The mathematics teaching in indigenous contexts often ignores the mathematical knowledge and teaching styles of the communities, positioning the western school domain. The consequences of this, merit formulating a proposal that is raised from indigenous peoples, so this research builds a model of mathematical tasks with cultural responsibility (MTCR) from the Mapuche context in three indigenous territories of Chile and their respective schools. The work with each establishment and its family context is carried out under the research cycles and the participatory action research process, from which a modelo MTCR is configured with mathematical artifacts, objectives, activities and class management as a founding structures of a third space integrated in a parallel dialogical way between local and school culture.