Beyond the numbers: the hidden power of mathematics in 21st century engineering

Abstract

The training of engineers worldwide requires a pedagogical approach that promotes the development of critical thinking and problem-solving skills, beyond the mere transmission of knowledge. These skills enable future engineers to tackle complex challenges, such as designing sustainable systems and optimizing industrial processes. However, it has been identified that a group of students develops an attitude of rejection towards mathematics, lacks motivation to learn, and shows little interest in participating in class, which impacts their academic and professional performance.

Various studies attribute this resistance to factors related to learning, such as the difficulty of applying mathematical concepts to real-world problems, gaps in their prior education, and the lack of a clear connection between mathematical theory and its application in engineering. This disconnect negatively influences their motivation and perception of the value of mathematics in their professional development.

Within the framework of an inter-institutional research project between the Engineering Faculties of the Institución Universitaria de Envigado, the Universidad de Los Andes, and the Pontificia Universidad Javeriana, interviews and focus groups are conducted with teachers and students from calculus courses. The results reveal a misalignment between classroom activities and the development of key mathematical skills, such as logical reasoning and problem-solving. Additionally, it is observed that evaluations focus on the reproduction of procedures, which limits deep understanding and the application of concepts.

Deficiencies in fundamental mathematical skills are identified, including reasoning, problem-solving, communication, modeling, the use of tools, understanding of concepts, and mathematical reflection. Furthermore, a lack of teacher reflection on teaching and learning processes is detected, resulting in study plans and methodologies that focus on content rather than skill development.

Faced with this situation, key questions arise: What mathematical skills should students develop in these courses? How to design activities that foster their development? What monitoring strategies can demonstrate progress? How should calculus and numerical methods courses be aligned to achieve this goal? This paper presents approaches to these questions based on specialized literature and research findings.

Finally, it is evident that a significant barrier in the teaching of mathematics in engineering lies in the teachers' conception of the teaching and learning process. It is necessary to move towards a model where the teacher acts as a facilitator of learning and students take an active role in their education. To strengthen mathematical thinking in 21st century engineering, it is necessary to review the mathematical skills required in engineering education, promoting deep understanding, creative application, and critical reflection on mathematical concepts.