Deficiencias críticas en matemáticas básicas: Un estudio diagnóstico transsemestral en estudiantes de ingeniería

Aztlán Elohim Bastarrachea Almodóvar; Alejandra Herrera Chew; María Concepción Fuentes Morales; María Elizabeth Portillo Gallardo; Guadalupe Navarro Enríquez

doi:10.61117/ipsumtec.v9i1.440

Authors

Aztlán Elohim Bastarrachea Almodóvar National Technological Institute of Mexico https://orcid.org/0000-0002-3577-6621
Alejandra Herrera Chew National Technological Institute of Mexico
María Concepción Fuentes Morales National Technological Institute of Mexico
María Elizabeth Portillo Gallardo National Technological Institute of Mexico
Guadalupe Navarro Enríquez National Technological Institute of Mexico

DOI:

https://doi.org/10.61117/ipsumtec.v9i1.440

Keywords:

Academic performance in engineering, diagnostic assessment, mathematical competencies in higher education, psychometric validation

Abstract

Mathematics is a fundamental pillar of engineering education. However, students often enter university degree programs with significant deficiencies in their mathematical preparation. The COVID-19 pandemic further exacerbated these deficiencies worldwide, particularly at the pre-university level.

This study evaluated the basic mathematics skills of 113 engineering students from first to seventh semester at TecNM campus Ciudad Juárez. A diagnostic instrument composed of nine items across four areas—arithmetic, algebra, geometry and trigonometry, and problem-solving—was used for this purpose. Psychometric analysis demonstrated acceptable reliability (Cronbach’s alpha = 0.74) and excellent factorial adequacy (Kaiser–Meyer–Olkin = 0.97), confirming the validity of the instrument for diagnostic assessment.

Results revealed critically low performance, with an average score of 1.78 out of 10. A total of 31.8% of the students scored zero, while only 4.4% scored above 6 out of 10 points. Cross-semester analysis showed no significant differences in performance, indicating that deficiencies persist throughout the university trajectory. Among the content areas, algebra items showed the highest difficulty (10.88%), followed by trigonometry (14.15%) and arithmetic (23.89%).

These findings underscore an urgent educational issue, reflecting structural deficiencies in pre-university mathematics training that remain unaddressed during the engineering degree program.

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Author Biographies

Aztlán Elohim Bastarrachea Almodóvar, National Technological Institute of Mexico

He studied Engineering Physics (2010) at the Autonomous University of Ciudad Juárez (UACJ), has a Master's Degree in Physics (2014) from the National Autonomous University of Mexico, and a Doctorate in Technology (2022) from the UACJ. He is currently a full-time professor at the National Technological Institute of Mexico, Ciudad Juárez Campus, with more than 12 years of teaching experience in basic science subjects. His research focuses on the area of mechanical design and education.

Alejandra Herrera Chew, National Technological Institute of Mexico

She studied for a Bachelor's Degree in Mathematics (1998-2001) and a Master's Degree in Mathematics Education (2003-2004), both of which he completed and obtained at the Autonomous University of Ciudad Juárez (UACJ). He has worked as a full-time teacher at the National Technological Institute of Mexico, Ciudad Juárez campus, since 2003, in both administrative and teaching positions. He also worked at the UACJ from 2005 to 2009, in both institutions belonging to the Department of Basic Sciences.

María Concepción Fuentes Morales, National Technological Institute of Mexico

She studied Biochemical Engineering and holds a Master of Science in Industrial Engineering. He has 10 years of work experience in the maquiladora industry in the area of advanced manufacturing. He has been a professor at the National Technological Institute of Mexico, Ciudad Juárez campus, for 25 years in the area of statistics at the undergraduate and graduate levels. He has 12 years with Perfil PRODEP, 20 articles published in scientific journals, 4 master's thesis advisors, and 8 undergraduate professional residency directors.

María Elizabeth Portillo Gallardo , National Technological Institute of Mexico

She studied Industrial Engineering and holds a Master of Science degree in Industrial Engineering. She has 10 years of work experience in engineering and service companies in the area of statistical control. She has 23 years of teaching experience at the Tecnológico Nacional de México campus in Ciudad Juárez in the area of basic sciences at the bachelor's degree level. She has published articles in scientific journals and supervised two bachelor's degree theses.

Guadalupe Navarro Enríquez, National Technological Institute of Mexico

She studied Industrial Engineering at the National Technological Institute of Mexico, Ciudad Juárez campus, and holds a Master of Science in Industrial Engineering (2009) with a specialization in the area of experimental design from the same institution. He has more than 15 years of professional and academic experience in the Electrical/Electronics Department at the National Technological Institute of Mexico, Ciudad Juárez campus, where he has contributed to the development of projects, teaching, and research in his area of expertise.

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