Resumo Neste artigo, fruto das nossas vivências enquanto investigadoras junto à comunidade Terras da Costa em Portugal, pretendemos apresentar os olhares investigativos a partir de dois focos distintos: o projeto Fronteiras Urbanas – A dinâmica de encontros culturais na Educação Comunitária/FU (2012-2014) e a Escola do Bairro, inserida tanto no projeto como no atual Movimento Fronteiras Urbanas/MFU (2015). Tal proposta será mediada pelas teorias do Programa Etnomatemática e da Educação Comunitária, proporcionando o trabalho com a Etnografia Crítica, na qual o processo botton-up mobilizou as ações e as investigações na/com a comunidade, enraizando-se no contexto da dialogicidade freireana e do currículo Trivium de D'Ambrosio. Nosso eixo central é o conceito de Fronteira, que nos fez refletir sobre as relações que os caminhos e as perspectivas das investigações em Etnomatemática mantêm com as comunidades envolventes, pois acreditamos que o investigador nessa área encontra-se em constante movimento e que a topologia das fronteiras, estabelecida face a este movimento, pode reconstituir de forma integrativa o papel humanizador e político do investigador na comunidade.
Abstract The present article is fruit of our shared experiences as researchers within the community of Terras da Costa, Portugal. Our goal is to present our view as researchers focusing on two different perspectives: the Urban Boundaries project - The dynamics of cultural encounters in community education/UB (2012-2014), and the Escola do Bairro (Community School), which was part of the project and remains part of an on-going initiative called Urban Boundaries Movement (2015). This goal is mediated by the theories presented in the Ethnomathematics Programme and in Community Education, which allowed for: (i) working with Critical Ethnography, where research and action with and within the community was a bottom-up process, and (ii) grounding our work in the context of Freire's dialogical process and D'Ambrosio' Curriculum Trivium. The concept of Boundary is our core axis, which lead us to reflect upon the relationship between the pathways and perspectives in Ethnomathematics research and the involved communities. We believe that researchers in this field are in constant movement, and that the topology of boundaries, which is also being constantly established as a result of this movement, can reconstitute the role of politician and humanizer exercised by the researcher inside the community, in an integrative way.