O ensino de números irracionais para alunos ingressantes na licenciatura em matemática - Broetto, Geraldo Claudio (2016)
The literature concerning the teaching and learning of irrational numbers points to shortcomings and inadequacies related to this issue, both in textbooks and in the training of mathematics teachers, with a view to their work in basic education. From this scenario, we conducted a qualitative research in mathematics education, qualitative, with intervention in the classroom. The objective of this doctoral work was to diagnose conceptual images of rational and irrational numbers brought by undergraduate students in mathematics, as well as analyze the movements of these images during the research. Data were collected in a group of undergraduate students initiating a course in mathematics teacher education at the Instituto Federal do Espírito Santo – Ifes – Campus Vitoria, during the year 2014. The theoretical framework used was the concept image (TALL; VINNER, 1981), instrumental understanding and relational understanding (SKEMP, 1976), prototypes examples and associations with relevant and irrelevant attributes (HERSHKOWITZ, 1994). Data analysis pointed to the precariousness of student’s knowledge of irrational numbers, especially in relation of prototypes and examples of an understanding - if at all - instrumental of the subject. The educational intervention was found to be cognitively able to unbalance the licensees, as well as contribute to the awareness of their own skills and limitations. The movement of conceptual images achieved by the participants also brought significant gains for the subjects, as well as pointed to new possibilities and future investigations.