An overview of mixed type situations in the Brazilian national high school exam (ENEM) tests

Abstract: This research aims to identify and classify mixed-type situations, associated with the affine function, present in Enem tests. The 2020 Enem tests were analyzed and 10 possible situations were identified to be written in the form f ( x ) = ax + b . Each situation was analyzed in terms of data presentation, resolution structure, and classified based on the combination of classes of additive and multiplicative conceptual fields, as proposed in the Conceptual Fields theory, which supports this research. Among the classes identified in the corpus, the most frequent one was simple double proportion and composition of measures, with three situations. For most students who take Enem, access to mathematical knowledge comes from the classroom; therefore, knowing the different classes of mixed-type situations is in the teacher's interest to provide students with the construction of the concept of the affine function.

摘要：本研究旨在识别并分类Enem考试试题中出现的与仿射函数（affine function）相关的混合型情境。本研究对2020年的Enem考试试题展开分析，共识别出10种可表示为$f(x)=ax+b$形式的情境。针对每一类情境，均从数据呈现形式、解题结构维度展开分析，并依据为本研究提供理论支撑的概念域理论（Conceptual Fields theory）中提出的加法与乘法概念域类别组合完成分类。在本次研究语料库所识别的类别中，占比最高的为简单双比例与度量复合情境，共涵盖3种具体情境。对于绝大多数参加Enem考试的学生而言，其数学知识均来源于课堂教学；因此，教师若能引导学生掌握各类混合型情境的解题思路，将有助于学生构建仿射函数的相关概念。