Four groups (three engineering students in each group) were videotaped while constructing concept maps in Linear Algebra. There are two aims of this study. The first is to characterize the discourse in the groups by addressing the following research questions: Do the students communicate in an "effective" way? Do the students' communications contain the elements typical for a mathematically productive discourse? The analysis indicates that the communication among the students is effective and contains the elements that are characteristic for a "mathematically productive" interaction. The two types of methods used to analyze the data were "focal" and "preoccupational" analysis. The mathematical content and the coherence of the conversations were examined through focal analysis. The participants' engagement in the discourse was examined by preoccupational analysis, carried out by means of "interactive flow chart". The second aim of this study is to evaluate the newly developed methodological framework used to characterize the discourses. The study shows that several aspects of the methodological framework need to be developed.