This paper presents a characterization of the theoretical framework of doctoral research that aims to review how mathematics education is contributing to the construction of peace processes, in the dismantling of violence as a "natural" characteristic of a society vulnerable by years of conflict. A literature review is carried out and as a result, a priori categories for the research instruments are presented, articulating two reference frameworks and a proposal for professional mathematical practices for the construction of peace processes framed in the description of some suggested elements taking different reference frameworks.

Colombia signed a historic peace agreement in 2016, which marked a significant event for the social transformation of the country, and in which the role of education is fundamental for the reconstruction of the social fabric and the consolidation of peace processes. Therefore, the different responsible parties (governments, institutions, teachers) have the responsibility of guaranteeing an appropriate and pertinent education that eradicates poverty, improves the well-being of people, faces the challenges in the search for peace, understands the relations between nations and peoples, comprehends, analyzes and questions war conflicts and generates actions to build peaceful, fair societies that respect diversity, as well as an education that increases learning opportunities for each individual. In this sense, it is considered that mathematics education must also assume a responsibility in relation to classroom instruction and developments to promote and contribute to the objectives of education for peace and the transformation of the country. The doctoral research project aims to identify relevant aspects in the teaching processes that allow for the analysis of didactic suitability in mathematics instruction and the relevance of mathematics education in relation to the objectives, challenges and needs of education. To this end, it is proposed to investigate/evaluate some practices/proposals for teaching and learning mathematics that have been carried out in territories affected by violence in Colombia after the signing of said agreement.

The objective is to make a literary review of theoretical approaches that approach a perspective of mathematical education, democratic, deliberative, dialogic and political that promote the school as a center of justice and equity in order to enable theoretical tools to generate elements that will constitute the Professional Practices in Mathematics for the Construction of Peace Processes [ and will be articulated and/or complemented with the selected didactic suitability analysis tool, the six criteria established in the EOS with which a priori categories are established for the analysis of some mathematical instruction practices in school settings in territories affected by violence.

Keywords: Education, Mathematics, Peace, Didactics, Democracy, practices.