In this paper we describe an educational proposal for prospective secondary school mathematics teachers in Mexico, whose aim was to contribute to the development of their didactic-mathematical knowledge about linear variation through mathematical tasks, the development of the competence of identifying primary mathematical objects and the reflection on hypothetical cases of teaching. The proposal is supported within both the Onto-semiotic Approach (EOS) and the Mathematics Teacher's Didactic-Mathematical Knowledge and Competence model. The proposal follows a design research methodology based on EOS. The results show the complexity related to the development of the competence of identifying primary mathematical objects, they also highlight the influence that competence has on the development of the epistemic and cognitive facets of prospective teachers' didactic-mathematical knowledge on linear variation. [For the complete proceedings, see ED629884.]