This work analyses the possibilities of transformation a proposal of Mathematic Education based on projects investigation that promotes transdisciplinaridade and the students participation on the teaching /learning process. It brings to the development of the reflexive and critical competence for the integral education of students from grade school which are riverain, these competences, according to Skovsmose (2004) and Mora (2005) are necessary for the citizen‟s participation in our society. Based on Santos (2010) and others, I analyze the crisis on dominant paradigm in the sciences, and its unfolding in the education process and also its consequences on life of the traditional culture as the riverain. As theory base on Ethomathematic, mainly on Ubiratan D‟Ambrosio (2005; 2012), Gelsa Knijnik (2001) and Alan Bishop (1999) works, it also stablishes a dialogue with Critic Mathematic Education, it has as a reference the searches of Ole Skovsmose (2000; 2004; 2006) and David Mora (2005), on search of connections and mutual articulations which propitiate the education work with riverain population. At “Poção” community on Cotijuba Island specifically at Escola Pedra Branca ( Grade School, only for initial series) where I restored the empiric part of this search. For this work, I dealt with 19 (nineteen) students of that level of studies, 07 (seven) parents/students responsible and the school teacher. For the Methodology, I utilized two different and complement moments: the first one consists on approximation of the searcher to the riverain cultural universal of “Poção” community, it happened on three articulated stages: the observation, the interpersonal dialogues with the inhabitant of the community and the searcher participation on activities which it is being observed riverain‟s social practices. The second moment is more pedagogical. It is about the development with the students and their teacher using four settings for investigation of social economic and cultural activities from “Poção” community: naval carpentry, fishery handicraft, the collect and commercialization of fruit, the plantation of small country and vegetable-garden, all of those strategies were used to dialogue with cultural knowing/doing of the riverain and about the forms of used measures on the community and their relations with the studied measure on that level of studying of Mathematic school. From the analyses “settings of investigation” on (SKOVSMOSE, 2000), I made clear that the investigative projects of “transdisciplinar” character enable the students respect as subjects which produces knowledge, having as consequence the students active participation on their process of learning, and also, they give the visibility, on the course, the knowledge of tradition “putting them on interlocution with knowledge legitimated in our society with the scientific knowledge” (KNIJNIK, 2001, p. 25), establishing useful relation and mutual articulations between the mathematic knowledge and the riverain knowledge at “Poção” community from Cotijuba.
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