Teaching-learning process under a Multidirectional Efficiency and Canonical Correlation Analysis

Abstract

The detailed study of the agents and factors involved in the teaching-learning process is vital to advance in the proposal of strategies that contribute to their improvement in all aspects (methodology, evaluation, resource management, between others). Today, many theoretical studies on the quality of education are known, which makes this a broad topic of discussion. However, education is a universe in constant motion which imposes the necessity of new systematic studies from different and relevant perspectives. This work aims to contribute to the study of the quality of higher education, evaluating the teachinglearning process, under two approaches. First, examining the technical efficiency of the institutions of higher education (approach 1), and also evaluating the performance of the students of these institutions, in accordance with the influence of the training of the teachers assigned to them (approach 2). Specifically, the use case study relates to 335 data units representing Colombian higher education institutions, corresponding to 165 institutions in the year 2016 (47 publics and 118 privates), and 170 institutions in the year 2017 (48 publics and 122 privates). The analysis considers variables of training/research for teacher and variables of graduation/performance for students. For the estimation of the efficiency (approach 1) has used a non-parametric, method based on the Multidirectional Efficiency Analysis (MEA). The study is focused on efficiency score, efficiency ratios and analysis of the output inefficiency index. For the exploration of the relationship, academic qualification/performance (approach 2), is executed a Canonical Correlation Analysis (CCA). Box-Cox transformations and filtering analysis to deal with outliers are applied. The statistical significance of the canonical correlations found, are shown with different statistical tests. The greatest contribution of this work is the appropriate combination of the MEA and CCA methodologies, which allows a broader vision of what happens in the scheme: institution efficiency/student performance/teacher training. Our results allow us to characterize the institutions in terms of efficiency, discriminating them into seven groups according to the training offer (doctoral programs, masters, specialization, etc.) and comparatively establish the most relevant relationships between teacher training / research and performance of the student.