INTRODUCTION TO PROOF: THE MEDIATION OF ... - IngentaConnect
50 MARIA ALESSANDRA MARIOTTI supported by the mediation of new external signs (offered by the software), that pupils autonomously create and use with that specific pupose. The evolution of the pupils’ internal context is rooted in the construction activities, where different processes such as conjecturing, arguing, proving, systematizing proofs as formal deduction are given sense and value. Our experiments also show that the contradiction highlighted by Duval between everyday argumentation and deductive reasoning, between empirical and geometrical knowledge, can be managed in dialectic terms within the evolution of classroom culture. In our experiment classroom culture is strongly determined by the recourse to mathematical discussion orchestrated by the teacher to change the spontaneous attitude of students towards theoretical validation. The introduction of computer environments in school mathematical practice has been debated for years, in particular the potentialities of Cabri, and dynamic geometry in general, have been described and discussed. With this experimental research study we hope to offer a contribution in illustrating the cognitive counterpart of classroom activities with Cabri that allows an approach to theoretical thinking. ACKNOWLEDGEMENTS The research project has received financial support from C.N.R., M.U.R.S.T. (National Project ‘Ricerche di Matematica e Informatica per la Didattica’, coordinator: F. Arzarello). I wish to thank the teachers of the research team, M.P. Galli, D. Venturi e P. Nardini, who carried out the classroom experiments and discussed with me the data on which this paper is based. I would also like to thank the many colleagues who in the past years have generously contributed to making me develop these ideas. NOTES 1. The following remark concerns types of software which share with Cabri the general feature of a ‘drag mode’; I mean for instance Sketchpad or Geometric Supposer. 2. In this section I will employ the term ‘tools’ as used in the current English translations of Vygotskij’s works. In current literature the terminology is rather confused, as different authors use the same words with different meanings. 3. This unusual construction, quite different from those which can be found in the textbooks, seems to provide a strong support to our interpretation. 4. After the construction of the angle bisector and the inclusion of the corresponding command in the available menu, the definition of perpendicularity was introduced.
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