Situações-problema que envolvem o conceito de função afim: uma análise à luz da Teoria dos Campos Conceituais

Abstract

Our main objective in this research is to categorize problem situations related to the concept of affine function, in the light of the theory of conceptual fields. To determine a typology for situations, we use the criteria established by Gérard Vergnaud for the classification of situations in the additive and multiplicative structures. These criteria include the types of relations - binary, ternary and quaternary - established between the elements present in the problems and the types of situations of the additive and multiplicative structures. Problem situations involving the concept of affine function have been classified as purely additive, purely multiplicative or mixed, the latter being those that present at least one relation from the additive structure and at least one from the multiplicative structure. As a data source for the analysis of problem situations considered for this research, four (04) Mathematics textbooks were adopted, two from the 9th grade of Elementary School and two from the 1st grade of High School, which were approved by the Programa Nacional do Livro Didático (National Textbook Program) - PNLD - 2017 and 2018. Considering the problem situations mapped in this research, we identified nine (09) categories of situations, and two (02) of these did not belong to the previously established categories. The identified categories resulted in a total of fifteen (15) subclasses of situations, considering the types of relations established between the elements present in their statements. Other factors identified as modifiers of the difficulty level and, consequently, the variation of the type of situation were: presentation of data in graph or table; presentation of data in figure related to the statement; scale interpretation; measurement conversion; absence of explicit rates in the statement - such as the absence of the ratio rate and the absence of the fixed value