The objective of this article is to identify the meaning attributed to the didactics of mathematics and what are the criteria with which an improvement in the teaching and learning process of mathematics is based, future teachers of mathematics, belonging to universities in three different countries (Brazil, Chile, and Ecuador). The qualitative analysis indicates that the majority of future teachers consider that the didactics of mathematics is a technical discipline that consists of providing strategies, resources, and procedures for teaching mathematics; few consider it as an art to teaching and almost none consider it as a scientific discipline that is concerned with studying the processes of teaching and learning mathematics. In addition, the results show that the criteria used by them, on how teaching and learning in this discipline can be improved, are focus, above all, in the cognitive, ecological, and emotional aspects and, to a lesser extent, to the interactional, mediational and epistemic. Finally, it is concluded that the improvement in teaching and learning is directly related to an improvement in the training programs of future mathematics teachers.