La teoría APOE y el álgebra lineal en la carrera de Matemática de la ESPOCH: transformaciones lineales

Abstract

Between 2017 and 2022, a trend of low academic performance in the Linear Algebra I course was identified, resulting in a 24% failure rate among 205 students in the Mathematics Program at ESPOCH. Consequently, the objective of the present research was to use the APOE (Action-Process-Object-Schema) theory for an initial representation of the teaching methodology for eigenvalues and eigenvectors of matrices associated with linear transformations in the Mathematics Program at ESPOCH, through genetic decomposition. This research falls within the domain of mathematics education and adopts a quantitative, explanatory approach. The systematic literature review is framed within a quantitative perspective, incorporating a meta-analysis. Thus, an updated “Systematic Review of APOE Theory in the Final Semesters of the Mathematics Program at ESPOCH” was conducted up to 2023. Furthermore, all genetic decompositions of the APOE theory in Linear Algebra were documented then through Israel Lerman’s similarity measure, and the application scenarios of APOE theory in Linear Algebra within the mathematics program at ESPOCH were determined. Finally, the genetic decomposition of the Scopus_014 article was adapted. Thereafter, the course was created in the Moodle platform by the Data Science Research Group (CIDED) for the fourth semester, employing the PACIE methodology (Presence, Scope, Training, Interaction, Elearning). Quantitative results were generated using the free software R, and the Mann-Whitney test was used to compare the medians of the experimental and control groups. In this context, it is concluded that there was insufficient evidence to reject the null hypothesis in relation to the diagnostic variable and test with a 95% confidence level. Therefore, it is recommended to use a larger study collective for future research.