O ensino de números irracionais para alunos ingressantes na licenciatura em matemática
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Data
2016-02-26
Autores
Broetto, Geraldo Claudio
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Editor
Universidade Federal do Espírito Santo
Resumo
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.
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Irrational numbers , Mathematics learning , Teacher training , Mathematics at university level , Aprendizagem em matemática , Formação de professores , Matemática no ensino superior