Análisis de la argumentación matemática de estudiantes de primer año

Fostering students at the beginning of university studies is an important issue not only in the international context but also in Chile. However, high dropout rates show that the transition from secondary school to university in mathematics is supposed to be difficult for many students. Mathematical argumentation is a core activity in mathematics and also very complex. Therefore it could be one of the main reasons for the difficulty at the secondary-tertiary transition in mathematics. This study analyzes the quality of students' argumentations, the proof scheme, and the formalism in students' answers of N = 86 first-year students in mathematics in order to better understand where the problems are in detail. The results show that the quality of argumentation, the use of appropriate arguments, and mathematical formalism highly varies in the two reported tasks: on the one side, 10% of students are able to prove one of the given geometrical theorems, on the other, 65% proved the other theorem correctly. This indicates that students are in a phase of developing their argumentative abilities. Consequently, the process of proving and constructing analytical arguments should be explicitly discussed in university lectures, so that students can improve their abilities for mathematical reasoning.