238 Sinikka Kaartinen and Timo Latomaa
simultaneously in the same classroom, carrying out their research designs for executing the
activities. In this paper, the empirical example of the usage of algebra tiles will be discussed.
3.4. Data Collection
The primary data for the study consist of videotaped and transcribed episodes of social
interaction in the collaborative problem solving situation. In the investigated activity, the role
of algebra tiles as semiotic vehicles is investigated in collaborative learning activity. Specific
research questions posed for the study are the following: “How are semiotic vehicles applied
to instruction building in primary mathematics?” and “What is the mediational role of
semiotic vehicles for algebraic/arithmetic computations in collaborative meaning making?”
3.5. Data Analysis
This paper applies discourse analysis (Kaartinen and Kumpulainen, 2001, 2002) in the
investigation of collaborative interactions within mathematics learning situations.
The analysis method and its specific categories were grounded in the discourse data of
the study. In the analysis procedure, the collaborative interaction is approached from three
dimensions, namely from the viewpoint of discourse moves, the evolving role of the sign and
from the viewpoint of cultural focus.
The analysis of discourse moves highlights the nature of the conversational exchanges
between the members of the learning community, and consequently sheds light onto the
participatory roles of the group members in communal activity. Moreover, the analysis of
discourse moves supports content analysis by highlighting thematic patterns emerging in joint
problem solving.
Discourse moves identified in the discourse data are initiating, continuing, extending,
organizing, agreeing, evaluating, tutoring, thinking aloud and concluding. To highlight the
interplay between problem solving elements in the collaborative activity of in-service
teachers, the second dimension in the analysis method investigates the cultural focus of the
social interaction on a moment-by-moment basis. The cultural focus of the interaction data
consisted of the procedural, identity, material and semiotic modes. To investigate the role of
sign in the meaning making process, the evolving role of the sign consisted of categories of
no elements of sign, elements of signifier, signifier aspect of sign, signifier connected to
signified, elements of signified, sign and social sign. Table 1 summarizes the analytic frames
and categories of the analysis method.
4. RESULTS
The results of this study are discussed via a case-based description derived from one
teacher group, to highlight joint reasoning and the application of cultural tools in the
collaborative learning of mathematics pedagogy.