Based on the analysis of the relationship among knowledge, comprehension and competence, we propose a set of competencies to be developed by the mathematics teacher, instrumental and systemic, that we considered appropriate to carry out a “didactic analysis” of his/her own teaching. The competences are based on the knowledge of didactic of mathematics that allows the teacher to assess the design and the development of the teaching and learning processes, in a reflective way.
The concept of competency has strongly permeated the education in mathematics, it is spoken of “teaching by competences” and it is assumed as a capacity to face or to solve a complex activity. In the research in didactics it seems that such a concept is so wide that more fine and adapted notions should be used to describe and to explain the cognitive and didactic processes.
The importance of the context is implicit in the definition, acquisition and building competency; this can only be expressed through social interactions contextually defined and it is related with the tacit rules and the expectations derived from the context.
The notion of competence is constituted as the general cognitive-epistemic construct that includes not only the know-how but also the justifying theoretic discourse plus the affective, attitudinal and axiological components.
In our research we described instrumental competences (for the learning and the training) and systemic (those offer an ample view and serve to negotiate the activity), that applied to the mathematics teacher can be concrete in what we call competency for the “didactic analysis and synthesis”, e.g. competency to analyze the mathematics teaching and learning processes and to synthesize the mathematic didactic knowledge, for the design, implementation and assessment of the own teaching activity.
Having in mind some aspects of the onto-semiotic approach to knowledge and mathematic instruction developed by Godino et al. 2007, we give a classification of the specific competences for training mathematic teachers, called competences for the didactic analysis:

1. Competencies referred to the design and implementation of processes of mathematics study.
2. Competencies referred to specific didactic knowledge and assessment of the didactic suitability.

We describe the application of a formative cycles based on problem-situations that allow to contextualize and to relate some mathematic content. Such experience is analyzed from the didactic point of view, having in mind diverse dimensions and components, in particular the assessment of the didactic suitability of the activity under study. Such formative cycle is described in Godino, Batanero, Roa y Wilhelmi (in press).

References
Godino, J. D. Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, Vol. 39 (1-2):127-135.
Godino, J. D., Batanero, C., Roa, R. y Wilhelmi, M.R. Assessing and developing pedagogical and statistical knowledge of Primary school teachers through project work. Joint ICMI/IASE Study Conference on Teaching Statistics in School Mathematics. Monterrey, México, Julio 2008.