Influence of Drawing and Figures on Secondary School Students’ Argumentation and Proof: An investigation on Parallelogram

In this article, we wish to explore the influence of the figure of the drawing on the argumentation of students who are involved in a proof task. It is about analysing the knowledge that students associate with parallelograms and the interactions between students and drawing. Our research is based on both Toulmin's model and Vinner's concept image and concept definition. After decomposing down the students' arguments, we analyse the data in order to identify their origin and the element of the concept image mobilized in argument. Our data suggest that the students' personal concept definitions do not correspond to the formal definition of the figure, the drawing causes a conceptual change in the students' personal concept definition. The data resulting from the abusive interpretation of the drawing is found in both the students' argumentation and proof.