The school system has always aimed to achieve quality teaching, which is able, on the one hand, to give adequate responses to the expectations of all the stakeholders and, on the other, to introduce tools, actions, and checks through which the training offer can be constantly improved. This process is undoubtedly linked to scientific research. Researchers and Academics start from the data available to them or collect new ones, to discover and/or interpret facts and to find answers and new cues of reflection. A favorable environment for this work was the Seminar "INVALSI data: a research and educational teaching tool", in its fourth edition in November 2019. The volume consists of six chapters, which are arise within the aforementioned Seminar context and, while dealing with heterogeneous topics, offer important examples of research both on teaching and on the methodologies applied to it. As a Statistical Service, which for years has taken care of the collection and dissemination of data, we hope that in this, as in the other volumes of the series, the reader will find confirmation of the importance that data play, both in scientific research and in practice in classroom.