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In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching-learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.

The paper presents a classroom experiment in which students were asked to solve an open problem. It is the authors' premise that this kind of task fosters à smooth' approach to proofs that are constructed around the production and validation of conjectures. This experiment is aimed at constructing a shared classroom culture. Classroom discussion and collaborative group work help to achieve this aim. The analysis of the experiment shows that the discussion makes explicit aspects of students' thinking which would be hidden in a normal activity. It is demonstrated that a deeper analysis of students' reasoning and behaviours can be better performed if lessons are video-recorded. There is a twofold pedagogic gain in using videotapes as a tool for analysing students' behaviour: ®rst, it o ers the teacher a tool that encourages students to re¯ect on their reasoning; secondly, and conversely, it o ers researchers a further tool for analysing students' performances.

In this paper we present a classroom experiment in which students were asked to solve an open problem. It is our premise that this kind of task fosters a 'smooth' approach to proofs that are constructed around the production and validation of conjectures. This experiment helps to construct a shared classroom culture, one of the aims of this activity. Classroom discussion and collaborative group work helps to achieve this aim. The analysis of the experiment shows that the discussion makes explicit aspects of students' thinking which would be hidden in a normal activity. We demonstrate that a deeper analysis of students' reasoning and behaviours can be better performed if lessons are video-recorded. There is a twofold pedagogic gain in using videotapes as a tool for analysing students' behaviour: firstly it offers the teacher a tool that encourages students to reflect on their reasoning; secondly, and conversely, it offers researchers a further tool for analysing students' performances.

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