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Research with Mathematics Teachers’ Specialized Knowledge – MTSK has grown in the world and in Brazil, although there are still few studies about creation and evaluation of training activities with such a theoretical framework. The purpose of this article is to discuss theoretically how a combination of the dimensions of the MTSK with scientific results in Mathematical Education can offer training sources to enhance the development of specialized teaching knowledge about fractions and operations, their teaching and learning. It is a qualitative analytical-descriptive research, of a theoretical-exploratory nature, in which we analyzed an excerpt from a training workshop in which a graduate was invited to reflect on the didactic sequencing to use the contents and based on his answer, we conducted a a posteriori reflective analysis on possible training paths. Our results show such paths, linked to everyone as MTSK dimensions based on scientific results, among which we highlight: (i) recommendations for linking concepts about fractions and procedures related to curricular specifications, scientific research or the opinion of experienced teachers, developed taking into account student learning characteristics, common mistakes and their likely sources; (ii) concepts, algorithms, procedures, justifications and phenomena related to fractions and their operations, as well as, different among such concepts; (iii) instructional and didactic clinical explanations that they use to understand through exercise, doing math, just memorizing it, including knowledge of the practice of defining and demonstrating.

POTENCIAIS OPORTUNIDADES FORMATIVAS COM MTSK E PESQUISAS CIENTÍFICAS SOBRE FRAÇÕES E OPERAÇÕES