Editorial to Special Issue: Mathematics in Engineering Education

1. Introduction

This Special Issue focuses on the role of mathematics in engineering education. The Italian philosopher, physicist, and astronomer Galileo Galilei (1564–1642) argued that mathematics is the language in which God has written the universe (Maddy, 2011). Mathematics itself is an abstract discipline with a “miraculous” and seemingly inexplicable effectiveness in describing the natural world (Wigner, 1960). Yet, mathematics is a foundational subject in both the natural and social sciences, and it is taught at all levels of education worldwide, including to engineering students. Mathematics is, without question, an essential tool for engineers, but how we teach it at the university level is another matter. Previous research has shown that, on the one hand, it is often a challenge for engineering students to learn mathematics and that, on the other hand, they require a different teaching approach than, for example, mathematics students. Mathematics teaching should take into account the specific uses in engineering science as well as new digital possibilities (from CAS and MATLAB to AI), even more than before. In view of this situation, numerous efforts are being made to appropriately modify content and to test new teaching methods.

2. Summary of the Papers in This Special Issue

This Special Issue contains five papers, each studying this topic from different angles and from authors from all over the world (Denmark, Ecuador, Israel, Mexico, the Netherlands, and the USA).

The study by Ovodenko and Kouropatov (2025) explores cognitive obstacles faced by engineering students in applying mathematical modeling of derivatives to real-world problems. Using case studies, they identify issues such as misunderstandings of variables, weak links between mathematical and economic contexts, and difficulties in graphical representation and validation. Students show procedural fluency but struggle with transitions between semiotic registers (verbal, algebraic, graphical, and contextual) and completing the modeling cycle. The findings suggest these challenges stem from representational gaps, highlighting the need for educational strategies that focus on these transitions and the iterative process of mathematical modeling in engineering.

The study by Altindis et al. (2025) examines how gender, engineering experience, and models influence high school students’ STEM interest and perceptions. Using surveys completed by 96 students, the study found that gender had a small but significant effect, with female students generally showing slightly lower interest in STEM than males. Students with engineering-related experiences displayed higher interest in and positive perceptions of engineering, while those without models in STEM reported lower interest and confidence. Conversely, students with models showed more positive STEM outcomes. The findings emphasize the importance of students’ experiences and the impact of models on STEM interest and confidence.

The study by Salinas-Hernández et al. (2025) explores how digital resources, specifically a feedback and progress monitoring dashboard, support engineering students in mathematical modeling within a Challenge-Based Education (CBE) course. Conducted in a second-year engineering course integrating mathematics, physics, and ethics, the case study of two student teams showed that the dashboard facilitated self-regulated learning, interdisciplinary collaboration, and iterative questioning. Students effectively employed data analysis and simulations to model real-world problems, such as crowd flow on train platforms. The study suggests that digital tools like dashboards enhance mathematics education by bridging the gap between abstract concepts and practical engineering applications, promoting student engagement and autonomous learning.

The study by Garcia Tobar et al. (2025) uses the Analytic Hierarchy Process (AHP) to determine the most suitable framework for classifying mathematical errors in first-year engineering students. Evaluating five models—Newman, Kastolan, Watson, Hadar, and Polya—against six criteria, the study finds the Newman framework to be the most effective due to its structured error analysis and applicability in formative assessments. Newman’s emphasis on reading, comprehension, transformation, and encoding is effective for addressing common early-stage mathematical errors. The study highlights the effectiveness of AHP in selecting educational models and supports the development of targeted interventions in mathematics education for engineering.

The concept paper by Abou-Hayt and Dahl (2025) (the latter being one of the editors) addresses the challenge students face in understanding the chain rule by using contextually rich problems to enhance learning. It presents four tasks designed to help students grasp the chain rule through meaningful contexts, aligning with existing research that suggests the use of realistic scenarios in teaching calculus. By applying Tall’s three worlds of mathematics—symbolic, embodied, and formal—the paper aims to bridge these concepts for engineering students, facilitating a deeper understanding of the chain rule.

3. Conclusions

The published papers apply various frameworks and methods, each tailored to their specific research focus. Ovodenko and Kouropatov (2025) utilize the Mathematical Modeling Cycle (MMC) and Duval’s theory of semiotic registers. The study involves a qualitative case study design to analyze students’ cognitive processes. Altindis et al. (2025) employ surveys with Likert-scale and open-ended questions to assess STEM interest and perceptions. The study applies ANOVA analyses to examine the effects of gender, experience, and models on STEM outcomes. Salinas-Hernández et al. (2025) use the instrumental approach to study the integration and adaptation of digital resources in engineering education. A case study is used to analyze how a digital dashboard supports mathematical modeling. Garcia Tobar et al. (2025) apply the Analytic Hierarchy Process (AHP) for multicriteria decision-making to select an error classification framework, incorporating expert judgment for priority weightings. Finally, Abou-Hayt and Dahl (2025) incorporate Tall’s three worlds of mathematics (symbolic, embodied, and formal) to design tasks that contextualize the chain rule within realistic problems.

The common themes across these papers are as follows:

• Most of the studies emphasize contextual and real-world applications and stress the importance of context (realistic problems and context-rich tasks) in enhancing understanding and application of theoretical concepts.
• All papers aim to improve educational outcomes, whether through better understanding (mathematical modeling and chain rule), selection of pedagogical frameworks (error classification), or enhancement of interest and confidence (STEM education).
• All studies are empirically oriented and use either qualitative or quantitative methods. In particular, they employ qualitative case studies, surveys, and decision-making frameworks to analyze and address educational challenges.
• Interdisciplinary and cross-domain perspectives dominate. Several studies integrate multiple disciplines or theoretical perspectives to enrich the learning experience, such as combining mathematics with engineering, physics, or digital tools.

The papers address some of the issues mentioned in the introduction in a constructive and novel way. In particular, they explore various possibilities for using digital tools. The new opportunities and challenges opened up by AI will require further efforts in the future to make them fruitful for even better student education. However, many questions remain, especially regarding the actual professional application of mathematics. On the one hand, it is clear that engineers, for example, typically do not need to compute integrals in their professional practice. On the other hand, integrals are an inherent aspect of physical and engineering concepts. Whether these can be acquired by students without experience in calculating integrals, etc., and, if so, how, is a question often posed in publications but not yet seriously addressed scientifically.