Propuesta de técnicas activas para la enseñanza de variaciones en el análisis combinatorio

Abstract

This didactic proposal presents a set of activities for teaching variations in combinatorial analysis, centered on the use of active techniques grounded in constructivism. Its objective is to support teachers in their instruction and thereby improve processes where there are difficulties in comprehension, abstraction, and conceptualization. Consequently, a theoretical review was conducted on the challenges in teaching combinatorial analysis, constructivism, and active techniques. Diagnostic interviews were then conducted regarding the methodologies, strategies, and resources used by mathematics teachers in the third year of high school at the Juan Montalvo Educational Unit for combinatorial analysis, leading to the generation of this proposal. Among the findings, it was noted that teachers indicated a need and a trend towards active activities for teaching, as well as technological and didactic resource deficiencies. Consequently, active techniques such as Pre-Lecture Essay, Poster and Questions, Didactic Game, Concept Map, Student Question Summary, Role-Playing Game, Fishbowl Technique (adaptation), Constructing Exam Questions, and Fingers or Symbols were employed. It is concluded that active techniques significantly involve students compared to traditional conventional classes, being flexible, dynamic, and novel, which helps break the monotony of the educational process. Therefore, a predisposition from the teacher to explore these new alternatives is also recommended.