The Role of Sign Vehicles in Mediating Teachers‘ Mathematical Problem Solving 243DISCUSSION AND CONCLUSIONS
In this study, the interplay between the three dimensions of the analysis procedure in
collaborative problem solving of mathematics teachers nicely highlights the nature of the
communicative meaning making of these mathematics teachers. The analysis of discourse
moves makes visible the nature of reasoning from the viewpoint of participation in social
activity. Four different participant roles emerged in the analysis of the discourse moves.
These roles were the tutor, clarifier, questioner and silent supporter. From a mathematical
point of view, the communicative problem solving consisted of procedural, identity, material
and semiotic modes of interaction. The patterns of interaction were constructed around these
modes when groups of teachers negotiated the mediational meaning of cultural tools. The
analysis of these patterns revealed diverse thematic episodes in collaborative meaning
making, such as problem posing, problem solving, clarification through mathematizing and
clarification through hands-on-activities.
This study shows an interesting connection between cultural focus of interaction and the
evolving role of the sign. Turns coded as procedural and semiotics modes of interaction
carried the key elements of the evolving role of the sign. Besides, the evolving role of the
semiotic vehicle was traced in discourse moves categorized as initiating, extending,
questioning and tutoring moves. The analytical method developed for the study brings in the
nature of educational interaction that is needed to support the collaborative negotiation of
abstract ideas.
The study suggests the power of mediational tools to make visible the abstract nature of
mathematical ideas behind the computational rules of algebraic procedures. Furthermore, the
analysis of the data revealed that the usage of cultural tools in the collaborative problem
solving of mathematics teachers aided them in elaborating their conceptual understanding of
mathematical ideas. On the whole, the study yields useful information about teacher learning
and development from both the social and the mathematical point of view, and provides
educators and researchers with tools to develop curriculum as well as instructional solutions
for mathematics classrooms, both at the school and at the teacher education level.
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