Relationship between drawing and figures on students’ argumentation and proof

In this article, we wish to explore the influence of the figure and the drawing on students’ argumentation and proof during the solving problem. Our research is based on both Toulmin’s model and Vinner’s concept image and concept definition. After analysing the arguments with the Toulmin model, we analyse the personnel concept definition, concept image evoked about the figure and the effect of drawing which intervene in students’ arguments. Our data suggest that wrong student’s arguments seem to be based on their concept image evoked on the figure manipulated which is in contradiction with the formal axiomatic system. Moreover, the data of the arguments seem to come from an abusive interpretation of the drawings. Observations that emerge from students’ oral and written speeches reveal continuities and gaps between their argumentation and proof.