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In this paper, we take a semiotic/dialogic approach to investigate how a group of UK 12–13-year-old students work with hierarchical defining and classifying quadrilaterals. Through qualitatively analysing students’ decision-making processes, we found that the students’ decision-making processes are interpreted as transforming their informal/personal semiotic representations of “parallelogram” (object) to more institutional ones. We also found that students’ decision-making was influenced by their inability to see their peers’ points of view dialogically, i.e., requiring a genuine inter-animation of different perspectives such that there is a dialogic switch, and individuals learn to see the problem “as if through eyes of another,” in particular collectively shared definitions of geometrical shapes.

Students’ collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach