Abstract
Purpose
This paper proposes a situated understanding of mathematics, which means recognizing mathematics as locally and collectively constructed knowledge, in opposition to the universalist and neutralist conceptions of mathematics. We consider proposals formulated by Brazilian intellectuals of the 1920s and 1950s, as well as the political and social conjuncture of contemporary Brazil.
Methodology
We start section “An Act of Vandalism” in a critical position regarding the current Brazilian social and political conjuncture. We show that this has been provoking the strengthening of education policies that are far from reflection and dialogue (“The Brazilian Common National Base Curriculum” section). In a counterpoint to these policies, we consider the ideas formulated by the Brazilian educator Paulo Freire from the 1950s onwards (“The Reversal of an Authoritarian Scenario” section), as well as the proposals formulated by the Brazilian intellectuals of the 1920s who founded the "anthropophagic movement". They argued in favour of a Brazilian translation and the appropriation of foreign knowledge in both the artistic and intellectual fields (“Anthropophagic Mathematics” section). We also consider the historical course of the construction of hegemonic mathematics to show a process of untying mathematical knowledge from the demands of life to constitute an abstract, neutral, universal and purified body (“Formal (Deductive) and Informal (Procedural) Mathematics, Both Social Constructions” section).
Result and Conclusion
Starting from these reflections and examples in the Brazilian scenario, we verified possibilities of constructions of local mathematics from the recognition of the social experience of mathematics. This opens the space for the development of mathematical proposals that best meet the demands of each locality, be it in Brazil or in India.
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Notes
Another author, in criticizing the myth of superiority of formal mathematics and the Greek primacy in the discovery of such mathematics, presents strong evidence that there has never been a Greek named Euclid. He argues that the emergence of this fictional character arose from the interests of the Crusading historians, and was later welcomed, meeting the interests of the construction of the modern historiography of Western mathematics. According to Raju, the proofs in The Elements are essentially empirical (non-deductive). However, there was a certain convenience on the part of the mathematical philosophers of the twentieth century in convincing that Euclid failed in his intention of deductive proof. Raju’s arguments can be found on his webpage (http://ckraju.net), especially in the paper “Education and the church: decolonizing the hard sciences”.
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Cafezeiro, I., Kubrusly, R., da Costa Marques, I. et al. Paulo Freire, Mathematics and Policies that Shape Mathematics. J. Indian Counc. Philos. Res. 34, 227–246 (2017). https://doi.org/10.1007/s40961-016-0088-0
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DOI: https://doi.org/10.1007/s40961-016-0088-0