Algorithms and kinship systems: ethnomathematical approaches in the training of indigenous teachers

Abstract

The goal of this paper is to present an ethnomathematical research and its use in the training of Kaingang indigenous teachers in Mathematics and Natural Sciences. The experience takes place within the Indigenous Intercultural Bachelor's degrees of the Community University of the Chapecó Region (Unochapecó), in Santa Catarina, Brazil. The text includes both the description of a pedagogical experience that is framed in the ethnomathematical paradigm, as well as the proposal of a specific ethnomathematical hypothesis, about the Kaingang people's kinship system. The postulation of the hypothesis was a necessary moment within the pedagogical experience, since there were no significant studies on the cited culture that would serve as ethnomathematical material for the classes, so we thought it would be interesting to investigate that area in order to obtain the cited material. The conjecture specifically postulates that the Kaingang kinship system can be expressed in the formal language of a predicate logic. This allows us to interpret the reasoning with which kinship relations (marriage, affiliation, inheritance) are calculated as algorithms, that is, as resolutions of problems in a finite and unambiguous number of steps. The hypothesis also provides that the system can be expressed as a computer program. In addition to presenting the experience together with the specific hypothesis, the work describes how it was used in the training of indigenous teachers and evaluates its results.

Keywords:
Ethnomathematics; Interculturality; Algorithm; Kinship; Indigenous education