The teacher’s argumentation is considered essential to promote the student’s mathematical education; the teacher’s argumentation is linked to the teacher’s didactic-mathematical knowledge and the achievement of instructional objectives. In this sense, a pragmatic proposal is required that links the teacher’s didactic-mathematical knowledge with argumentation. Toulmin’s (2007) model makes it possible to study the structure of teacher or student argumentation; in contrast, pragma-dialectic considers that in the face of a difference of opinion, the parties involved try to persuade their counterpart while observing argumentative discourse standards. In the context of an argumentative class, both argumentation models do not consider the particularities of the argumentation of a didactic nature that the teacher uses. This document presents a proposal for argumentation suited to mathematics education, based on a mapping of literature and a model of the teacher’s knowledge, contrasted in an actual class. The analysis and discussion of data let us conclude that a teacher’s argumentation is characterized by epistemic, cognitive, interactional, emotional, and communicative features that reaffirm not only the complexity of educational practices but also the teacher’s argumentation for educational purposes and the adequacy of the proposed definition.