Conceptions and didactic-mathematical knowledge of the teacher in teaching the concept of function by projects Concepciones y conocimiento didáctico-matemático del profesor en la enseñanza del concepto de función por proyectos

Abstract

This article communicates the results of a qualitative study carried out with six (6) mathematics teachers from a Higher Education Institution (HEI) in the city of Santiago de Cali-Colombia, which describes their experiences of teaching the concept of mathematical function through four categories. that relate: the training of the mathematics teacher, the curriculum, the mathematical content and the project work model. The research was ethnographic in nature to provide methodological complementarity by crossing various procedural, instrumental and analysis strategies, derived from different methodological references such as: case studies, documentary research, didactic analysis as research methodology and triangulation. The information obtained from the documentary review and the semi-structured interview by guide questionnaire was analyzed through the didactic content analysis of the mathematical concept of function. The results show that not all the teachers in the study were initially trained to be mathematics teachers. But, despite their initial training in different private and public universities and professional programs, they were all trained in the mathematical concept of function during the first semesters of their undergraduate, in courses such as: fundamental mathematics, calculus or related subjects such as physics and the most of them teach the concept of function as they were taught and learned by reproducing traditional, conventional, academic models of psychoeducational approaches such as behaviorism. However, those in professions other than educator teach the concept of mathematical function using course, classroom, or integrative projects. It is concluded that a mathematics teacher who teaches the concept of mathematical function through the project work model must have investigative competence, in addition to the disciplinary and pedagogical component, which impacts the curriculum of programs that train education professionals.