient methods of teaching are related to more contextualized introduction of the concept of function, the use of classroom software (mainly to explore the graphical representation more dynamically) and articulated interpretation of the various ways to represent a same function. The analysis procedure showed that the authors of the research presented in ENEM already use this concept valuing the intrinsic meanings to it. With that, this research invites us to other studies on the relationship between research in mathematics education and what happens in classrooms.