Diagnostic study of mathematical reasoning in novice university students

Abstract

This paper presents the results of a study aimed at diagnosing how newly enrolled mathematics majors reason from a mathematical standpoint when they are required to perform inductive and deductive processes and validate or refute claims of a general nature. The theoretical framework underpinning this research comprises studies and investigations related to mathematical reasoning. The results of this diagnostic reveal that students lack mathematical reasoning skills that would allow them to justify statements of a general nature. In addition, they face difficulties in the development of deductive reasoning, are prone to generalize based on specific cases and lack skills in mathematical argumentation. On the other hand, they lack basic algebra skills such as developing square binomials and factoring. These findings highlight the need to design and implement a didactic proposal that fosters the development of reasoning and argumentation in students.