The article shares some elements of comprehensive type about “mathematical argumentation in the classroom”; whose analysis, was made from two fundamental categories in the development of an oral mathematical argumentation process for the conviction, contradiction and validation of a written mathematical argumentation process. The research addressed two central categories of argumentation as a discursive form, the first one is the epistemic position, and the second one is the discursive position that students unveil at the time of mathematically arguing the solution to a problem situation. The research was developed under the interpretative paradigm through the design of a case study directed by the theory and technique of a focal group, for the collection of information. In the findings, difficulties in the passage were evidenced from the semantic to the theoretical from the epistemic position; regarding the discursive position, the presence of three discursive forms was revealed: description, explanation and argumentation, the latter being the least used by the students.

This article discloses some considerations and reflections in the teaching of random thinking and data systems based on a documentary review. A documentary sample was used consisting of 40 documentary sources (articles, postgraduate dissertations and books), published in indexed journals, about random thinking. The research was based on a qualitative content analysis method which used the coding and categories saturation process. The results let us establish conceptual relationships considering three dimensions linked to the random thinking teaching, they are: epistemological corpus, theoretical corpus and the social function. The results allow to base new proposals of curricular, didactic and evaluative type for the teaching of this thinking, at the same time, it allows to carry out processes of self-assessment of the teaching practice and of the need that currently exists before the research in the classroom and the contextualization of mathematical knowledge.