Proving general sentences in mathematics and justification of mathematical statements by learners of mathematics. The anthropomathematical studies

The article contains theoretical considerations and the description of the didactic research which I carried out. Theoretical reflections relate to one of the most important components of mathematical knowledge and skills of students, such as the proving, explaining and justification, as necessary elements included in the mathematical methodology. Theoretical considerations also include the establishment of research-theoretical approach to exploring learning-teaching mathematics process, called anthropomathematics. The article describes the results of the didactic research which the main objective was diagnosis relating to the question: what criteria decide that a mathematical statement can be considered (by students) to be true? Their main part of mentioned research was presented in my monograph entitled: The methodology of mathematics as a subject of anthropomathematical studies (Żeromska, 2013).