This book explains the results of a bibliographic and field research that proposes an instrument to evaluate Mathematics classes built in the patterns and conceptions of the Japanese model of teacher training called Lesson Study. In addition to being a simple means of evaluation, the instrument has proved to be able to provide teachers with information for making decisions about the process of teaching their own mathematics classes and preparing an environment that prioritizes interaction and dialogue, creation and active participation of students, keeping them engaged with the connections of the idea and procedures proper to mathematics. And, it proved promising to guide teachers to investigate and reflect on their own teaching practices, to analyze the disparity between their planning and the execution of their classes, and even to assist in the preparation of new planning.