The book: Forma??o do professor de matem?tica e sua atua??o no ensino remoto durante a pandemia: comparativo escola p?blica e escola privada presents a comparative study between a public school and a private school.The study is based on the assumptions of the legislation that organized and guided the implementation of remote teaching - legal devices of the Federal Government, the State Government of S?o Paulo, and the municipal government. It is also based on authors who deal with teacher training, such as N?voa, Lib?neo, Tardiff, and Shulman, as well as authors such as Barcelos, Behar, Passerino, Miranda, Ponte, and Canavarro, who discuss the relationship between technology and teaching, and between mathematics teaching and the resources used. The objective of this research is to compare how a state public school and a private school offered remote teaching, comparing aspects of infrastructure, training and teaching performance of the mathematics teacher and contributing to a reflective and amancipatory practice in the process of knowledge construction.