O ensino de teoria de grupos nos cursos de licenciatura em Matemática

Abstract

This study explored which type of algebra should be taught on mathematics teaching certification programs and was centered on the question: What group theory content in teaching certification provides future teachers with the best grasp of the subjects related to these topics in elementary education? The study objective was to investigate which group theory content should be included in mathematics teaching certification programs. The theoretical ideas were drawn from studies on training mathematics teachers, particularly by Shulman, and supported discussion on the knowledge held by teachers. A qualitative study was conducted providing an overview of the origins and development of the group concept. The curricula of disciplines involving group theory on Mathematics teaching certification programs of seven Brazilian higher education institutions were analyzed. Five semistructured interviews were held with teachers and researchers who taught group theory or carried out research in this area. The data were treated using content analysis presupposes, as described by Bardin. Results showed that all interviewees were concerned about teacher training. Core topics that should be covered include: definition and examples of group; subgroups; normal subgroups; cyclic groups; group homomorphism and isomorphism; permutation groups; transformations of plane and space groups; symmetry groups; quotient groups; and demonstration of theorems (of Cayley, Lagrange, and/or Sylow)