The research study, this article is based on, aims to develop principles to enable the transfer of research knowledge to teaching. In this article are presented the design and implementations of a research project intended to support teachers in understanding their practice and improve it. Furthermore, the central idea was to improve the communication in mathematics between teachers and teachers-students. Issues that arose from practice were framed in terms of learning. In addition, the variation theory formed the background to our work. The students’ tests, examination of students’ mathematical work, the teachers’ lessons plan and reports of the lessons’ instructions are the data base for this article. The analysis indicated that teachers were not able to describe the critical aspects in students’ learning in the beginning of the project. By giving teachers the training that allows them to become reflective teachers, they also get the possibility, as professional decision makers, to develop the ability to identify the critical aspects in students’ learning and consider how opportunities for learning can be enhanced. Furthermore, if the teachers base their instructions on the identified critical aspects and open up dimensions of variation in these aspects, the students’ learning seems to be facilitated. The findings suggest that developing an understanding of the students’ critical aspects can be a productive basis in helping teachers to make a fundamental change in their instructions and to improve the mathematical communication in the classroom.