a qualitative study on the influence of perceptible information provided by drawings on lebanese grade 8 students’ argumentation and proof in the study parallelograms
The focus of our study is on the influence of perceptible information provided by the drawings on the construction of arguments and mathematical proofs among students in grade 8 at schools in the Akkar region, Lebanon. In Lebanon, mathematical proofs hold a central place in the teaching of geometry in Cycle 3, aligned with the mathematics curriculum. However, previous studies reveal that students’ difficulties in producing formal proofs stem from their lack of understanding of the nature and specific requirements of proofs. Our work is organized into seven chapters. The first four chapters present our problem statements, a literature review, the theoretical framework of the study, and an analysis of the mathematics curriculum and textbooks. The last three chapters describe the methodology employed, the results of our experiments, and our discussion. Our experimental situation was structured into three categories of students, each tackling a problem-solving situation leading to a mathematical proof. All categories worked on the same problem statement, but each had their own type of drawing presenting distinct perceptible information. These experiments highlighted that perceptible information in drawings has a significant influence on students’ argumentation and their proofs, both in terms of data and the warrants of arguments. It also influenced students’ approach to problem-solving. These experiments also shed light on how students apprehend drawings and use their knowledge of the figure to construct their arguments and proofs. Our study confirms that students’ concept-image related to their figure plays a crucial role in constructing their arguments and proofs. The informal arguments of students appear to arise from the inconsistency in their concept images with respect to the manipulated figures. (Author’s abstract)