The theory of conceptual fields and logical-mathematical thinking: a didactic bet La teoría de los campos conceptuales y el pensamiento lógico-matemático: una apuesta didáctica

Abstract

From Gerard Vergnaud's Theory of Conceptual Fields, research was conducted with the aim of formulating a set of didactic guidelines to strengthen logical-mathematical thinking, which is a matter of concern in the education of Colombian students. Using the criteria characteristic of qualitative research, a semi-structured interview was administered, documentary work was conducted, and three workshops were implemented for students in the Programming I course. This generated consistent information that allowed for the establishment of some didactic guidelines that can bring about significant changes in the way mathematics courses are approached at both the secondary and high school levels. These guidelines will contribute to a more consistent development of logical-mathematical thinking, emphasizing conceptual strengthening, a greater focus on educational intent rather than the execution of the class or program, diversity in resources, increased support for student groups, and a stronger connection with courses related to critical reading. It is important not to reduce didactics to the mere completion of exercises and workshops.