Os Níveis do Pensamento Geométrico de Van Hiele em Questões de Geometria Espacial do Exame Nacional do Ensino Médio: uma Análise de Protocolos de Acadêmicos Ingressantes na Educação Superior

Abstract

The research question of this work is the following: which levels of Van Hiele model of geometric thinking do undergraduate Mathematics students mobilize when solving spatial geometry questions of the National High School Exam (ENEM)? The objective is to analyze the protocols followed by higher education students when faced with spatial geometry questions adapted from ENEM tests. The specific objective is to analyze the incoming students’ argumentative capacity (justifications) to answer spatial geometry questions adapted from ENEM, considering one of the five levels of Van Hiele model of geometric thinking. This is a qualitative research, as it is determined by the characteristics of the research question, which implies documentary data, i.e. answers provided by Mathematics students to questions adapted from ENEM that can be subject to description and interpretation (LÜDKE; ANDRÉ, 1986). The participants were attending a public university situated in the western border of the State of Rio Grande do Sul. The sequence of recursive movements of the Textual Discourse Analysis were used: unitarization, categorization and production of meta-text. The first three levels of Van Hiele model of geometric thinking were found in the students’ protocols: Visualization, Analysis and Abstraction. This means that the incoming students were still transitioning from Basic Education to Higher Education, that is, along the Mathematics course they might reach the highest levels, i.e. Level 4 (Formal Deduction) and Level 5 (Rigor), as expected from Higher Education.