| Summary: | Dissertation presented for the PhD Degree in Education Science – Curricular Theory and Science Teaching, by Universidade Nova de Lisboa, Faculdade de Ciências e TecnologiaThis work explores the urban experiences of marginal social lives through the mathematical epistemic regimes at the core of their survival strategies. It focuses in particular on the mathematical epistemic regimes of children in a street situation and seeks to recognize, understand, and validate forms of mathematics constructed and used outside of the established institutions of mathematical production. This work rests on the foundation of "The Mathematical Imagination",which draws together social constructionism (as it is developed in Sal Restivo's sociology of mathematics) and Ubiratan D'Ambrosio's conception of ethnomathematics. These two central ideas contribute to the objective here of connecting the production of formal mathematics and the praxis of informal mathematics, the mathematics produced at the margins where survival is more important than reflecting and reproducing professional cultures. The fact is that professional institutionalized mathematics within the contemporary mode of production has domesticated mathematical objects. Informal mathematics arises and is broadcast in the positions and voices at the margins of society and mathematics. The bringing together of marginal and non-marginal positions and voices results in and is an activist social practice. This practice represents the end of verbalism and the beginning of a situated knowledge that is engaged with our everyday lives, with our very being. Only through this form of practice, a practice that links the formal and the informal, can we realize the full power of mathematical knowledge as a social thing (in Durkheim's sense), a product of the collective consciousness that expresses collective realities and a category of knowledge present in every culture. This is as true for mathematics at the margins as it is for professional mathematics. The point of this work is to contribute to an emerging political manifesto of the marginal that demonstrates the social realities and social power of their mathematics. This is made possible through the application of social theory, and the practices of ethnography (especially in the traditions of action anthropology and the new ethnography) and history. These tools, melding science and action, help to reveal otherwise invisible and ignored cultural connections and social coherences, and in the end all is clarified and linked through a social construction guided by a concern for love and community.III Quadro Comunitário de Apoio, existing between European Social Fund and the national fund of MCTES, in the Fundação para a Ciência e a Tecnologi
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