Developing students' critical aspects to improve mathematical communication in the classroom

This article investigated teachers' abilities to identify the critical aspects. The analyses suggest the teachers were able to accurately identify and describe such critical aspects of students' learning, but they were unable to identify all of the aspects. By debating the numerous types of critical aspects and their causes, as well as instructional approaches and procedures to overcome them, the teachers improved their ability to identify the critical aspects and open up dimensions of variation in these aspects.