This research refers to an investigation, of a qualitative nature, which resulted in a master's thesis, carried out in the space of Popular Education (PE). The pandemic that broke out in 2020 is the context of this work, which took place nearly entirety in the context of Emergency Remote Teaching (ERT), with the use of Information and Communication Technologies (ICT). In this way, the research sought to articulate the theoretical frameworks of the Lesson Study (LS) practice with the Didactic Suitability Criteria (DSC) in an extension course in the training of teachers who worked in the teaching of Mathematics in PE. The proposed extension course was held in 2021, where teachers participated in a complete LS cycle with planning, execution and reflection of classes implemented in this context. The production of data took place in a totally remote way in which recordings of the meetings and classes taught by the researcher were produced. The analyzes are concentrated on the productions of the group of teachers participating in the training course and the main objective of the research was to analyze which and how the DSC were used by this group of participating teachers.Based on an analysis of the data produced in the research, it can be said that there is a gap between theory and practice in teaching planning. In this case, the importance of these moments of reflection on teaching practice provided by LS is reiterated. From our analysis, we understand that the discussions promoted in the extension course expanded the theoretical framework of the professors on a reflection of the lesson plans elaborated and implemented by them. In addition, our expectation was to engage the group of participating teachers in moments of collective reflection, which could be integrated and taken beyond the scope of the training course.