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.
The purpose of this article is to better understand how proof is introduced into the study of quadrilaterals and triangles in high school. To do this, we designed a grid to analyse mathematics textbooks in Cameroon francophone subsystems (7 th Grade and 8 th Grade). The Anthropological Theory of Didactics and the paradigms in geometry served as a theoretical framework for our analyses. The results of our analysis indicate that problems in the lessons section correspond to guided problems. These kinds of problems do not develop students' spirit of research and initiative. The authors of the textbook choose to teach the functioning of deductive reasoning in the 8 th Grade. They choose to introduce proof in the commented exercise section rather than lessons section. The learning problems proposed in the textbooks contain drawings wish have informative function and representative function. The preponderance of drawings with a representative function that have the same shape and name observed in textbooks can contribute to the construction of constant visual models in students' minds. This could lead to the superficial use of drawings in proof tasks.
Cet article a pour objectif d’explorer les connaissances des étudiants sur la figure et ses dessins en situation de construction d’une définition en géométrie. Il en résulte que les difficultés des étudiants pour construire une définition acceptable proviendraient d’un concept-image incohérent sur les figures manipulées, leurs images mentales semblant prendre le dessus sur les propriétés conceptuelles des figures.
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