STATE OF THE ART ON RESEARCH DEALING WITH METACOGNITION IN THE TRAINING OF TEACHERS WHO TEACH MATHEMATICSMetacognition; Initial training; Continuing training; Teacher who teaches mathematicsThis research aimed to analyze what theses and dissertations defended in Brazilian programs that deal with metacognition in the initial and continuing training of teachers who teach mathematics express. In the theoretical foundation, references from the field of Education, Psychology and Mathematics Education were used for the initial and continuing training of teachers. Methodologically, the investigation uses a qualitative, state-of-the-art research approach. The mapping of theses and dissertations took place in the CAPES and BDTD database. The time frame adopted covers the decade from 1980 to 2023. In this version of the dissertation, partial data was presented regarding the analysis of the first three specific objectives that deal with: Identify theses and dissertations that address metacognition, and its various subtopics, in training initial and ongoing training for teachers who teach mathematics; verify indicative aspects of the theses and dissertations raised, detailing research authorship, year of defense, academic title, institution, program and line of research and geographic distribution; Analyze theses and dissertations, objectives, thematic focuses, theoretical and methodological aspects and research results. At the end of the research, it is expected that the results will provide reflections on the knowledge produced by the research already produced on the use of metacognition in the training of teachers who teach mathematics and that their analysis can contribute to greater emphasis on metacognition in the spaces of mathematics processes. training of future teachers who teach mathematics.