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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 mathematicallyproductive 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 flowchart. 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.

Sfard and Kieran [Kieran, C., Educational Studies in Mathematics 46, 2001, 187-228; Sfard, A., Educational Studies in Mathematics 46, 2001, 13-57; Sfard, A. and Kieran, C., Mind, Culture, and Activity 8, 2001, 42-76] have developed a methodological framework, which aims at characterizing the students' mathematical discourses while they are working in groups. In this study, I focus on an important aspect of this methodological framework, namely the interactive flowcharts. The aim of this study is to suggest two complementary analyses for the construction of the interactive flowcharts: an additional analysis by means of the analytical construct of contextualization as well as an analysis of types ofmathematical discourses. Based on data from a study of how four groups of Swedish engineering students collaboratively construct concept maps in linear algebra. I show that the two complementary analyses make the construction of the interactive flowcharts more coherent and transparent, and hence, more reliable. Furthermore, the two complementary analyses dramatically changed the picture as to whether the studied discourseswere to be seen as mathematically productive or not. In the end of the article, I discuss the possibilities of performing the suggested additionalanalyses within the original methodological framework.

The aim of this study is to characterize the discourse of two problem-solving courses for prospective teachers. The data, consisting of audio recordings and field notes, were examined from a dialogical approach combined with the theory of contextualization. I show not only the substantial differences between the two classroom discourses but also elaborate on plausible reasons for the divergency found. The findings then serve as a basis for a discussion of how to develop a problem-solving course within the mathematics teacher program.