Models for understanding teacher knowledge do not consider the possibility of teachers themselves generating it. The model of Verástegui and Úbeda (2022) has developed in response to the need to overcome this limitation, which it does by including teacher agency as a key element for understanding teacher knowledge. The aim of this research is to define the degree of operationalisation of the Systemic Model of Educational Teacher Knowledge, using a qualitative methodology comprising discourse analysis of a semi-structured interview and focus groups with a total of 25 teachers. The main findings show that the model is comprehensible to teachers, it partially approximates their experience, and it incorporates new elements for understanding the nature of the concept. Consequently, this research makes it possible to overcome some dichotomies in the conceptualization of educational teacher knowledge and incorporate collaborative dynamics into its comprehension and generation. Finally, updates to the model are suggested, highlighting the inclusion of three elements of pedagogical content knowledge -- personal, enacted, and collective -- and new research lines are proposed to validate its capacity for researching the object of study.