This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by using the pre-test results and divided into an experimental group and a control group. The learning environment for the two groups was designed to be the same except for jointly manipulating Geogebra on the laptop in the experimental group. Students' discourse was analyzed using an analysis framework that applied both Piaget's (1959) linguistic categories and Rutherford's (2011) neo-Piagetian model. We found that the dynamic geometry environment improved communication among students and their achievement levels. In particular, graphic and dynamic representations created by dragging stimulated students' interest and increased communication among them. Although the quality of communication was somewhat different in the discourse analysis of the two groups, each participant's role was confirmed in the co-construction of knowledge among all cases of eight students. We expect that precise verbal information on various representations of mathematical content in the process of understanding the concepts of students could be an opportunity to prepare educational environments corresponding thereto.