Capture modes: Tensions caused by ethnomathematics between State science and minor science

Abstract

This article aims to discuss the power relations arising from the modes of articulation proposed by some researchers between the different mathematic rationalities and school mathematics. For this purpose, eleven utterances of the IV Brazilian Congress on Ethnomathematics were divided into two groups and subjected to a process of analysis, considering the theories of Wittgenstein, Foucault, and Deleuze/Guattari. In the first group we find that the “encounter” of the “other” mathematics with school mathematics serves to facilitate the learning and development of concepts pertinent to mathematics education, motivating learning and giving meaning to school mathematics. In the second group we find a condition that seems much more problematic and concerns the need for an “exercise of translation” aiming to “qualify and legitimize” the different mathematics through the possibility of turning them into scientific knowledge. Considering these two capture operations we propose the encounter of different mathematics – the “other” mathematics, school mathematics and academic mathematics – from the logic of the encounter of flocks, without fear of risks, so that one does not impose its logic on another. However, for this encounter to take place one must consider the need for academic mathematics and school mathematics to take a less arrogant position vis-à-vis other mathematics.

Key words: ethnomathematics, state science, minor science.