This paper presents research on the argumentation that preservice teachers perform when designing and teaching geometry. Argumentation is associated with speech acts carrying didactical intentions. This research study features of preservice teachers' argumentation when explaining geometry tasks both to peers, during preparation and discussion of designed activities, and to students in the classroom. This is qualitative research and the results support establishing relationships between the didactical dimension of the didactic-mathematical knowledge model and some characteristics of the argumentation that preservice mathematics teachers exhibit during their planning and teaching.

We present a qualitative study aimed at devising a theoretical-methodological tool to assess students’ conceptual understanding of physical phenomena through the argumentative qualities of their written texts. The proposed relationship between argumentation and understanding is elaborated through the notions of knowledge, purposes, methods, and communicative forms, as well as the use of data, warrants, modal qualifiers, claims, and rhetorical resources. In order to exemplify the tool’s use, the current understanding of six students attending a physics seedbed course was assessed according to four levels: naïve, novice, apprentice, and mastery. We then discuss the possibilities and limitations of the tool and the need to broaden the assessment of students’ understanding to include argumentative tasks in the classroom.