A Mamdani Type-Fuzzy Inference - Alignment Matrix Method Aimed to Evaluate Competencies Acquired by Students Enrolling at the Mexican Higher Middle Education System I: Formulation and Explanation Based on Simulation, and A Real but Incomplete Data Set

Abstract

The last reforms at the Mexican educational system attempt to modify graduates' traditional profiles to enable them to investigate, develop and propose solutions to various problems, think more assertively, form opinions, interact with multidisciplinary groups of people, and ultimately assume a proactive role in the community. The implementation of curricula promoting the development of competencies becomes essential in achieving envisioned goals. The alignment of competencies to study plans and the evaluation of the development of related skills becomes critical at the scheme's implementation. Currently, relating duties mainly depends on the teacher's will, but the lack of a systematic protocol to achieve involved endeavors promotes designs based on subjectivity. On top of this, concurring student's performance grading scheme relies on a thorough alphabetic character rating approach, thereby masking objective scoring. Assessment at the Mexican educational system realm conceives upon criteria designed abroad. Thereby linking particularities are left behind at performing evaluation tasks. This contribution proposes a method based on a fuzzy inference approach that aims to provide a formal structure that allows teachers to achieve the alignment of competencies and evaluate their development by students relying on a quantitative paradigm. We offer a comprehensive display of the formalities of the proposed fuzzy method. Explanation of its functionality relies on both simulated and real data. The aim here is on addressing the student-teacher aspect of alignment and evaluation procedures. Extension to other precincts within the whole Mexican educational system also contemplates and intends to appear in further contributions.