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.
Our work focuses on logic and language at a university in Cameroon. The mathematical discourse, carried by the language, generates ambiguities. At the university level, symbolism is introduced to clarify it. Because it is not taught in secondary school, it becomes a source of difficulties for students. Our thesis is as follows: "The determination of the logical structure of mathematical statements is necessary in order to properly use them in mathematics." We conducted our study in the predicate calculus theory. In the first part of the paper, a summary of the theory is presented, followed by a logical analysis of two complex mathematical statements. The second part is a report of two sequences of an experiment that was conducted with first-year students that shows that knowledge of the logical structure of a statement enables students to clarify the ambiguities raised by language.
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